WO2009004661A2

WO2009004661A2 - Method and computer system for performance analysis and for dimensioning a gsm access network

Info

Publication number: WO2009004661A2
Application number: PCT/IT2008/000387
Authority: WO
Inventors: Salvatore Lucifora
Original assignee: Salvatore Lucifora
Priority date: 2007-07-02
Filing date: 2008-06-11
Publication date: 2009-01-08
Also published as: WO2009004661A3; ITPO20070018A1; WO2009004661A4

Abstract

A method and a computer system for analyzing the performance and for carrying out the dimensioning of at least one network portion of a telecommunication system, in which the communication channels requested by the mobile terminals are allocated and in which the corresponding communications are sustained on high-bit- rate and/or low-bit-rate traffic channels, characterized by the fact of comprising the further steps of providing a configuration of resources in said network portion and of providing the characteristics of said communication-channel requests. Said configuration of resources comprises the possibility of setting a feature that imposes the switching from a high-bit-rate traffic channel to a low-bit-rate traffic channel for at least one ongoing communication in said network portion when, for the case of a new call-request, said network portion is congested. Said configuration of resources comprises the setting of a threshold value such that if the occupation level of said resources is higher than or equal to said threshold value, a new call-request is preferentially allocated on a low-bit-rate traffic channel. Said characteristics of said communication-channel requests comprise the capability, of said mobile terminals, to sustain calls on high-bit-rate and/or on low-bit- rate traffic channels. Said telecommunication system comprises a cellular telecommunication system in compliance with the GSM standard.

Description

METHOD AND COMPUTER SYSTEM FOR PERFORMANCE ANALYSIS AND

FOR DIMENSIONING A GSM ACCESS NETWORK TECHNICAL FIELD

The present invention regards a method and a computer system for carrying out performance analysis on a cellular telecommunication network, in particular a cellular network of the GSM Standard for the case of coexisting half-rate and full-rate traffic channels. Moreover, the present invention regards a method and a computer system for dimensioning the resources of a cellular telecommunication access network of the GSM Standard for the case of coexisting half-rate and full-rate traffic channels. BACKGROUND ART It is well-known that the GSM telecommunication system utilizes an FDMA/TDMA (Frequency Division Multiple Access/Time Division Multiple Access) radio access technique in which the network is able to sustain the user voice-calls within time-slots assigned to communications. It is well-known that when a time- slot is fully assigned to a single communication the traffic channel is defined as "Full-Rate" (abbreviated FR). Nevertheless, in the GSM standard, it is possible to assign the same time-slot to two simultaneous communications, dividing the time-slot into two sub-slots: in this case, the traffic channel mapped onto a sub- slot is defined as "Half-Rate" (abbreviated HR). According to the GSM Standard Specifications, issued by the European Telecommunication Standard Institute (ETSI), the full-rate communications provide a better quality than the half-rate communications. Nevertheless, new voice and channel coding techniques exist that allow the voice quality of the supplied service to be appreciably improved, being better able to adapt to the diverse propagation conditions of the radio-electric signal, even for half-rate traffic channels. An example is the case of "Enhanced Full Rate" (EFR) or "Adaptive Multi Rate" (AMR) traffic channels. In particular, the AMR technique is available both for full-rate traffic channels (in the form of A-FR) and for half-rate traffic channels (in the form of A-HR). In such cases, the band occupation and the resource occupation can be considered to be equivalent to the corresponding FR or HR traffic channel, therefore, in this document they will be understood to be referred to also whenever the FR or HR acronyms are used. Generalizing, a traffic channel that requires a time-slot to be assigned only to a single communication is called a "high-bit-rate traffic channel" (including for example, FR, EFR or A-FR traffic channels, though also including other possible traffic channels) while a traffic channel that requires a sub-slot to be assigned to a single communication, in a manner such that a time-slot can be assigned to two simultaneous communications, is called a "low-bit-rate traffic channel" (including for example, HR or A-HR traffic channels, though also including other possible traffic channels). In the GSM Standard Specifications other possible traffic channels may also exist where voice and data communications could be mapped onto a time-slot or onto a sub-slot; such traffic channels could be considered to be an equivalent versions of the high-bit-rate or low-bit-rate traffic channels mentioned above. In this document, a mobile terminal that is unable to support a low-bit-rate traffic channel is defined to be a "single-rate terminal," while a mobile terminal that is able to support both high-bit-rate or low-bit-rate traffic channel is defined to be a "dual-rate terminal." Currently, the case of a terminal that is unable to support the high-bit-rate traffic channel is not anticipated in the GSM Standard (the FR traffic channel is mandatory for all terminals which comply with the GSM Standard, whereas the HR traffic channel is not mandatory). The term "terminal" refers to an electronic telecommunication device, such as a mobile phone or a laptop or a desktop computer, that is able to make a voice communication or a data communication in compliance with the GSM standard. According to that above considerations, the HR traffic channels provide the same service as FR traffic channels with the half the amount of resources though with a lower quality of service. In order to counterbalance the reduction in voice quality associated with the increasing capacity of the resources, a wireless cellular communication network configuration has been proposed with features that assign an FR traffic channel when the occupied capacity of a cell is less than a predetermined threshold value or which assign an HR traffic channel when the occupied capacity of the cell has exceeded the predetermined threshold value. Said traffic-channel-assignment feature in this document is hereafter called "-Dynamic Half Rate Allocation' (abbreviated DHRA) and is amply described in US patent no. 6292664 "Channel Quality in wireless communications." To summarize, if the number of communication channels (or the number of time-slots) occupied in the cell is less than the predetermined threshold value, the network will accommodate every new service request in an FR traffic channel. If, instead, the number of communication channels occupied by the cell is above (or equal to) the predetermined threshold value, the network will attempt to accommodate every new service request in an HR traffic channel with the condition that the mobile terminal is able to support the half-rate traffic channel (otherwise the network will assign an FR traffic channel, even if the threshold value has been exceeded). The way in which this algorithm works is illustrated in Fig. 1 and 2, where a GSM cell is configured with 12 time-slots (24 sub-slots) assigned to voice service and with a threshold value of 50% (in this case 6 time-slots, which corresponds to 12 sub-slots). With a low traffic load in the cell, the number of occupied time-slots is normally less than the threshold value and, regardless whether or not the terminal supports a half-rate traffic channel, the network nevertheless assigns an FR traffic channel, favoring communication quality over efficiency. For the case of a high traffic load in the cell, when the number of occupied resources exceeds the threshold value (Fig. 2), the network attempts to accommodate every new voice-call onto an HR traffic channel. As can be seen, a single-rate terminal T_SR will nevertheless be served with an FR traffic channel; if a full time-slot is not available, the voice-call request could be refused by the serving cell. The threshold value could also be determined in a similar though complementary manner, i.e. taking into account the number of non-occupied resources: if the number of non- occupied resources is less than the predetermined threshold value (the complement of the first mentioned threshold) then the network will attempt to assign a low-bit-rate traffic channel to every new service requests, on condition that the terminal is able to support it. In support of the DHRA, a "packing" feature might operate allowing the fragmentation of the resources of every cell to be reduced. This feature, in particular, re-allocates some ongoing half-rate communications to the least possible number of time-slot, performing a certain number of intra-cell handovers or a certain number of mode-modify procedures, in this way the probability that "a service request originating from a single-rate terminal might be refused, even though there are few non-occupied sub-slots mapped into different time-slots" is reduced. This is the case of the example shown in Fig. 2 where two ongoing HR communications allocated in two different time-slots (10 and 12) could be joined together in a single time-slot, for example, performing an intra-cell handover from time-slot 12 to time- slot 10 (or vice-versa). If the network does not implement the packing feature, a greater loss of calls originated from single-rate terminals and an unwanted increase in the number of low-quality HR traffic channels could result. With the goal of increasing the available resources of a cell in a telecommunication network, furthermore configuration the cellular wireless communication network with a feature that re- allocates an ongoing communication from an FR traffic channel to an HR traffic channel in the case of a new service request has been proposed. This feature is named "Enhanced Preemption" and is amply described in US patent no. 5940763 "Enhanced Preemption within a mobile telecommunications network." Obviously, such a re-allocation from FR to HR (as can be seen, for example, in Fig. 3) is permitted only for those ongoing communications that have been assigned to dual-rate terminals. However, this feature is not always utilized by mobile operators because in so far as It results in unwanted quality deterioration in several ongoing communications and generates excess signaling procedures between the network and the mobile terminals so as to possibly result in a larger number of dropped calls. Nevertheless, with the forthcoming advent of the AMR techniques and with the improvement in computer processing capabilities of electronic equipment used in telecommunication networks, it is reasonable to expect a further exploitation of said features. The above-mentioned features can be handled at a single cell-level: i.e. in a specific geographic area covered by the radio signal generated by a corresponding GSM base station. In general, the cells of a GSM telecommunication system may belong to the same frequency band or to different frequency bands (for example, in Europe these frequency bands may be 900 MHz or 1800 MHz). Usually, the cellular coverage is ensured with cells that operate in a primary frequency band (for example, at 900 MHz) while in order to meet localized high traffic level demands, another cell layer operating on a secondary frequency band (for example, at 1800 MHz) is utilized. SUMMARY OF THE INVENTION

Based on the considerations mentioned above, it is obvious that a reliable method to analyze the performance of a GSM cell, in particular a cell operating with the above-mentioned complex features, is necessary, also with the aim of being able to predict the cell performance depending on the cell configuration and depending on the relevant network parameters. Similarly, it is obvious that a method needs to be implemented to effectively dimension the resources of a GSM cell in order to sustain the offered traffic of a cell with the best quality possible. For these purposes, methods not fully satisfactory are employed to conduct performance analysis and dimensioning, for example, certain methods based on simulations that can potentially provide incorrect results, and for example, which may result an overestimate of network resources needed to sustain a given level of offered traffic with a desired loss of calls or which may result in an underestimate of the cell performance depending on the threshold value of the DHRA algorithm. Such methods may also entail a great deal of processing time. Therefore, the aim of this present invention is to provide a method to correctly analyze or predict the performance of a GSM cell in which FR or HR traffic channels may be allocated and in which the DHRA and/or the enhanced preemption features could be implemented. In particular, the aim of this invention is to provide a method to analyze the performance of a GSM cell in terms of carried traffic, grade of service (that is the mean blocking-probability of the service requests) and the steady-state occupation probabilities of the resources, being known the cell resources and the corresponding configuration and characteristics of the offered traffic. Another further purpose of this invention is to provide a method to dimension the resources of a GSM cell, in terms of time-slots, in particular, and therefore in terms of the number of transceivers needed to sustain a given offered traffic with a desired grade of service, taking into account the cell configuration (for example, the threshold value, the activation/deactivation of the enhanced preemption, etc.). Again another purpose of this invention is to provide a method to analyze the performance of a GSM cell allowing the grade of service and the offered traffic of a cell in a given configuration to be correctly estimated, being known the sustained traffic (a measurement of the carried traffic), also allowing the percentage of the dual-rate mobile terminals participating in voice calls in a given time period to be obtained. Furthermore, an aim of this invention is also to provide a method to predict the performance of a GSM cell, allowing the assessment of the capacity of the cell in terms of maximum carried traffic. In this document, the capacity of a cell is defined as the maximum amount traffic that can be potentially sustained by the cell with a desired grade of service, being known the cell equipment and its corresponding configuration. Finally, this invention also has the purpose of providing a computer system, comprising a software application, that is able to carry out the performance analysis method and dimensioning method described in this document. These purposes are achieved with a method and a computer system in conformity with the enclosed claims. Amongst the advantages that could be obtained with this method and computer system, is the possibility of ascertaining the optimal configuration of some network parameters, useful to optimize the network and the equipment of the access network — the number of antennas, the number of base stations and the relevant components, the number of A-bis interface links, and so on - offering at the same time voice calls service having optimal quality. Furthermore, the proposed method and computer system can also be applied in base stations that provide both voice calls and data services compliant with second or third generation mobile systems such as SMS, GPRS, EDGE, GERAN and so on. These and other advantages of the present invention will be well amply described, together with the technical characteristics, by the following detailed description that is inclusive of several examples that are not restricting of all the possible practical embodiments of the invention. BRIEF DESCRIPTION OF THE DRAWINGS A more complete understanding of the method and the computer system for the present invention may be had by reference to the following detailed description when considered in conjunction with the accompanying drawings wherein, in the figures:

- Fig. 1 is an example of the FR/HR traffic-channel-allocation algorithm based on a threshold value for the case of a low traffic load in a cell; - Fig. 2 is an example of the FR/HR traffic-channel-allocation algorithm based on a threshold value for the case of a high traffic load in a cell;

- Fig. 3 is an example of the FR/HR traffic-channel-allocation algorithm based on enhanced preemption;

- Fig. 4 and 5 are two diagrams of the states of a Continuous Time Markov Chain (CTMC) with relevant birth and death processes for a cell with four time-slots, a threshold value of 50% and enhanced preemption; - Fig. 6 is an example of a flowchart illustrating the steps performed by a software application in conformity with the present method;

- Fig. 7a and 7b illustrate two different cases of cellular coverage for the same geographic area;

- Fig. 8 is an example of a flowchart illustrating the steps performed by a software application in conformity with the present method of conducting performance analysis on a cell; - Fig. 9 is an example of a flowchart illustrating the steps performed by a software application in conformity with the present method for dimensioning or predicting the performance of a cell;

- Fig. 10 is an example of a flowchart illustrating a software application that entails the steps performed by the proposed method and in which the input data of an arbitrary number of cells are included in an input file. DETAILED DESCRIPTION OF THE INVENTION The present method of performance analysis and dimensioning applies to a portion of a telecommunication system, for example, to a cell of a cellular network compliant with the GSM standard, that is able to sustain voice calls generated by the following kinds of terminals: dual-rate terminals and single-rate terminals. Each portion of such a network can, independently of each other, utilize the DHRA algorithm and/or the enhanced preemption algorithm mentioned above. The application of this method to the main configurations of said portion of a telecommunication system will be hereafter described. CASE 1 - STAND-ALONE CELL

The possibility of having traffic components originating from neighboring cells (overflow traffic components) is excluded: this case entails a significant simplification of the actual situation but nevertheless it is a widely agreed assumption that provides useful information for dimensioning and for conducting performance analysis on a telecommunication system. In this case, it is well-known that the dimensioning and the carrying out of the performance analysis on a telecommunication system, in which the offered traffic is only composed of voice calls, can be treated with a M/M/N/0 queue model where the first "M" refers to the exponential distribution of the calls offered to the system, the second "M" refers to the exponential distribution of the duration of the sustained voice calls, "N " refers to the number of servers (i.e. the number of telephone lines of the system) and "0" stands for the number of awaiting calls that can be queued in the system. The well- known "Erlang B" formula, shown here below, can be applied to this model:

y °ff in which: _kT^_N M B_e is the blocking-probability of the system; A_Bff is the offered traffic of the system.

To also take into account the awaiting calls queued by the system, the "Erlang C" formula can be applied. Even though, the "Erlang B" formula has always been the most common method for dimensioning and for carrying out performance analysis, especially in cellular systems in which mobile users participating in handover procedures cannot be queued (this will be further described in the paragraphs which follow). For example, the US patent no. 6246880 "Determining subscriber demands on a communication system" describes a method for determining the optimal number of resources of a cell of a cellular telecommunication system depending on the traffic level (offered traffic of the cell) and based on a "GOS table" to which the Erlang B formula applies. Nevertheless, if the network sustains the voice calls through different types of traffic channels entailing different resource occupations, such as FR or HR traffic channels, the Erlang B formula cannot be applied because the number of servers (that is the number of available communication channels of the cell) is not fixed, on the contrary, it can have a value between a minimum value (N) and a maximum value (2xN), in which N is the number of time-slots assigned to the voice service. Furthermore, the number of available communication channels of the cell can vary depending on the offered traffic characteristics and depending on the configuration of the cell (i.e. the threshold value of the DHRA algorithm, the number of time-slots assigned to voice service, the activation/deactivation of the enhanced preemption feature, and so on). The inventor has furthermore noted that, in this complex case, the reference theory that should be applied however is the Continuous Time Markov Chains (CTMC), with the following assumptions:

- The offered traffic originating from single-rate terminals and the offered traffic originating from dual-rate terminals both have a Poisson distribution;

- The duration of the calls served by the cell has an exponential distribution with the same parameter μ-l/τ and with the same mean value τ (μ is also referred "service rate of calls").

The CTMC mentioned is formed by a set of states, each defined with an index pair: "/, " "j. " In conformity with the proposed method, "/" is the number of FR users served by the cell, regardless whether they are equipped with a single-rate or a dual-rate terminal, while "j" is the number of HR users served by the cell; therefore, the number of busy time-slots of the cell is "n = / +j/2. " In order to correctly handle this case, the following parameters must be considered:

- the value λ of the mean call arrival rate of the cell in a predetermined time period (for example, 30 minutes); - the value P_m of the average percentage of calls originated by dual-rate terminals relative to said arrived calls in said predetermined time period;

- the value N of the number of time-slots assigned to voice service; and

- the value "x" of the DHRA algorithm threshold, which is the number of time-slots that will be compared with the number "n" of busy time-slots of the cell in order to decide whether to allocate an HR traffic channel or instead an FR traffic channel for each new service request. The value "x" can assume one of following values from the set: [0, Vz ,1 ,.., N- ¹A , N] or it also can be expressed as a percentage of N.

If the network utilizes the complementary threshold, the value "x_D" of said complementary threshold shall be compared with the number of free time-slots: "x_D" can easily be determined from the relationship "x = N - x_D." The following description takes into account the value "JC" but obviously the description also holds for the case of the complementary threshold.

In conformity with the proposed method, for each state of the system (ij), the following birth rates of the CTMC, which are the transition rates from the state (ij) to the states (ij+1) and (i+lj), are defined:

If the network attempts to assign HR channels when and only when the threshold has been exceeded, it is suffices to replace the condition "i+j/2<x" with the condition " i+j/2 ≤x" and the condition "x ≤i+j/2 " with the condition " x < i+j/2," in Eq. 1 and in Eq. 2 without altering the reasoning that follows. In conformity with the proposed method, the birth rates X₁ and X₂ besides been a function of the call arrival rate λ, are also function of the percentage of calls originated by dual-rate terminals and of the threshold value. They substantially represent the probability of passing from a generic state (ij) to the state (ij+1) of the CTMC and the probability of passing from a generic state (ij) to the state (i+lj) of the CTMC, respectively, in other words the probability of selecting a low-bit-rate traffic channel (for example, HR) and the probability of selecting a high-bit-rate traffic channel (for example, FR), in the presence of a new call request, respectively. The death rates of the generic (ij) state, which represent the transition rates from the state (ij) to the states (i- Ij) and (ij-1), are obtained by multiplying the number "/" of communications sustained in high-bit-rate traffic channels by the service rate of calls μ and by multiplying the number "j" of communications sustained in Iow-bit-rate traffic channels by the service rate of calls μ, respectively. The diagrams shown in Fig.4 and 5 (which are actually superimposed and have been separated for the sake of clarity) illustrate an example of a CTMC for the birth process and for the death process, respectively, for the case of a cell with four time-slots assigned to the voice service and with a threshold percentage of 50%, i.e. x = 2 time-slot. Every state is defined with the index pair (ij) with "i" being the number of FR users and "j" being the number of HR users served by a cell. In conformity with the proposed method, if we wish to take into account the enhanced preemption feature, it would be necessary strictly speaking to re-define a new CTMC with a set of states, each one having three variables (isi_bhi_bj)- Iⁿ particular, "/D_Λ" refers to the number of users equipped with a dual- rate terminal and allocated in a high-bit-rate traffic channel (for example, FR), "i_SΛ" refers to the number of users equipped with a single-rate terminal and allocated in a high-bit-rate traffic channel (for example, FR), while "/' refers to the number of users allocated in a low-bit-rate traffic channel (for example, HR). Consequentially, a new set of three birth rates must be defined similarly as was done in Eq. 1 or Eq. 2. Nevertheless, in this way the number of CTMC states would increase enormously with a consequential lengthening of the processing time in the method. However, an efficient solution is available that provides results with satisfactory precision, taking into account the CTMC previously defined with the (ij) index in which "/ = i_SR + i_DR" and considering an additional transition rate /T, and certain rectifying coefficients:

otherwise Eq. 3.b

^* (

AA] (i, j) = * -0 - ^ )- P 1 - P \ '-" τ}._Λ q\(.i - q)\ K ^uκ N ) ^ N if t+jl2 = N; i>\ Q- otherwise

The term λ^*, is defined as the transition rate (or also the transition intensity) from a generic state of the cell in which all the resources are occupied to the adjacent state of the cell in which all the resources are occupied

(Fig. 4). Essentially, it refers to the probability of selecting a low-bit-rate traffic cannel when, in the presence of a new service request, all the time-slots of the cell are occupied by ongoing communications. The term Aλ",- of Eq. 3b is normally added to the term λ^*, if, being congested the resource of the cell and in the presence of a new service request originated by a single-rate terminal, the network is able to fee-up a full time-slot switching two ongoing FR communications, previously assigned to dual-rate terminals, to two HR-type traffic channels; failing to do so, it will assume a zero value because, by assumption, the probability of selecting an

FR channel would be zero. The term Aλ, of Eq. 3c is normally added to the λ, term of Eq. 1 if, being congested the resources of the cell and being free only a single sub-slot and in the presence of a new service request originated by a single-rate terminal, the network is able to fee-up a full time-slot switching an ongoing FR communication, previously assigned to a dual-rate terminal, to an HR-type traffic channel; failing to do so, it will assume a zero value because, by assumption, the probability of selecting an FR channel would be zero. Said rectifying coefficient, Aλj, refers essentially to the probability of selecting a high-bit-rate traffic channel when, for the case of a new service request originated by a single-rate terminal, only one sub-slot within the cell is free. In conformity with the proposed method, if the network does not apply the DHRA algorithm based on a threshold value or if the threshold value is N, then an HR-type traffic channels may been allocated only if the enhanced preemption feature is activated. In this case, the network can be correctly analyzed taking into account a fictitious threshold value x = N- 1/2 in Eq. 1, Eq. 2 and Eq. 3. Therefore, the method applies also for the case of a network utilizing the enhanced preemption feature, regardless whether or not the DHRA algorithm is implemented: in this way, the operator is able to ascertain under what conditions the DHRA and the enhanced preemption features could be advantageously used for handling the mobile voice service on a GSM network portion. If enhanced preemption is not activated within the cell, then the term λ^*j will be absent or null on the corresponding CTMC; this also holds for Eq. 3. In order to determine the performance of a network portion of a cellular telecommunication system implementing the above-mentioned features, the proposed method utilizes the evaluation step of the steady-state occupation probability of each single state (i,j) of the CTMC described above. It is a well-known step, given that every method that utilizes the Markov theory will entail the use of this step which requires the formulation of the so-called flow-balance equations of the Markov process. Said set of steady-state occupation probabilities is indicated with the term π,_r In general, formulating the flow-balance equations and the normalization condition for the present method, the following system of(l+N)² equations is obtained: Eq.4

Vi(i,^j)+Λχ(U)+(i⁺ J)' **]^■*„ = fc('-l,/K-,,, +A(U-I)-W_1J-. +(i+l)-μ-π_l+lJ +(j + ϊ)-μ-π,_J+ι] for each i,j ≥ 0 i+j/2 ≤ N w__{Ij S}=0 if /-K0; «^•„_, =<> // y-KO βi_+u =0 // 1 + 1+772 > AT; π,_J+ι =0 if i+(j + l)/2 >N

If the offered traffic A_off is known, being that in accordance with the state of the art the offered traffic can be obtained from the ratio between λ and μ, the system of equations in Eq. 4 can be solved independently of the individual values of λ and μ. This means that if only the value of the offered traffic A_off is known, Eq. 4 can be solved assigning an arbitrary value (for example, 1) to the parameter μ, in order to determine a useful value for the parameter λ in Eq. 1, Eq. 2 and Eq. 3 and hence in the system of equations of Eq. 4. Obviously, Eq.4 can be adapted to take into account the enhanced preemption feature: Eq. 5 +^^{^}

Briefly, Eq. 4 holds for a cell that utilizes the DHRA on a threshold basis and that does not utilize enhanced preemption, while Eq. 5 holds for a cell that utilizes enhanced preemption and, if necessary, DHRA. In Eq. 5, the term δ(y) is the well-known indicator function that equals 1 if y is true or equals 0 if y is false. Given that the sum total of the steady-state occupation probabilities must be 1, the normalization condition must be applied to both Eq. 4 and Eq.5. Solving the previous systems of equations is very complicated. Nevertheless, a numerical solution can be found for these systems of equations, making use of the mathematical methods of reduction or substitution or, better yet, creating the so-called system matrix. With the assistance of a well- known software applications (such as MATLAB or UMFPACK), these system of equations, converted into matrix format, may be solved automatically, quickly and reliably. These systems of equations are said to be "sparse" because most of the matrix coefficients are 0 while a minority have non-zero values. From the steady-state probability vector Jt — \π_{0 Q} ; π₀ _, ; π_{l 0} ; ... ; ^₀,2ΛΓ-I » ^π _\,_2N-_{2 >} ^πo_,2N ) _> which is the solution of Eq. 4 or Eq. 5 inclusive of the normalization condition, the information needed to correctly carry out the performance analysis of the cell can be obtained, determining the overall steady-state occupation probabilities (i.e. the set of CTMC steady-state probability for each state), the blocking probabilities, the carried traffic and all of its components. In this way, the following information can be determined, when either the system of equations defined in Eq. 4 or in Eq. 5 is solved:

An important technical advantage of the proposed method is the evaluation of the performance parameter "the probability that k time-slots of the cell are occupied" (as indicated in Eq. 6.χ) which proves to be very helpful when conducting performance analysis and dimensioning a network portion that provides both voice and data services (such as GPRS or EDGE) in which, by sharing the resources assigned to the voice service, the network utilizes said shared resources for data services when said resources are not occupied by any voice services. Eq. 6.χ, in fact, must be evaluated to correctly assess the so-called "throughput" and "mean-delay" of the data service which utilizes said resources with a priority lower than the voice service. However, a more detailed description of instances of coexisting voice and data services is beyond the scope of the proposed method therefore no further mention will be given thereto. Another important and innovational result of the proposed method is the correct estimation of the carried traffic components FR and HR (Eq. 6.d and Eq. 6.e) in this complex technological environment, as well as the correct estimation of the blocking probabilities of both calls originated by single-rate or dual-rate terminals (Eq. 6.g and Eq. 6.i). It can be seen that the blocking probability of a call originated by a single-rate terminal is higher than the blocking probability of a call originated by a dual-rate terminal.

If the network portion, utilizing the enhanced preemption feature and with its resources having become congested, is able to switch one or two ongoing communications from FR to HR in order to free-up a sub-slot or a full time-slot, respectively, for a new service request, then Eq. 6.g and Eq. 6.i must be adapted since certain states of the CTMC, included within the summation range, are not blocking. Eq. 6.g and 6.i can be easily adapted in order to correctly take into consideration the states of the CTMC which are no longer blocking if enhanced preemption is activated: Eq. 6.h

Eq. 6.j

π B,SR +

The general and well-known relationship among the offered traffic of a cell (A₀^), the carried traffic of the cell (A_s), and the average blocking probability (π_B), which is the grade of service (GOS) of the cell, is indicated in the following Eq. 7: Eq. 7

Given that the state of the art is unable to determine the correct value of the average blocking probability of a cell utilizing the complex features mentioned above, rough estimates of the offered traffic of a cell are normally used, such as the following: Eq. 8

where TC refers to "time-congestion," i.e. the time portion (of a predetermined time period) during which all the resources of a cell are occupied; it can be seen that time-congestion is not the same as the grade of service of a cell because it does not represent the probability that a service request will be attempted and consequently refused by the network portion due to the congestion of the cell resources. If enhanced preemption is activated, the difference between the time-congestion and the grade of service may attain higher values, with a correspondingly greater error in estimating the offered traffic utilizing Eq. 8. The proposed method, being able to correctly determine the actual blocking probability of a cell, is not hampered by such rough estimates. Together with the performance parameters of a cell, as indicated in Eq. 6, the proposed method also provides, as additional information, the number of time-slots N₁₁₁, that would need to be assigned to the voice service if the low-bit-rate traffic channels cannot be used, in order to obtain the same cell capacity, holding the offered traffic constant and with the same grade of service requirements; for this reason, in order to determine the unknown N₀₁₁ the following Eq. 9 can be applied:

It can be seen that if within the cell the HR traffic channel was never assigned, for example, because the term P_DR equals 0 or because the threshold value x is equal to N, the only value of N_eq that satisfies Eq. 9 is precisely N. An instance where N_cq is utilized is shown in example 3. CASE 2 - REGULAR CELL

In the previous paragraph, the case of a stand-alone cell of a telecommunication system was considered thus the contributions of traffic components originated by neighboring cells due to the mobility of the users and/or to the overflowing traffic components of the neighboring cells were not considered. The foregoing case is valid assuming that the user calls are originated, handled and concluded in a single cell, also assuming that users can move with limited mobility within the cell, i.e. only inside the coverage area of the cell. In reality, these assumptions are highly restrictive considering that a GSM system utilizes the so-called "handover procedure" in order to ensure both wide geographic coverage and continuity for every conversation in a generic mobility regime, efficiently handling each transition phase from one cell to another neighboring cell. The proposed method also allows the incoming calls from the neighboring cells and the manner in which the network manages the handover procedures to be taken into account. In conformity with the proposed method, instead of the conversation duration, the continuous time segment during which a call remains within the analyzed cell must to be considered. The Markov theory, in fact, is applicable based on the mean occupation time of a resource rather than the mean duration of a communication. Furthermore, when evaluating the arrival rate 2 in a predetermined time period, the contributions of the incoming calls subsequent to the corresponding handover from neighboring cells must also be considered. It is necessary to determine how the network handles said incoming calls in accordance with a feature that henceforth will be referred to as the "handover policy:"

1. if the network is configured in such a way that no particular constraints are imposed in the presence of a handover procedure, the method may be applied without any particular adaptations;

2. if, contrariwise, the network is configured in such a way that It attempts to maintain continuity in the quality of each ongoing communication, even after a handover procedure, then the proposed method must be adjusted as follows.

In particular, if the network imposes any particular constraints so as to maintain the same channel-type for every ongoing communication participating in a handover procedure, then the incoming calls, which had been allocated on FR-type traffic channels in the origin cells, would again have to be allocated in the destination cell on FR-type traffic channels, even if the load of the destination cell was high and even if the threshold value of the destination cell had been exceeded. In this case, the corresponding terminal, regardless whether or not it is dual-rate, would be handled by the network as if it were a single-rate terminal. Likewise, the incoming calls that had been allocated on HR-type channels in the origin cells, would again have to be allocated in the destination cell on HR-type traffic channels, even if the load of the destination cell was low and even if the threshold value of the destination cell hadn't been exceeded. In this case, the corresponding terminal would be handled by the network as if it supported only HR-type traffic channels (more generally, low-bit-rate traffic channels). The transition rates of Eq. 1 and Eq. 2 must be adapted based on these considerations. In conformity with the proposed method, within the same predetermined time period of said call arrival rate A, it is necessary to establish:

- the average percentage P OR of calls originated by dual-rate terminals, including those calls incoming from neighboring cells through handover;

- the average percentage P_HR of calls originated by dual-rate terminals that, within said predetermined time period, would be handled by the network as if they supported only low-bit-rate traffic channels.

Based on this definition, P_m is always less than or equal to P_DR;

- the average percentage P_3Rh of calls originated by dual-rate terminals that, within said predetermined time period, would be handled by the network as if they supported only high-bit-rate traffic channels. Based on this definition, P_SRh, is always less than or equal to P_DR; - the average percentage P_DWl of calls originated by dual-rate terminals to which the network can assign a low-bit-rate traffic channel, Le. P_DRh = P_DR- P_SRI,;

If the "average percentage of calls originated by dual-rate terminals within said predetermined time period" is not known, said term P_DR can assume the value of the "probability that an incoming call is originated by a dual-rate terminal"; the same reasoning can be applied for the others average percentages PRR , Ps_{Rh 5} PDRI_I- In conformity with the proposed method, the transition rates from a generic state (i,j) to the state (i,j+l) of the CTMC and the transition rates from a generic state (i,j) to the state (i+l.j) of the CTMC must be determined. Said transition rates represent the birth rates X₁ and X₂ of the CTMC, based on the following definitions:

Eq. 2.h _f . . . ,

\*- 4 - ^p _m ) f ^{n < x}

A₂ = U - (I - ^ ) '/ x ≤ n < N - l/2 J O otherwise

If the constraints of guarantying the continuity of the traffic channel during a handover procedure were to be imposed only on those calls initially allocated on an FR-type traffic channel (and not on those calls allocated initially on an HR-type traffic channel), then the term P_HR equals zero therefore Eq. l.h and Eq. 2.h would have the same formulation of the corresponding Eq. 1 and Eq. 2, otherwise the term PHR would also take into account the service requests originated by a subset of the dual-rate terminals that, within said predetermined time period, for some reason, might utilize only HR-type traffic channels, even if the load of the cell were to be less than the threshold value. Similarly, the term P_SRh could take into account a subset of the dual-rate terminals that, although not necessarily participating in handover procedures, might utilize an FR-type traffic channel within said time period even if the load of the cell were to be higher than (or equal to) the threshold value. Because of these adaptations, the new defined birth rates λ_\ e X₂ can be utilized in Eq. 4 to determine the information needed to analyze the performance of a cell utilizing said configuration of resources (the threshold value, enhanced preemption, the handover policy, and so on). The performance parameters always refer to those indicated in Eq. 6, in which the term P_DR/, replaces the term P_DR, in particular to correctly determine the grade of service of the cell (Eq. 6.1). If the network were to utilize said handover policy, which attempts to maintain the quality of any ongoing communication participating in a handover procedure unvaried, the network in general could also utilize the enhanced preemption feature. In fact, especially for mobile telecommunication systems, the ■ probability that "an ongoing communication, participating in a handover procedure and directed towards a congested cell, might be disconnected by the network" must be minimized. This fact is also one of the main reasons why a cell must be dimensioned with an average blocking probability less than or equal to a desired grade of service (for example, a grade of service of 1% or 2%). In conformity with the proposed method, in order to take into account the handover policy and, if necessary, enhanced preemption, Eq. 3, together with Eq. Lh and Eq. 2.h must be considered with the system of equations Eq. 4 or Eq. 5; then, when solved, the information needed to correctly analyze the performance of the cell can be obtained from Eq. 6. In conclusion, all the information needed to analyze the performance of a cell operating under the various conditions and configurations indicated above may be determined from the parameters indicated in Eq. 6. It should be noted that the above described procedure, which comprises the numerical solution of Eq. 4 or Eq. 5, requires that the following input data be known:

- the offered traffic of a cell (A_Ojj), being defined by the ratio of the call arrival rate λ and the service rate of calls μ;

- the average percentage of calls originated by dual-rate terminals (PDR) or, instead, the probability that an incoming call is originated from a dual-rate terminal; - the amount of resources, for example, the number of time-slots assigned to the voice service;

- the configuration of the resources, in particular:

■ the value of the threshold (x) above which the network attempts to allocate every new service request onto a low-bit-rate traffic channel;

^■ the activation or deactivation of enhanced preemption [optional]; ■ the handover policy [optional].

The "offered traffic" and the "number of time-slots" parameters are already utilized in the state-of-the-art methods and techniques, while the new parameters needed for the proposed method are: the average percentage of calls originated by dual-rate terminals and the configuration of the resources of the cell, in particular the threshold value, the activation/deactivation of the enhanced preemption and the handover policy. With respect the state of the art, an innovational aspect of this proposed method is that the average percentage of calls originated by dual-rate terminals and the configuration of the resources of a cell are correctly taken into consideration when determining the CTMC states of the cell and when determining the probability of selecting a high-bit-rate or a low-bit-rate traffic channel for the case of a new service request. Furthermore, only by solving the system of equations (Eq. 4 or Eq. 5) can the set of the steady-state occupation probabilities of each generic CTMC state (π_tJ) be determined and, from them, the information needed to carry out a complete and detailed performance analysis (Eq. 6) of a network portion configured with the described features. In the following paragraphs, the described procedure is generically referred to as the "performance analysis" method, advantageously utilized to carry out the dimensioning and the estimation of the capacity of a network portion. The following paragraph shows some possible embodiments of the proposed method in a computer system (including a software application) useful for implementing the invention.

BEST WAY FOR CARRYING OUT THE INVENTION

A computer system able to concretely implement the proposed method comprises: an electronic computer equipped with a CPU, RAM devices, hard disk devices, operating system, keyboard, mouse, monitor, and so on. Said computer system is able to carry out dimensioning and performance analysis on at least one network portion of a cellular telecommunication system, in particular, on a cell or on a number of time-slots of a cell, based on software components (modules) memorized and processed into said computer system in order to implement the proposed method compliantly with this document. Fig. 8 shows a flowchart, in which a preferred embodiment of a software application (B_L module) that implement the steps of the proposed method for conducting performance analysis on a GSM cell or, in general, on a network portion is illustrated. The B_L module asks for the following input data (block 110): the value of the offered traffic (A₀^), the value of the average percentage of calls originated by dual-rate terminals (PDR), the value of the threshold in percentage (Λ:%), the value of the number of time-slots (N) assigned to the voice service (step 112). Optionally, the input data to the B_L module could also include the enhanced preemption configuration (step 114) and the handover policy configuration (step 116). In particular, if the enhanced preemption feature is activated, block 110 furthermore asks: 1) if the network can or cannot switch two ongoing communications from the FR-type to the HR-type for the case of a new service request when all the time-slots of the cell are occupied; 2) if the network can or cannot switch an ongoing communication from the FR-type to the HR-type for the case of a new service request when only a sub-slot of the network portion is free. As far as the handover policy is concerned (block 116), if the network places no particular constraints on those ongoing communications originated by neighboring cells, then block 110 requests no further input data. Whereas, if the network attempts to maintain the quality of any ongoing communications participating in handover procedures and allocated on FR-type traffic channels unchanged, then block 110 requests new input data, in particular, the percentage P_SRh or the percentage P_DRh. If the constraints apply also on ongoing communications allocated on HR-type traffic channels, then block 110 also asks for the percentage P_HR. Step 120 ensures that the values of the parameters λ and μ, based on the offered traffic value introduced in step 110, are determined. In particular, if said parameters λ and μ are not provided separately and only the value of the offered traffic has been provided, then block 120 assigns an arbitrary value to μ (for example, 1) and it determines a suitable value for λ with the relationship λ=A_Off ■ μ. Furthermore, block 120 ensures that the threshold value x is determined as a number of time-slots and therefore, the possible values of λi , λ₂ and, if necessary, λ ; are determined, according to Eq. 1, Eq. 2 and Eq. 3 (or Eq. l.h, Eq. 2.h and Eq. 3) based on input data (block 110), in particular based on the main parameters λ, μ, P_DR , x , N (step 112) and based on the others optional parameters (steps 114 and 116). Step 130 ensures that the matrix of the system of equations (Eq. 4 or Eq. 5) is created as a function of λ_u λ₂, λ"; and μ. Step 140 ensures that the system of equations is solved and that the overall steady-state probability vector is determined. For example, the UMFPACK algebra library can be utilized for said block 140. Block 150 ensures that the performance of the network portion is determined based on Eq. 6. Block 160 [optional] ensures that the "equivalent number of time-slots" of the network portion (N_eq) is determined according to Eq. 9. Block 170 ensures that output data (i.e. the performance parameters determined by block 150 and 160) are provided to the software application that has called up the B_L module or that they are directly provided to a graphical interface purposely set up to display said input and output data. Fig. 6 shows a flowchart illustrating a generic and iterative utilization of said B_L module in order to obtain the information required for planning or dimensioning an existing cell or a new cell (not yet installed). A few embodiments of such iterative utilization of the B_L module are indicated here below:

1. dimensioning cell resources: first of all, the number of time-slots required to sustain a given offered traffic level, and hence the number of GSM radio carriers, is determined for the cell. In fact, generic rules of the GSM standard which allow the signalling channels to be associated with the traffic channels are well-known, furthermore it is well-known that every GSM radio carrier is composed of 8 time-slots. Having determined the number of time-slots and the number of radio carriers of the cell, the overall frequency bandwidth of the cell and the optimal equipment for the cell can be also determined;

2. optimal cell configuration (for example, the optimal threshold value of the DHRA algorithm): in this case, the previous dimensioning procedure can be also utilized in order to determine the optimal configuration of the cell (for example, whether or not the enhanced preemption feature needs to be utilized, the optimal handover policy of each network cell, and so on); 3. predicting cell performance, varying the configuration and the relevant parameters of the network

(for example, varying the threshold value, the enhanced preemption parameters, the handover policy of each cell of the network, and so on). For example, with this procedure, an exact estimation of the maximum carried traffic of the cell, i.e. the capacity of the cell, can be determined: in particular, the maximum value of the traffic that can be sustained by the cell with a desired grade of service is estimated, being known the resources of the cell, the configuration of the cell and the probability that an incoming call is originated by a dual-rate terminal;

4. offered traffic and/or grade of service estimation, being known the cell resources, the cell configuration and the sustained traffic in the cell; furthermore, an estimate of the average percentage of incoming calls originated by dual-rate terminals can also be determined. Obviously, the determination of said planning information could be accomplished utilizing a software application. Such a software application in general follows the scheme shown on Fig. 6. In particular, the software components B_L, COND and REG are illustrated in Fig. 6. The B_L module is a set of software routines that includes the main innovational characteristics of the invention. The COND and REG modules, though possibly well-known, are utilized together with the B_L module in a manner such that they engender an extremely advantageous embodiment of the invention. In particular, the COND module verifies the planning condition desired, for example, that the mean blocking probability of the cell is less than a given value

(normally 1% or 2%) or that the FR-type carried traffic and the HR-type carried traffic have certain values.

When this condition or conditions are true, then the iteration stops and the software application provides the useful information needed that corresponds to the planning condition (or conditions) entered, otherwise the software applies the REG module. The REG module enters and regulates the unknown input data needed by module B_L, also adjusting them, if necessary, depending on the results obtained in previous iterations. In general, a well-known iterating method such as the Newton-Rapson or the dichotomy iteration process is used. Said well-known iteration methods, that are not described in this document, could influence the processing time of the software application but, obviously, not the correctness of the solutions. Fig. 9 shows a flowchart illustrating a software application that utilizes the B_L module in an iterative process for various purposes (such as "dimensioning," "performance prediction," "offered traffic estimation," "maximum carried traffic estimation" or "capacity estimation," and so on) and illustrating a specific example of the REG and

COND software components of Fig. 6. A software application operating in the "dimensioning" mode in order to dimension a cell of a cellular telecommunication network, in conformity with the proposed method, asks for the following input data (block 310): a value of the offered traffic, at least one average value of the percentage of calls originated by dual-rate terminals, at least one desired performance value (for example, the desired grade of service of the cell) and the configuration of the resources. Said "dimensioning" software application can operate based on said B_L module of the "performance analysis" method. Block 315 ensures that minimum and maximum value of the unknown input data needed to the B_L module are determined: when dimensioning the cell, the number of time-slots N of the cell is unknown. Block 320 ensures that an optimal attempted value of the unknown input data (for example, an attempted value of N) is assigned for each step of the iteration process, in accordance with the Newton-Rapson process or with the dichotomy process. Block

550 is the B_L module of the "performance analysis" method. Block 330 ensures that the cell performance parameters (in accordance with Eq. 6) are memorized with the current value of the unknown input data (for example, with the current value of N in the corresponding iteration). Block 340 and 350 ensures that the desired planning condition has been attained (for example, the average blocking probability π_B determined by the B_L module is below the desired grade of service with a minimum value of N). When dimensioning, block 340 verifies whether π_B is less than the desired grade of service; in this case the software application continues on to block 350, otherwise it continues on to block 326. Block 350 ensures that all possible iterations have been carried out, in this case, the software application continues on to block 360, otherwise the planning conditions have not yet been attained hence the software application continues on to block 324. Blocks 324 and 326 ensure that the corresponding unknown input data are regulated for the next iteration in the iterative process. Block 360 ensures that the output data, i.e. the optimal value of the unknown input data of the B_L component (for example, the optimal value of N) and the corresponding performance of the cell according to Eq. 6, are provided to the software application which called up the procedure (for example, the dimensioning procedure) or directly to a graphical interface set up to display the input and output data. The choice of an optimal number of cells and an optimal positioning of said cells in a predetermined geographic area can be achieved with the proposed method operating jointly with existing software applications already available for planning cellular telecommunication networks based on traffic requirements, which can be properly analyzed and handled with the proposed method, and based on radioelectric coverage requirements that are beyond the scope of the proposed method. The output data from the dimensioning software application include the optimal equipment for the network portion (for example, the optimal number of time- slots, the optimal number of GSM carries, etc.) and/or the optimal configuration of the resources, together with the performance parameters listed in Eq. 6 relating to said optimal number of time-slots and said optimal configuration. Similarly, a software application operating for a different purpose (for example, "offered traffic estimation," "capacity estimation," "performance prediction," and so on) can iteratively utilize the B_L module of the "performance analysis" method, in accordance with the flowchart of Fig. 9. Through said software applications, it is also possible to conduct "performance analysis," "offered traffic estimation," "capacity estimation," "performance prediction," and so on, allowing said process to be carried out automatically for an arbitrary number of cells of a wide cellular telecommunication system (Fig. 10). For example, the input data of a set of network cells can be provided within a file (input file) having a predefined structure. Thus, the process in accordance with the proposed method, can be automatically carried out for every cell, determining the output data of each cell and memorizing said input and output data of every cell inside a new file (output file). An example of said input file is the file extracted by the Mobile Switching Center (MSC), which is a node of the GSM telecommunication network that handles a large number of cells through other nodes called BSC (Base Station Controller). Said files that are extracted by the MSC have a predefined format and contain the main information regarding each handled cell: this information is periodically updated, for example, every week. The information enclosed in said file extracted by the MSC, include: the identification of the cell, the number of available time-slots assigned to the voice service, the FR-type and the HR-type sustained traffic, the time-congestion of every cell, and so on. In order to speed up the processing time of the proposed method, the values relative to the input data and the corresponding output data of a software application that implements the proposed method can be memorized or reported in tables. Said tables, in printed or digital format, could be used to interpolate said tabulated values in order to quickly perform the performance analysis or the dimensioning of a cell, with consequent advantages of not being forced to utilize each time the software application and not having to go through the all the processing steps that it requires: in fact, solving a large system of equations can be a time-intensive processes, requiring up to a few seconds for every cell. INDUSTRIAL APPLICABILITY

In the following paragraphs, a few examples implementing the invention are illustrated. Example 1 Assume that we want to estimate the grade of service and the offered traffic of an existing cell equipped with the DHRA algorithm, being known the values of the sustained traffic on FR and on HR traffic channels and being known the configuration of the resources (a threshold value of 70% and with enhanced preemption not activated). Furthermore, a maximum error of l%₀ (one per thousand) is assumed in the comparison between the sustained traffic (coming from real measures performed by the network) and the carried traffic determined by the proposed method through a software application. In particular, the following data are known: TRAFFIC CHARACTERISTICS T= 30 [min] predetermined time interval;

A^* _SιFR = 15 [erl] sustained FR traffic; Λ "^ = 10 [erl] sustained HR traffic;

A^* _s = 25 [erl] total traffic sustained by the cell;

TC = 2.5% time-congestion (also obtained from measurements made by the network).

AMOUNT OF RESOURCES

TV= 30 CONFIGURATION OF RESOURCES x = 21 enhanced preemption not activated and no constraints on the handover policy.

In this case, both the offered traffic (A_off) and the average percentage of calls originated by dual-rate terminals (P_DR) are unknown. Some well-known methods would estimate the value of P_DR simply as the ratio between the sustained HR traffic and the total sustained traffic: in this example, this would result in P_DR= 10/25=0.4 -> PDR ⁼ 40%. Said estimation could be correct only if the value of the threshold is 0, i.e. the network assigns the HR traffic channels in any occupation level of the cell. The proposed method works differently. First of all, the B_L module is utilized iteratively, attempting to assign a suitable value to the unknown variables (in this case, A_off and P_DR) utilizing the dichotomy or the Newton-Rapson iterative process. The COND module of the software application checks the results determined by the B_L module for each step of the iterative process, which is governed by the REG module. The COND module stops the iterations when the desired condition is attained (see Fig. 6 and Fig. 9). The proposed procedure allows the grade of service of the cell to be correctly estimated. In fact, the B_L module provides the FR/HR carried traffic values as well as the steady-state occupation probabilities and the grade of service of the cell (in accordance with Eq. 6). In this example, the grade of service determined by the proposed method is 0.004% thus, the difference with the TC value measured by the network (2.5%) is quite surprising. If the TC applies in place of the grade of service (as in Eq. 8), x an offered traffic value of 25.64 erl would be determined in this example whereas the proposed method has determined the correct value of 25.02 erl. Similarly, the proposed method determines the correct value of the average percentage of calls originated by dual-rate terminals, in this example 91.5% compared to the value of 40% value determined by other said existing methods. Example 2

Assume that we want to estimate the capacity of a cell operating with the DHRA algorithm having set a threshold value of 70%. In particular, known is the: AMOUNT OF RESOURCES N=30

CONFIGURATION OF RESOURCES

* = 21 enhanced preemption not activated and no particular constraints on the handover policy.

TRAFFIC CHARACTERISTICS A_Off offered traffic (unknown)

P _DR - 80% the probability that an incoming call is originated by a dual-rate terminal

DESIRED PERFORMANCE

Grade of service 2%

As in the previous example, we proceed using the dichotomy iterations. After the elaborations carried out by the iterative process, the software application determines that the capacity of the cell is 37.93 erl, in particular that: the maximum carried traffic of the cell with the desired grade of service (2%) is 37.93 erl; the HR carried-traffic is 27.54 erl; the FR carried-traffic is 10.39 erl. Note that if the average percentage of dual-rate terminals increases, the capacity of the cell also increases. Note also the considerable difference between the capacity of the cell as determined by the proposed method (37.93 erl) and the capacity of an only-HR-cell (a fictitious cell that allocates only HR traffic channels) having the same number of time-slots though twice as many servers; the capacity of an only-HR-cell can easily be determined with the well-known Erlang B formula applied on a cell with 60 servers: in this case, the capacity is 48.65 erl. Therefore, if the capacity of an only-HR-cell is used instead of the capacity determined by the proposed method, a large overestimation (+28%) of the actual capacity of a cell operating with the DHRA and configured with a threshold value of 70% will result! Example 3

This example demonstrates how the proposed method allows the growth in the capacity of a network beginning to utilize DHRA to be determined in a city covered by 10 cells operating on the 900-MHz frequency band and equipped as follow: TABLE 3.1

The maximum carried traffic and the offered traffic of the cells have been determined utilizing the Erlang B formula - because initially the network uses only FR traffic channels - setting a grade of service of 1% and being known, for every cell, the number of carriers and the number of time-slots assigned to voice service. As the network begins to utilize DHRA, the above reported table can no longer be utilized to accurately assess the true capacity of the network: in this case, we will use the proposed method. Assume that the average percentage of calls originated by dual-rate terminals (PDR) is known, in particular 80%, and assume that (to simplify) said percentage is the same for every cell in the city; furthermore, assume that the DHRA threshold is 70% for every cell. Utilizing the B_L module iteratively, we determine the desired information listed in Eq.6. The final results are indicated in the following table 3.2. The growth in the network capacity in terms of the maximum carried traffic is: η=293.1/166,5=1.76 -> + 76%

Let's assume that the operator's customers provide a mean traffic level of 0.01 erl per user (this is the time- weighted average of the ratio between the number of users in dedicated mode and the overall number of users in idle-mode or dedicated mode, relative to the voice service). This means that the number of customers that can be served by the city's network has increased from 166.5/0.01=16,600 to a maximum of 293.1/0.01=29,300 users! It would be useful to repeat the same comparison with a different value of the average percentage P_DR, for example, equal to 90% and assuming P_DR again to be constant for every cell in the city. In this case, we will demonstrate how the network capacity has increased (TABLE 3.3). TABLE 3.2

TABLE 3.3

In this case, the growth in the network capacity in terms of the maximum carried traffic is: η'=329/166.5=1.98 ^ 98%.

This also means that the number of customers that can be served by the city's network has increased from 16,600 users to a maximum of 329/0.01=32,900 users! Therefore, substituting the terminals for only a portion of the customers (only 10% in this case, not for all the customers), and with DHRA activated, the network capacity has essentially been doubled with respect the original condition in which only FR traffic channels were used (Table 3.1). Hence, the proposed method allows the operator to also determine the effect which the types of terminal (owned by his customers) have on the network capacity and, consequently, it also allows the operator to plan the most appropriate commercial policy in order to optimize the resources of the operator's already existing network, in particular promoting the substitution of the single-rate terminals (owned by a subset of the customers) with new terminals supporting the HR-type traffic channel. We also notice that table 3.3 demonstrates that if we cannot or choose not to utilize DHRA and instead wish to increase the network capacity installing new base stations and new cells or increasing the equipment for the existing cells (for example, adding new carries for every cell), at least 24 new radio carriers would have to be installed (see Δcarriers on table 3.3) as compared with the 36 carriers already operating in the city. This fact would however entail considerable drawbacks because each new GSM radio carrier requires the reservation of a frequency bandwidth of at least 200 kHz however the frequency bandwidth assigned to the operator is always limited and often inadequate. The purchasing of new frequency bandwidth furthermore involves huge financial expenses. In addition to the above economic considerations, the proposed method is also a helpful aid for determining the mean quality of service supplied to the operator's customers. In fact, the GSM standard includes certain parameters that allow the quality of service to be evaluated as a function of the traffic channel type (FR, HR, EFR, AMR, and so on) and as a function of the radioelectric coverage conditions of the cellular system: said quality of service is also called Mean Opinion Score (abbreviated MOS). For example, associating a score 3.5 (more than sufficient) to the quality of the FR communications and a score 3.3 (poor) to the quality of the HR communications, we will evaluate the following mean quality indicators for voice service supplied to customers in the city for the cases indicated in tables 3.2 and 3.3: TAB. 3.2 average score for the city = (94 x 3.5 + 199 x 3.3)/(94 + 199) = 3.36 TAB. 3.3 average score for the city = (65.4 x 3.5 + 263.6 x 3.3)/(329) = 3.34

The quality of service has been reduced with respect the case of only-FR traffic channels (average score 3.5), nevertheless the difference between tab. 3.2 (average score 3.36) and tab 3.3 (average score 3.34) is rather insignificant. If the quality of service is considered to be adequately sufficient with an average score of 3.4, for the case of high network load the quality of service would be inadequate: in order to improve the quality it would be necessary, for example, to increase the threshold value (form 70% to 80%). But increasing the DHRA threshold value reduces the network capacity with respect the capacity that was indicated in tab. 3.3. To avoid this drawback, in order to maintain the same optimal configuration of resources, the operator could promote the replacement of single-rate terminals with new mobile phones supporting EFR traffic channel that effectuate voice calls with a MOS of 4.2 (optimal) or with mobile phones supporting AMR-HR traffic channels that effectuate voice calls with a MOS of 3.7 (good). However, the operator would have to upgrade its network in order to support the EFR traffic channels and/or the AMR traffic channels, incurring the corresponding costs. In this way, utilizing the proposed method, the operator can choose the most suitable strategy for improving the quality of service supplied to its customers, keeping the same increasing in network capacity and, consequently, maximizing the profitability of its business environment. It is obvious that the proposed method is also a useful tool both for evaluating profitability and for estimating the quality of service. The proposed method may also entail, even indirectly, the use of many GSM network parameters. Example 4

In this example the proposed method is compared with other well-known methods, illustrating in particular the difference in the results (and the conclusions) obtained by using the proposed method. Let's again assume that we want to estimate the capacity of the same GSM network in example 3, composed of 10 cells operating on the 900-MHz frequency band and in which the operator wants to utilize the DHRA. As in example 3, the capacity of a network composed of only-FR-cells can be determined through the well-known Erlang B formula (table 3.1). As the DHRA starts to operate, the network capacity is increased but the operator doesn't know the exact extent of said increased capacity. Therefore, we will compare the proposed method with four well-known methods. METHOD A

Given that the HR traffic channels allow the number of servers of every cell to be doubled and that a subset of the mobile terminals cannot support the HR traffic channel, we will estimate the network capacity using a weighted average of the carried traffic through the Erlang B formula. A plausible value of said weighted average can be determined assuming that the terminals are all single-rate types: the number of servers of every cell therefore is equal to the number of time-slots and the Erlang B formula can be applied to evaluate the maximum carried traffic of each only-FR-cell. Another plausible value of said weighted average can be determined assuming that the terminals are all dual-rate types and that the network assigns HR channels for every call request (disregarding the effect of the DHRA threshold, as if it had a value of 0). Thus, the number of servers of every cell is twice the number of time-slots and in this case the Erlang B formula can be applied again to evaluate the maximum carried traffic of each only-HR-cell. Therefore, calculating the weighted average of said two capacity values of each cell, and considering the average dual-rate percentage P_DR (in this case 80%) as the weighting factor of the weighted average, the table 4.1 is obtained. TABLE 4.1

The result of method A is that, after DHRA activation, the network capacity (which should be the maximum carried traffic with a desired grade of service) has attained the following value: η_A= 343.64/166.5 = 2.064 (+106.4%)

In accordance with method A, the network capacity has essentially doubled.

METHOD B

Given that the HR traffic channels allow the doubling of the number of servers of every cell, though the network attempts to assign the HR channels only if the threshold value has been exceeded, the estimation of the capacity of every cell is conducted considering a weighted average of the number of servers and again utilizing the Erlang B formula.

In this case, the effect of single-rate terminals is disregarded, so the weighting factor is simply the threshold value and the weighted average of the number of servers is consequentially: N_iervers = int[N_TS • (x_%)] + 2 • {N_ra - int[iV_ra • (x_%)]}

The following table summarizes the network capacity assessment utilizing said method B:

T 4.2

The result of method B is that, after DHRA activation, the network capacity (which is the maximum carried traffic with a desired grade of service) has attained the following value: η_B= 235.08/166.5 = 1.412 (+ 41.2%)

In accordance with method B, the network capacity has increased 41.2%.

METHOD C

In this case, the estimation of the capacity of every cell is again conducted considering the weighted average of the number of servers and utilizing the Erlang B formula but not-disregarding the effect of single-rate terminals. Therefore, the average number of servers must consider that every single-rate terminal occupies

"two servers" with respect a dual-rate terminal. Thus, the weighting factors for the average are both the threshold value and the average percentage of calls originated by dual-rate terminals (PDR), SO the weighted average of the number of servers is:

^_server_s = ^l^ ^■ (x_% )] + 2 ^• {N_τs - M[N₇₈ ^■ (x_% )]} ^• P_DR + {N_τs - Wt[Nn ' (**)]} ^• G - ^_D*)

The following table summarizes the capacity evaluation conducted with said method C, in which the Erlang B formula is applied for a non-integer number of servers:

TABLE 4.3

After DHRA activation, method C results in the following value for the network capacity (which is the maximum carried traffic with a desired grade of service): ηc= 221.71/166.5 = 1.33 (+ 33%) In accordance with method C₃ the network capacity has increased 33%.

METHOD D

In this case, the estimation of the capacity of every cell is conducted with a simulation tool considering the performance of the network operating with said resource configurations, taking into account the characteristics of the offered traffic. Let's assume that, using method D after DHRA, the following result is obtained for the network capacity: η_D = 233.1/166.5 = 1.4 (+ 40%)

In accordance with method D, the network capacity has increased 40%.

CONCLUSIONS

To summarize, the above results obtained from the utilization of said known methods, to which several other plausible methods can be added and that which may also provide results that differ considerably from the reported results, the following table is obtained:

Examining the above reported results, an operator wanting to utilize DHRA, could be inclined to attribute an increased capacity of 40% to its network (in accordance with the simulation tool result), given that method B and C substantiate said result. Therefore, if the operator's network capacity must be doubled in order to satisfy the increasing demand of the customers, a consequential increase in network equipment would appear to be necessary, in particular an increase in the number of network cells would appear to be required (at least 6 new cells, in this example), with a further complication of being forced to deploy the new cells on a new frequency band because the existing frequency band could be congested. Nevertheless, the proposed method (which the inventor considers to be the only one capable of correctly determining the performance of a network operating with said features and said traffic characteristics) would provide an overall capacity of 293 erl (as demonstrated in table 3.2) with an increase in capacity of 76%. None of the methods A, B, C or D has determined a similar value for the capacity. Moreover, example 3 demonstrated that operator is able to double the capacity of its network without deploying any new cells, merely substituting the terminal type for a portion of the customers (in particular, only for 10% of customers). It has been proved that well-known methods, for example, those based on Erlang B formula, are not suitable for adequately taking into account the offered traffic characteristics and the resource configurations. Example 5

Assuming the same network as in the previous examples 3 and 4, let's suppose that operator chooses not to double the capacity of its network because the operator is unable to increase customer demand. Instead, let's suppose the operator decides to economize its network resources, taking the excess equipment out of service. The decommissioning of the redundant cells could be very profitable for the operator because the operator is now able to fee-up a few frequency bandwidth to be resold or to rented out to other operators. Furthermore, the redundant equipment can now be managed by other operators or service providers, enabling the so-called "network sharing." In order to select the essential cells, both the capacity requirements and the radioelectric coverage requirements must be considered: this objective can be obtained utilizing powerful cellular planning tools. Considering that this document regards only capacity requirements, let's suppose for the sake of simplicity that all the cells in the network have a rectangular shape: Fig. 7a and Fig. 7b illustrates a hypothetical distribution of said cells before and after the optimization process of said removal from service. The following table indicates a possible example of useful information for the decisions to be made during the decommissioning process. Let's suppose that the maximum sustained traffic of each cell is known (having been measured by the network) and that all the equipment for each cell and the configuration are known.

The gray columns of table 5.1 contain the known data: the FR and HR sustained traffic components, the number of carriers and the number of time-slots of each cell, moreover each cell is configured for the sake of simplicity with a threshold value of 70%, enhanced preemption not activated and without any particular constraints regarding the handover policy. Utilizing the "offered traffic estimation" procedure of the proposed method, the corresponding white columns, relative to the unknown data, may be completed using the following parameters: the offered traffic of every cell, the average percentage of dual-rate terminals (PDR) requesting voice service within the coverage area of every cell, and the true grade of service of every cell. Therefore, based on the data of table 5.1 and considering Fig. 7, a justification for joining cells C₁ and C₂, for example, decommissioning cell C₁, can be found. The new cell C ₂ obtained has a new surface coverage of 8 km², which is the sum of the coverage area of cells C₁ and C₂ before being joined. First of all, the estimation of the offered traffic of the new cell C ₂ is 58 erl, which is the sum of the offered traffic components of the original cells C₁ and C₂. Second, the estimation of the average percentage of dual-rate terminals handled within the new coverage area would obviously be the weighted average of the original average percentage of each cell, in which the weighting factor equals the corresponding original offered traffic component (in this example we obtain a new P_DR equal to 82%). Obviously for the other cells, we would continue on in a similar manner. Having completed this example of network optimization, a new table (table 5.2) can be obtained, containing all the information needed to re-dimension the network with the proposed method. In particular, the optimal number of time-slots of each new cell of the network is determined, being known both the new values of the offered traffic and the new average percentages of dual-rate terminals for each cell, with the constraint that the desired grade of service must be less than or equal to 1%, and having set the desired DHRA threshold value (70% for every cells, in this example). Said dimensioning procedure can generally be applied for the deployment of a new GSM network in each city. However, in this particular example we can consider that some resources have already been installed and only an upgrade of existing equipment will be required. Setting a grade of service of 1% for every new cell, in conformity with the proposed method, the following table is obtained, in which the gray columns represent the input data for the dimensioning procedure while the white columns represent the output data: TABLE 5,2

Note that, in the table above, the exact number of carriers, C₅ has not yet been determined because the minimum number of time-slots to be assigned to voice service should be 24 (as determined by the dimensioning procedure) but 24 is a multiple of 8 which is also the number of time-slots for each GSM carrier. This means that at least 3 carriers are needed. Given that each cell of a GSM network is normally configured with a known number of time-slots reserved for signaling channels (said number can be determined by well-known rules) and given that one time-slot is always reserved for the BCCH channels, it therefore follows that cell C₅ needs to be equipped with 4 carriers for which at least 4 time-slots must be reserved for the signaling channels, while the remaining 28 time-slots could be assigned to voice service: in this case, the grade of service of cell C₅ would be less than the value indicated in table 5.2, in particular it would only be 0.13% which corresponds to 12.3 erl for the FR-carried-traffϊc of and to 14.6 erl for the HR- carried-traffic. If the operator instead wishes to reduce the number of carriers of cell C₅ from 4 to 3, a further adjustment would be needed for the dimensioning procedure in order to verify if, acting on the set of user terminals (for example, reducing the percentage of single-rate terminals) or acting on the resources configuration (for example, reducing the threshold value or activating the enhanced preemption only for cell C₅), the number of time-slots to be assigned to voice service can be reduced to 21 or 22, in order that only 3 carriers need be installed. Nevertheless, the implementation of enhanced preemption could be costly, especially if implemented only on a limited number of cells: the operator, thanks to this proposed method, can select the best strategy to be adopted. Note that, in accordance with the information indicated in table 5.2, the operator needs to deploy only 24 GSM carriers (to be precise, 24 GSM transceivers) in order to satisfy the user service requirements, as compared to the 36 GSM carriers initially operating in the city before DHRA was implemented (as in example 3). In this way, the operator can fee-up a frequency bandwidth previously occupied by 12 GSM carriers. Said frequency bandwidth could be returned to the competent authority, rented out or literally sold to another operator, or even still it could be utilized to supply other services such as data service (internet browsing, e-mails, MMS delivery, and so on) or videophone services. Moreover, freeing up the frequency bandwidth occupied by 12 GSM radio carriers also signifies being able to utilize a new frequency bandwidth of 2.4 MHz within the city, with exactly the same network capacity used in the initial state. Furthermore, being that a new frequency bandwidth is available, planning is facilitated for the new cellular network, i.e. the optimization of the radioelectric quality of the network is easier, hence the best quality of service can easily be provided. In fact, it is well-known that GSM cells can be grouped together in so-called "clusters" in such a way that every cluster can utilize the entire frequency bandwidth available to the operator. In particular, each GSM radio carrier may be assigned only to one cell in each cluster (i.e. the same carrier cannot be assigned to two different cells belonging to the same cluster). Therefore, as the average number of radio carriers utilized by every cell of a cluster increases, the number of cells of a cluster decreases. However, as the number of carriers per cell increases, the "amount" of co-channel interference originated by neighboring cells (belonging to other clusters) also increases significantly, since said neighboring cells are closer. Vice-versa, if the average number of radio carriers of each cell of the cluster is reduced (though maintaining the same capacity and the same grade of service) or, similarly, if the number of cells of the cluster can be increased, the "amount" of co-channel interference from neighboring clusters can be significantly reduced, in this way obtaining a consequential improvement in the radioelectric quality of the entire network. The last example has also demonstrated indirectly that the offered traffic of each cell can be modified acting appropriately on the coverage area of each cell in the city, for example, utilizing well-known network parameters, even those not described in this document (for the sake of simplicity). Therefore, the method may entail the use of numerous parameters, including those radioelectric parameters regarding coverage and operating conditions of the GSM system, even if they appear not to be directly pertinent to performance analysis and dimensioning procedures proposed. Although the preferred embodiments of the proposed method and computer system of the present invention have been illustrated in the accompanying drawings, tables and examples, it will be understood that the invention is not limited to the embodiments disclosed but is capable of numerous rearrangements, modifications and substitutions without departing from the essence of the invention as set forth and defined by the following claims.

Claims

1. A method for analyzing the performance of at least one network portion of a telecommunication system, in which the communication channels requested by the mobile terminals are allocated and in which the corresponding communications are sustained on high-bit-rate and/or low-bit-rate traffic channels, comprising the steps of:

- providing an average number per unit time (λ) of said requests, in a predetermined time interval;

- providing an average service duration (τ) of said communications, in said predetermined time interval;

- providing an amount of resources of said network portion; characterized by the fact of comprising the further steps of: - defining every state of said network portion with a number "i" of communications sustained on high- bit-rate traffic channels and with a number "j" of communications sustained on low-bit-rate traffic channels;

- determining, for every state (ij), a first probability (λi) of selecting a low-bit-rate traffic channel and a second probability (λ₂) of selecting a high-bit-rate traffic channel, for the case of a new call-request, said first and said second probability of selection being based on said average number of requests per unit time (λ) and on said amount of resources;

- determining, for every state (i j), the probability, for said network portion, of being in said state (i j), based on said first and said second selection probability (λ_b A₂), based on said number "i" and said number "j" of sustained communications and based on said average service duration (τ); - determining the performance of said network portion based on the overall set of probabilities (πy) of said network portion being in each state (i,j).

2. A method according to claim 1, characterized in that it comprises the further steps of: providing at least one percentage (PDR) of call-requests originated by dual-rate terminals, or else the probability (P_DR) that a call-request is originated by a dual-rate terminal, said dual-rate terminal being capable of sustaining calls on high-bit-rate or on low-bit-rate traffic channels; providing a configuration of said resources in said network portion; said first and said second selection probability (λ_l5 IQ) being also based on said average percentage (P_DR)_> or else on said probability (P_DR), and on said configuration of resources.

3. A method according to claims 1 or 2, characterized in that said amount of resources comprises a number of communication channels, at low-bit-rate or at high-bit-rate (N), assigned in said network portion to a service requested by the users.

4. A method according to any one or more of claims 1 to 3, characterized in that said configuration of resources comprises the setting of a threshold value (x) such that if the occupation level of said resources is higher than or equal to said threshold value, a new call-request is preferentially allocated on a low-bit- rate traffic channel.

5. A method according to any one of the aforesaid claims, characterized by the fact of providing the value of the offered traffic A_0FF= λ-τ in place of the individual values of said average number of requests per unit time (λ) and of said average service duration (τ).

6. A method according to any one of the aforesaid claims, characterized in that said configuration of resources comprises the possibility of setting a feature that imposes the switching from a high-bit-rate traffic channel to a low-bit-rate traffic channel for at least one ongoing communication in said network portion when, for the case of a new call-request, said network portion is congested.

7. A method according to any one of the aforesaid claims, characterized by the fact of associating to said number "i" of communications sustained on high-bit-rate traffic channels, for every state of said network portion, a number "i_DR" and a number "i_SR," "i_DR" being the number of communications sustained on high-bit-rate traffic channels with said dual-rate terminals, "i_SR" being the number of communications sustained on high-bit-rate traffic channels with terminals that do not support the low-bit-rate traffic channel (single-rate terminals).

8. A method according to claim 7, characterized by the fact of comprising the further step of determining, for every state of said network portion, a third probability of selecting (λ^*j) a low-bit-rate or a high-bit- rate traffic channel when, for the case of a new call-request, said network portion is congested, said set of probabilities (πy) being also based on said third selection probability (λ^*j).

9. A method according to any one of the aforesaid claims, characterized in that said configuration of resources comprises the setting of a feature that imposes the maintaining of the traffic channel types for the component of said average number of requests per unit time (λ) originating from neighboring network-portions by way of handover procedures.

10. A method according to claim 9, characterized by the fact of providing several other percentages (PHR, PsRh_> PoRh) of call-requests originated by dual-rate terminals, or else several other probabilities (PH_R, Ps_Rh) P_DRK) that a call-request is originated by a dual-rate terminal, said terminals are able to sustain communications on high-bit-rate and/or low-bit-rate traffic channels in said predetermined time interval based on said configuration of resources, said first, said second and said third selection probability (λ_u X₂, λ^*j) being also based on said several percentages or on said several probabilities (PHR, Ps_Rh_> Pu_Rh)-

11. A method according to any one of the aforesaid claims, characterized in that said performance comprises one or more of the following parameters: - a grade of service (GOS) of said resources of said network portion;

- the overall carried traffic and/or the carried traffic in low-bit-rate traffic channels and/or the carried traffic in high-bit-rate traffic channels, of said resources of said network portion;

- the component of said offered traffic that is not carried by said resources of said network portion;

- the set of probabilities that a certain number of communication channels in said network portion are occupied; - the blocking probability of a call-request originated by said dual-rate terminals and/or the blocking probability of a call-request originated by said single-rate terminals.

12. A method for dimensioning resources in at least one network portion of a telecommunication system, in which the communication channels requested by the mobile terminals are allocated and in which the corresponding communications are sustained on high-bit-rate and/or low-bit-rate traffic channels, comprising the steps of:

- providing a value of the incoming traffic offered to said network portion;

- providing at least one desired performance of said network portion;

- ascertaining an amount and/or a configuration of resources, in said network portion, capable of allocating said communication-channel requests with said desired performance; characterized by the fact of providing, before said ascertainment step, at least one percentage value for dual-rate terminals and by the fact of determining, during the course of said ascertainment step, the performance of said network portion in conformity with one or more of the aforesaid claims.

13. A method for predicting the carried traffic of at least one network portion of a telecommunication system, in which the communication channels requested by the mobile terminals are allocated and in which the corresponding communications are sustained on high-bit-rate and/or low-bit-rate traffic channels, said prediction method comprising the steps of:

- Providing an amount of resources in said network portion;

- Providing a desired performance of said network portion; - Assigning a value to the offered traffic (A_OFF);

- Ascertaining if said amount of resources, with said assigned value of offered traffic, is able to allocate said communication-channel requests with said desired performance; characterized by the fact of comprising the further steps of:

- Providing, before said ascertainment step , a configuration of said resources; - Providing, before said ascertainment step, at least one percentage of dual-rate terminals;

- Determining, during the course of said ascertainment step, the performance of said network portion, including the carried traffic, in conformity with one or more of the claims from 1 to 12.

14. A method for estimating the offered traffic and/or the grade of service of at least one network portion of a telecommunication system, in which the communication channels requested by the mobile terminals are allocated and in which the corresponding communications are sustained on high-bit-rate and/or low-bit- rate traffic channels, said method comprising the steps of:

- Providing an amount of resources in said network portion;

- Providing at least one value of the sustained traffic in said network portion;

- Assigning a value to the offered traffic; - Ascertaining if said amount of resources, with said assigned value of offered traffic, is capable of sustaining at least one said value of the sustained traffic; characterized by the fact of comprising the further steps of:

- Providing, before said ascertainment step, a configuration of said resources;

- Assigning, before said ascertainment step, at least one percentage of dual-rate terminals; - Determining, during the course of said ascertainment step, the performance of said network portion, including the offered traffic and/or the grade of service, in conformity with one or more of the claims from 1 to 12.

15. A method according to claim 1 or 12, characterized by the fact of determining an amount of equivalent resources (N_eq) capable of allocating said communication-channel requests with said desired performance for the case in which low-bit-rate traffic channels cannot be assigned in said network portion, being given the same offered traffic and the same desired performance.

16. A method according to any one of claims 12 to 14, characterized by the fact of comprising the step of utilizing a Newton-Rapson iteration process or a dichotomy iteration process in order to determine the optimal values to be used for each iteration to unknown data needed for said step of determining the performance.

17. A method according to claim 14, characterized in that said sustained traffic comprises the traffic sustained on low-bit-rate traffic channels and the traffic sustained on high-bit-rate traffic channels.

18. A method according to any one or more of the aforesaid claims, characterized in that said telecommunication system comprises a cellular telecommunication system in which the communication channels are mapped onto said time-slots in conformity with the TDMA or the TDMA/FDMA technologies.

19. A method according to any one or more of the aforesaid claims, characterized in that said network portion comprises a cell of a cellular telecommunication system.

20. A method according to any one or more of the aforesaid claims, characterized in that said resources comprise a number of time-slots, a number of radio carriers, a number of transceivers, a radio-frequency bandwidth, a number of antennas, a number of A-bis interface links and a set of software and hardware equipment of which said cell is composed.

21. A method according to any one or more of the aforesaid claims, characterized in that said communication channels are also able to sustain voice calls and that said service requested by the users comprises telephony service.

22. A method according to any one or more of the aforesaid claims, characterized in that said high-bit-rate traffic channel comprises the full-rate traffic channel and that said low-bit-rate traffic channel comprises the half-rate traffic channel.

23. A computer system comprising a computer configured to carry out the method according to any one or more of the aforesaid claims.

24. A software application comprising software modules (B_L, COND, REG) that, when memorized and run by said computer system, carries out the method according to any one or more of the aforesaid claims.

25. The entire set of values relative to the input data and output data of a software application according to claim 24, said set of values being memorized in a tabular format, the performance analysis and dimensioning of the resources of said network portion being conducted by way of interpolation of said tabulated values.

26. A method for analyzing the performance and dimensioning the resources of at least one GSM network portion substantially as described and illustrated and for the indicated aims.