WO2009011005A1 - Method and computer system for analyzing the performance and for dimensioning an underlay/overlay cell of a telecommunication system - Google Patents

Abstract

A method and a computer system for analyzing the performance and for carrying out the dimensioning of at least one portion of a telecommunication system, including a first and a second network subportion capable of allocating communication-channel requests by mobile terminals, said first network subportion being able to sustain the corresponding communications in high and/or low-symbol-rate traffic channels, said second network subportion being able to sustain the corresponding communications in high and/or low-symbol-rate traffic channels, characterized by the fact of comprising the further steps of providing an average service duration (TOL) of said communications in said first network subportion and an average service duration (TUL) of said communications in said second network subportion, providing the characteristics of said communication-channel requests, providing an amount of resources and the resource configuration in said first and in said second network subportion, comprising a step of reducing the number of the possible states of said network portion. Said characteristics of said communication-channel requests comprise the capability, of said mobile terminals, to sustain calls on high-symbol-rate and/or on low-symbol-rate traffic channels and the capability to support a primary and/or a secondary frequency band. Said portion of a telecommunication system comprises a GSM underlay/overlay cell, said first network subportion comprises an overlay cell and said second network subportion comprises an underlay cell.

Description

METHOD AND COMPUTER SYSTEM FOR ANALYZING THE PERFORMANCE AND FOR DIMENSIONING AN UNDERLAY/OVERLAY CELL OF A TELECOMMUNICATION SYSTEM TECHNICAL FIELD

This invention regards a method and a computer system for carrying out performance analysis on an underlay/overlay cell of a cellular telecommunication network, in particular for a second generation network in accordance with the GSM standard and also for the case of coexisting Full-Rate and Half-Rate traffic channels. This invention also regards a method and a computer system for dimensioning the resources used in an underlay/overlay cell of a cellular telecommunication network of the type indicated above. This patent extends the field of application of patent no. PCT/IT2008/000387 which is to be considered as reference incorporated in the description which follows. BACKGROUND ART

The underlay/overlay cell is a portion of a telecommunication network, GSM, for example, used to sustain the call requests by users in high-symbol-rate and/or in low-symbol-rate communication channels in a first network subportion or in a second network subportion. In particular, the first network subportion is in general configured as an overlay cell, so that the call requests are preferentially sustained in said first network subportion, while the second network subportion is in general configured as an underlay cell, so that the call requests not sustained by the first network subportion may be sustained in this second network subportion: when the coverage area of the second network subportion (underlay cell) contains the coverage area of the first network subportion (overlay cell), this portion of the telecommunication-network is called "underlay/overlay cell." If the users make voice calls, it is understood that the term high-symbol-rate communication channel signifies, for example, the "Full-Rate" (FR), "Enhanced Full Rate" (EFR), or AMR- FR (A-FR) traffic channel, whereas the term low-symbol-rate communication channel signifies, for example, the "Half-Rate" (HR) traffic channel or the AMR-HR (A-HR) traffic channel. It is well-known that the FR- type communications offer better conversation quality than the HR-type communications but with higher resources occupation. If the network provides also 8PSK-based traffic channels for voice communications, then a time-slot can be configured to sustain up to 6 simultaneous communications. Thus, the term high- symbol-rate refers also to the HR-type traffic channels when the term low-symbol-rate refers to the 8PSK-type traffic channels, which offer the same service of the HR-type communications but with lower resources occupation and with lower quality. This method is also valid for the mixed voice and data traffic channels which can be equated to the corresponding high- or low-symbol-rate traffic channels mentioned above. A "single-rate terminal" is defined to be a mobile terminal that does not support the low-symbol-rate traffic channel, while a "dual-rate terminal" is defined to be a mobile terminal that supports both the high-symbol- rate and the low-symbol-rate traffic channels. In the GSM standard, there currently are no terminals anticipated that do not support the FR traffic channel. The term "mobile terminal" signifies an electronic telecommunication device, such as a mobile phone or a portable computer, capable of making vocal and/or data communications according to the GSM standard.

The possible resource configurations of the overlay cell and of the underlay cell that take part in the selection of the FR- or HR-type traffic channel are similar to those considered in the reference patent no. PCT/IT2008/000387. In particular, the following configurations are considered: "Dynamic Half-Rate Allocation" [abbreviated DHRA] described in patent US6292664B1; "enhanced preemption," described in patent US5940763; and the handover policy described in the reference patent no. PCT/IT2008/000387. It's necessary however to consider additional resource configurations for the current case of an underlay/overlay cell. In particular, the "overlay cell," managed by a specific radio base station, covers a region of space fully contained within the region of space of another cell, named the "underlay cell," which could be managed by another radio base station or by the same radio base station as the overlay cell. Furthermore, the two cells established in this way can belong to the same GSM frequency band or to different frequency bands (for example 900 MHz or 1800 MHz). Typically, the underlay cell is configured to operate on a primary band (for ex., 900 MHz) and has the main function of guaranteeing the radioelectric coverage of the network; the overlay cell is configured to operate either on the primary band (for ex., at 900 MHz) or on a secondary frequency band (for ex., at 1800 MHz) and has the main function of sustaining localized traffic requests of low-mobility users, for example in the so-called "hot-spots" (airports, markets, squares, railway stations, offices, etc.), to make up for deficiencies of the underlay cell resources. Due to the low mobility of the users, the overlay cell covering the hot-spot can utilize 8PSK-based traffic channels, increasing enormously the capacity of the underlay/overlay cell and sustaining the voice calls with an acceptable quality of service. Nevertheless, mobile terminals capable of supporting the 8PSK-based traffic channels are still not so diffused but, for the future, it is reasonable to foreseen such a possible evolution of the technology. The so-called "dual band - dual rate cell" consists in an underlay/overlay cell configured so that the underlay cell operates in the 900-MHz GSM band and the corresponding overlay cell operates in the 1800-MHz GSM band; both cells can be configured to support HR- and/or FR-type traffic channels, or in general to support high-symbol-rate or low-symbol-rate traffic channels. A discussion of underlay/overlay cells also includes the case in which a single cell operates on a frequency band (for example at 900 MHz or also at 1800 MHz) managed by a single GSM base station and in which its carriers may be grouped into two independent and distinct groups from the perspective of the DHRA and the enhanced preemption features. Furthermore, the coverage area of the overlay cell may also coincide with the coverage area of the underlay cell. The configuration of two collocated cells in the underlay/overlay mode is very useful for operators who already have a diffuse network of base stations. In fact, if the network were to be expanded, it would be very economical to use the sites already occupied by existing base stations, in order to share costs, authorizations, and infrastructure between the new installation and the existing one.

As regards the terminals, those that support only the 900-MHz GSM band will hereafter be called "single- band terminals," while those that support both the 900-MHz and 1800-MHz GSM bands shall be called "dual- band terminals." Under present conditions, the GSM standard does not permit terminals that do not support the 900-MHz band. A cell operating in the 1800-MHz frequency band may not therefore provide the service to single-band-type terminals, whereas a cell operating in the 900-MHz frequency band can sustain the communications generated both by the dual-band terminals and by the single-band terminals. SUMMARY OF THE INVENTION

The present method of performance analysis and dimensioning can apply to a portion of a telecommunication network, in particular to an underlay/overlay cell of a telecommunication network according to the GSM standard, capable of supporting the voice traffic generated by the following four types of cellular phones: single-band and single-rate cellular phones; single-band and dual-rate cellular phones; dual-band and single- rate cellular phones; dual-band and dual-rate cellular phones.

The method described in patent no. PCT/IT2008/000387 is not fully satisfactory for analyzing the performance or for dimensioning an underlay/overlay cell because it cannot correctly take into account the component of incoming traffic of the overlay cell which the overlay cell cannot sustain and which is thereby transferred to the underlay cell (the so-called overflow traffic). It is in fact well-known that this overflow traffic component has the characteristic of being non-Poissonian; it cannot be correctly considered among the known methods, which in this case would result in an underestimation of the blocking probability of call requests to an underlay/overlay cell and an overestimation of the maximum carried traffic, especially, in the presence of a non-negligible, non-Poissonian component of overflow traffic incoming to the underlay cell. Some methods may already exist based on simulations; they however can provide incorrect results or results very difficult to verify and may also entail very long processing times, on the order of minutes or also hours to analyze or to dimension each individual underlay/overlay cell, especially if comprehensive, precise and reliable results are desired. From what has been indicated above, it is obvious that a method needs to be provided in order to correctly analyze the performance of a GSM-standard underlay/overlay cell, in the configurations described above in particular, also for the purpose of being able to predict the behavior of the cell as the configurations and the significant parameters vary. Likewise, it is obvious that a method is needed to effectively dimension the resources of an underlay/overlay cell, for the configurations described above in particular, in order to sustain the offered traffic of the cell with the best quality attainable. The purpose of this invention therefore is that of providing a method to correctly analyze or predict the performance of an underlay/overlay cell, in particular of an underlay cell and of an overlay cell in which there are Full-Rate-type and/or Half-Rate-type traffic channels and in which the DHRA and/or the enhanced preemption features can be implemented. In particular, the purpose of the invention is that of providing a method to analyze performance, in terms of carried traffic, grade of service (i.e., the call-blocking probability) and the steady-state resource occupation probabilities, being given the resources of the underlay cell and of the overlay cell, their configuration and the characteristics of the incoming traffic to the overlay cell and to the underlay cell. An additional purpose of the invention is that of providing a method which also allows the dimensioning of the underlay/overlay cell resources, in particular in terms of time slots and therefore of radio carriers needed to sustain a given offered traffic with a predetermined grade of service and taking into account the configuration of the underlay/overlay cell (for ex., the threshold value, whether or not enhanced preemption is implemented, etc, both for the overlay cell and for the underlay cell). Moreover, the purpose of the invention is to provide a method which also allows a correct estimate of the grade of service and the offered traffic that an underlay/overlay cell is exposed to in a given configuration, being known the traffic sustained (i.e., the measured traffic sustained), also obtaining the characteristics of the incoming traffic to the underlay cell and to the overlay cell, or also obtaining the average percentages of calls originated by dual-rate terminals. Furthermore, the purpose of this invention is to provide a method for predicting the performance parameters allowing the evaluation of the capacity of an underlay/overlay cell, the capacity of an underlay/overlay cell being defined as the maximum traffic that can potentially be sustained by the overlay cell and by the underlay cell with a desired grade of service, being known the equipment and its configuration. Finally, it is the puipose of this invention to provide a computer system that also encompasses a computer program implementing the performance-analysis and dimensioning method of at least one underlay/overlay cell under the GSM standard in accordance with the invention.

Said purposes are achieved with a method and a computer system in conformity with the attached claims. The advantages obtained with this method also include the advantage of being able to establish the best configuration of several parameters useful for optimizing the network and the equipment - the number of antennas, the number of base stations and the corresponding components, the number of A-bis interface links, etc. — offering at the same time an optimal quality of service. Moreover, the indicated method may also be employed in base stations that provide both voice service and data transmissions in second or third generation networks, using for example SMS, GPRS, EDGE networks, etc. An additional advantage is that the method may be utilized in cellular telecommunication systems with characteristics and operating modes similar to those of the' GSM standard. These and additional advantages of the invention will be better understood, together with the technical characteristics, through the detailed description of a few non-limiting embodiments which follow.

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 illustrates an example of an underlay/overlay cell managed by a base station;

- Fig. 2 illustrates the general network to be analyzed or to be dimensioned for a dual-band/dual-rate cell; highlighted are the main significant parameters.

- Fig. 3 illustrates an innovational technique of reducing the states (ij,k) of an underlay/overlay cell; - Fig. 4 illustrates the innovational technique of reducing the possible states of a single-service cell, for example, of an overlay cell that assigns only FR traffic channels.

- Fig. 5 illustrates the state diagrams of a one-dimensional CTMC (Continuous Time Markov Chain) equivalent to the evolvement of the overlay cell in the event that it can assign FR and/or HR traffic channels;

- Fig. 6 illustrates a flow diagram of a software module which includes the steps in the method to analyze the performance of an underlay/overlay cell.

DETAILED DESCRIPTION OF THE INVENTION

The present performance analysis and dimensioning method can be applied in general to a portion of a telecommunication network, in particular to an underlay/overlay cell of a telecommunication network under the GSM standard such as that shown in Fig. 1, capable of sustaining the call requests of the users in a first network subportion (overlay cell) or in a second network subportion (underlay cell). The two network subportions can operate in different frequency bands or in the same frequency band, furthermore they can be configured independently of each other, in particular each one of them can utilize DHRA and enhanced preemption algorithms previously described. Fig. 2 illustrates a block diagram of the network of Fig. 1 indicating the traffic flows and the main parameters that characterize the network portion. The application of this method to the main configurations that the network portion in Figures 1 and 2 can assume will be described hereinafter.

CASE 1 - Overlay cell with only one type of traffic channel

First of all, considered is an overflow network portion in which the overlay cell, for example operating at 1800 MHz, uses only FR-type (or only HR-type) traffic channels while the underlay cell, for example operating at 900 MHz, can assign an FR- or HR-type traffic channel as a function of the cell load, based on the DHRA threshold and/or the enhanced preemption feature. In case of a dual-band/dual-rate cell, the traffic generated by the dual-band cellular phones is preferentially addressed to the overlay cell. This operating mode of the network is useful for operators because it allows frequencies to be freed-up in the primary band (for example the 900-MHz band), which is the one most interfered with and also the one having the greatest band limitations, in this way improving the radioelectrical conditions of the entire cellular network and providing optimal quality of the provided service. Furthermore, it's possible to effectively utilize the radio-frequency channels available in the secondary band (for example 1800-MHz).

The performance analysis of the overlay cell may be carried out with known methods, in particular using the well-known Erlang B form

in which:

is the cell blocking probability is the offered traffic to the cell is the number of servers of the cell

In patent no. US 6246880B1, for example, a method is described to determine the optimum number of resources of a cell in a cellular telecommunication network as the offered traffic varies; such method is based on a "GOS table" compiled using said Erlang B formula. Notice that if the overlay cell provides only FR-type traffic channels, then the number of server N_s is equal to the number of time-slots assigned to the voice service. Otherwise, if the overlay cell provides only HR-type traffic channels, then the number of server N$ is equal to twice the number of time-slots. As regards the underlay cell, in which voice calls can be sustained in FR and/or in HR, the inventor has noted however that in order to also take into account the overflow traffic component (of a non-Poissonian type) not sustained by the overlay cell, the reference theory to be applied is that of the Continuous Time Markov Chains (CTMC). Here the underlying assumption is that the incoming offered traffic of the underlay/overlay cell is Poissonian. Furthermore, the duration of the served communications, both in HR and in FR, of the incoming traffic of the overlay and underlay cells is assumed to have an exponential distribution with the parameter μ=l/ τ having the same mean value r (μ is also called the mean service rate). Nevertheless, given that the GSM network utilizes the so-called "handover" to guarantee both broad coverage and continuity for each conversation in a general regime of mobility, effectively managing the transition phase from one cell to another neighboring cell, the method which is the subject matter of this patent allows the calls originating from neighboring cells and the manner in which the network manages the handover procedure to be taken into consideration. In conformity with the method, the duration of the served communication must be understood to be the entire uninterrupted segment of time in which the communication remains within the (overlay or underlay) cell subject to the analysis. The Markov theory, in fact, operates based on the average duration for which a resource is occupied and not on the average duration of the communication. Furthermore, given that the coverage area of an overlay cell may be less than that of an underlay cell, especially if the overlay cell operates in the 1800-MHz band and the underlay cell in the 900- MHz band, and given that the users can move in any mobility regime whatsoever, it follows that in the case of an underlay/overlay cell, the mean value (

of the duration of the communications served by the overlay cell could be less than the mean value

) of the duration of the communications served by the underlay cell: it is therefore advantageous to be able to distinguish these two average values and or rather to be able

to distinguish two mean service rates from the overlay cell

and from the underlay cell (μu_L=l/τ_UL) to correctly implement the proposed method. The values of L and of can be measured or can

also be determined by analysis or statistics carried out cell by cell. To determine the incoming traffic of the overlay cell and of the underlay cell for a dual-band/dual-rate cell (cf. fig. 2), first of all the average number λ of call requests per unit time (the so-called arrival rate) incoming to the underlay/overlay cell in a predetermined time interval (for example 1 hour) is considered. Given that, because of radioelectrical problems, some users equipped with dual-band terminals might not be able to connect with the overlay cell operating at 1800 MHz, these users would be rerouted by the network directly to the underlay cell without passing through the overlay cell: this flow of dual-band cellular-phone traffic which does not connect with the overlay cell operating at 1800 MHz is still Poissonian and may be evaluated multiplying the average number of requests per unit time generated by the totality of calls originated by dual- band cellular phones present in the entire coverage area of the underlay/overlay cell (λ_DB) by the so-called "overlay failed-connection probability" (PM_A), which can be determined cell by cell based on radioelectrical- type analysis or based on statistics. An offered traffic component originating from the single-band terminals (λ_SB) and an offered traffic component originating from the dual-band terminals which did not make connection with the overlay cell operating at 1800 MHz ( and finally a non-Poissonian-type traffic

component originating by overflow from the overlay cell are therefore offered to the underlay cell operating at the primary frequency band (for example 900 MHz). The first two traffic flows can be directly summed together because, by assumption, they are independent and Poissonian; furthermore, it is also possible to determine, taking weighted averages of the corresponding values of the offered traffic, the average percentage of calls originated by dual-rate terminals for the two offered traffic components of the cells. In the general case of an underlay /overlay cell, to correctly apply the method, it is therefore necessary to first of all provide the values for λu_L and λ_0L of fig. 2 and the values for and If the values for and

P_MA are provided instead, for example in case of a dual-band/dual-rate cell, the useful values of

and of

can be determined by the equations indicated below. In particular, the average number of incoming requests of the overlay cell per unit time is equal to: whereas the average number of requests incoming

to the underlay cell per unit time (which does not include those originating by overflow from the overlay cell) is equal to:

The procedure continues-on however with the more general case of an underlay /overlay cell, assuming that the values of and λo_L and the values of and are given.

In compliance with the method, the CTMC which describes this case is represented by a set of states defined by a triplet of indexes: " in which represents the number of FR-type users served in the

underlay cell, regardless whether they are equipped with single-rate or dual-rate terminals, "/' represents the number of HR-type users served in the underlay cell, and "k" represents the number of users served in the overlay cell; having set the state (ij,k) of the underlay /overlay cell, the total number of time-slots occupied in the underlay cell is therefore equal to

while the number of time-slots occupied in the overlay cell is precisely equal to "k" if only FR-type traffic channels are supported or is equal to "k/2" if only HR-type traffic channels are supported by the overlay cell. Obviously, the set of states can be easily generalized to the case in which the more generals high-symbol-rate and the low-symbol-rate traffic channels are considered. To correctly deal with this case therefore, the following parameters are required: the characteristics of the incoming traffic of the overlay cell, in particular the average number λ_0L of incoming calls to the overlay cell per unit time in a predeteπnined time interval, the corresponding average percentage P_DROL of calls originated by terminals that support the HR-type traffic channel (dual-rate terminals) and the mean service rate of the overlay cell

the characteristics of the incoming traffic to the underlay cell, in particular the average number λ_υL of incoming calls to the underlay cell per unit time (not included among the calls incoming to the overlay cell), the corresponding average percentage PDR_UL of calls originated by terminals which support the HR traffic channel (dual-rate terminals) and the mean service rate of the underlay cell

the amount of resources of the underlay/overlay cell, in particular the number N_OL of time slots of the overlay cell assigned to voice service and the number N_UL of time slots of the underlay cell assigned to voice service; the underlay cell threshold "x," expressed as numbers of time-slots, such that if, for a new arrival, the total number n of fully occupied time-slots is greater than or equal to x, then the network attempts to preferentially allocate the new call in an HR-type traffic channel, contrariwise it is allocated in an FR-type traffic channel. This threshold "x" can assume one of the values of the interval [0, '/2,.., NUL- '/2, NuJ- If the threshold x is equal to _L, then the underlay cell also allocates only FR-type traffic

channels, even if dual-rate mobile terminals are present at its input. It is furthermore necessary to consider how the network manages the incoming calls from neighboring cells according to the "handover policy" feature:

1. if the network is configured so as not to place particular constraints on the ongoing communications originating by handover from neighboring cells, the method requires no additional parameters;

2. if, contrariwise, the network is configured so as to maintain continuity in the quality of each ongoing communication subsequent to the handover phase, then certain additional parameters must be considered to correctly apply the proposed method.

In particular, for the case in item 2, the calls originating by handover from other cells and originally allocated in an FR-type traffic channel would in any case be allocated in the destination cell, again in an FR-type channel, even if the destination cell load were to be greater than the set threshold value: 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. Similarly, the calls originally allocated in an HR-type traffic channel arriving by handover would be in any case allocated in the destination cell in an HR-type traffic channel even if the destination cell load were to be less than the set threshold value: in this case, the relative terminal would be handled by the network as if it supported only an HR-type traffic channel. In compliance with the method, if there are no constraints on the traffic originating by handover from neighboring cells, the following parameters must also be provided among the characteristics of incoming traffic to the cells:

- the dual-rate percentage which, in said time interval, would be handled by the network as if it

supported only the HR-type traffic channel. Based on this definition, P is always less than or equal

to the corresponding value of P_DRUL or PD_ROL', - the dual-rate percentage PSRI, which, in said time interval, would be handled by the network as if it supported only the FR-type traffic channel. Based on this definition, P_SRι, is always less than or equal to the corresponding value of

- the dual-rate percentage

to which the network can directly allocate an HR-type traffic channel. This percentage may be determined for each cell based on the PS_RI, values, in particular, the following relationships hold:

■

for the component of the incoming traffic to the overlay cell;

■ for the component of the incoming traffic to the underlay cell.

If the average percentage of calls originated by dual-rate terminals arriving in said predetermined time interval is not known, the probability that a call is originated by a dual-rate terminal can be assigned to P_DRO_L ^and to PD_RULJ the same reasoning also holds for the other percentages PH_R, PSR_{U >} P_DRI_I-

In conformity with the method, for each possible underlay/overlay cell state (ij,k), the following birth rates, that is transition rates from the state (i,j,k) to the state (i+lj,k), (ij+l,k) are determined:

If the network attempts to allocate the HR channels when and only when the threshold value has been exceeded, it suffices to replace the condition "n < x" with the condition " n ≤x" and the condition "x ≤n " with the condition " x < n " in Eq. 1 and Eq. 2 without altering the reasoning which follows. Obviously, the above mentioned Eq. 1 and Eq. 2 can be adapted to consider the general case of the high-symbol-rate and low-symbol-rate traffic channels, comprising the case in which 8PSK-based traffic channels are utilized by the network to sustain voice calls. It is noted that if there are no particular constraints on the handovers, then the percentages P_HR have a null value and the percentages P_DRh assume the precise value of the corresponding percentages P_DRUL and

The transition intensity

(also called "birth intensity, " "birth coefficients," "birth rates," or "transition rates") essentially represent the probability of passing from one general state (ij) to the state (ij+l) and, the probability of passing from one general state ( ) to the state (i+lj) in the underlay cell, respectively, having set the state of the overlay cell

. These therefore represent the probability of selecting an HR-type (in general a low-symbol-rate) traffic channel in the underlay cell and the probability of selecting a FR-type (in general a high-symbol-rate) traffic channel in the underlay cell, respectively, taking into account the occupation state of the resources in the overlay cell, in the presence of a new incoming service request to the underlay/overlay cell. These birth rates are already known for the case of individual cells (see patent no. PCT/IT2008/000387) and are adapted accordingly to the present case of an underlay/overlay cell.

The transition rate

from the state (UjJc) to the state ) is instead simply given by when

k is less than or equal to N_0L. The death rates for the state (i,j,k) are the transition rates from the state (ij,k) to the state (i- IJJc), given by the product of the number of communications "i" carried in FR-type channels of the departing state by the mean service rate of the underlay cell μ_UL, the transition rates from the state (ij^'Jc) to the state (ij-ljc), given by the product of the number

of communications carried in HR-type channels of the departing state by the mean service rate of the underlay cell and the transition rates from the state

to the state given by the product of the number "k" of communications carried in the overlay

cell by the mean service rate of the overlay cell μ_0L- With respect to the known art, the possibility of distinguishing the death rates as a function of the average duration of resources occupation in the overlay cell

^or in. the underlay cell is ipso facto an innovative fact.

If one wishes to also take into account the enhanced preemption feature, similar to as done in patent PCT/IT2008/000387, it is necessary to rigorously redefine a CTMC foπned by a set of states each of which having four variables ( In particular would represent the number of users with a dual-rate

terminal allocated in an FR- traffic channel in the underlay cell and "isn" would represent the number of users with a single-rate terminal allocated in an FR traffic channel in the underlay cell, whereas "j" would again be the number of HR users served in the underlay cell and "/c" would again be the number of users served in the overlay cell. In this way, however, the number of network portion states would increase considerably with a consequential slowdown in the processing phase of the method. It is however possible to adopt a solution immensely more functional that provides results with suitable precision, starting from the same CTMC previously defined with states (UjJc) where it is assumed

and considering a transition rate λ^*j for the underlay cell in addition to those of Eq. 1 and Eq. 2:

In Eq. 3, the term P_DR is the average weighting of the percentages PDRUL and P_DROL for the corresponding

and λou i.e.:

The term defines the transition intensity from a generic state of the underlay cell in which all the underlay cell resources are occupied to the immediately neighboring one in which all the resources of the underlay cell are occupied. It essentially represents the probability of selecting an HR-type (in general a low-symbol-rate) traffic channel in the underlay cell when, in the presence of a new arrival to the underlay/overlay cell, all the time-slots of the underlay cell are occupied by ongoing communications.

The term λ^*, of Eq. 3 is accordingly adapted if the network, being saturated the resources of underlay cell and in the presence of a new call generated by a single-rate terminal, allows an entire slot to be freed-up acting on two ongoing FR communications assigned to dual-rate terminals in the underlay cell (also see patent no. PCT/IT2008/000387). If the DHRA feature is not implemented in the underlay cell as a function of a threshold or if the threshold is equal to HR traffic channels may only be utilized if the enhanced

preemption feature is activated. In this case the underlay cell may be correctly analyzed considering a fictitious threshold x to be present in Eq. 1 , Eq. 2 and Eq. 3 equal to

Thus, the method can be applied and extended also in case of utilization of the enhanced preemption feature in the underlay cell, regardless whether the DHRA feature is implemented or not. If enhanced preemption is not implemented in the underlay cell, then the term is absent or has a null value in the corresponding

CTMC. To determine the performance of an underlay/overlay cell operating in the modes mentioned above, in particular to determine the performance of the underlay cell, also taking into account the overflow traffic component from the overlay cell, this method anticipates the assessment of the steady-state occupation probabilities of each individual state (i,j,k). These probabilities shall be indicated with the term In

general, foπnulating the flow balance equations for each state, the following system of

equations is obtained, with the corresponding boundary conditions: Eq. 4

If the underlay cell also assigns only FR-type traffic channels or only HR-type traffic channels, then Eq. 4 presents, in the first case, only

equations and the same number of unknowns given that, to define the state of the underlay/overlay cell, it would suffice to set j

0 for each possible value of/ and Jc of the state (ij,k), or also, in the second case, Eq. 4 presents

equations and the same number of unknowns, given that, to define the state of the underlay/overlay cell, it would suffice to set i=0 for each possible value of/ and k of the state (i,j,k). Returning to the more general case in which the underlay cell can allocate FR- and HR-type traffic channels, to determine the values of

λu_L and λ_0L useful for equations 1, 2, 3 and the system of equations 4, it is possible to operate, based on the well-known relations which associate the offered traffic of a cell

with the arrival rate λ and with the mean service rate μ, in particular, for the present case of an overlay cell and of an underlay cell: offered traffic at the overlay cell;

offered traffic at the underlay cell.

If the offered traffic of each cell is known, strictly speaking it would be necessary to provide the individual values μo_L and in order to determine the correct values of λo_L and of _ or also, contrariwise, to provide

the individual values of λ and of in order to detennine the correct values of μo_L and of

Nevertheless, whenever the mean service rate is equal in both the underlay and overlay cells

or if the average duration of the resource occupation is the same in both the underlay cell and in the

overlay cell, which is also an assumption widely accepted and used within the field of the known art, then an arbitrary value may be assigned to μ (for example 1) in order to determine the values of λ and of useful

for equations 1, 2, 3 and thus to the system of equations Eq. 4. Furthermore, Eq. 4 can be adapted to take into account, if necessary, the implementation of the enhanced preemption feature in the underlay cell (in the overlay cell instead this is not possible, given that, by the assumptions made in this case, the overlay cell can assign only FR-type channels): Eq. 5

Eq. 4 is valid for an underlay cell which utilizes the DHRA on a threshold basis and on which the enhanced preemption feature is not activated. Eq. 5 is valid for an underlay cell that can utilize both the DHRA on threshold basis and the enhanced preemption feature. In Eq. 5 the term δ(y) is the well-known indicator function, which assumes a value of 1 if y is true or a value of 0 if y is false. It is necessary to add the normalization condition to the solution for Eq. 4 and Eq. 5, considering that the steady-state occupation probabilities must sum to 1. The explicit formula of the solution of the two previous systems of equations is quite complicated. A solution however can be found in numerical form, resorting to the well-known reduction or substitution methods, or also by creating the so-called system matrix. With the help of specially prepared software and available for sale in the market (for example MATLAB or UMFPACK), it's possible to automatically, quickly and reliably solve said systems of equations, represented in matrix form, which is a sparse matrix, given that the corresponding system matrices have only a few non-zero elements in each row. The steady-state probability vector of the underlay/overlay cell is:

with dimension

and in which the individual vectors are the set of steady-state probabilities of the underlay cell, having set the user in the overlay cell.

Being known the vector that is the solution of Eq. 4 or Eq. 5, it's possible to deduce the information

needed to conduct a correct performance analysis on the underlay cell and on the underlay/overlay cell, determining the steady-state probabilities, the blocking probabilities and all the components of the carried traffic (Eq. 6). One of the advantages of the proposed method is the evaluation of the performance parameter "probability that k time-slots of an underlay cell are occupied" (expressed by Eq. 6.ε) also taking into account the (non-Poissonian) overflow traffic from the overlay cell. This probability of time-slots being occupied is a great aid in performance analysis and in dimensioning of network portions that provide also data transmission, such as GPRS or EDGE, which sharing the resources assigned to voice services, utilize such resources only when not occupied by the voice service. The determination of the values of Eq. 6. ε, is in fact indispensable for a correct estimation of the so-called "throughput" and of the "mean delay" of a data service that operates in the cell with a lower priority than the voice service. A more in-depth discussion of the case of the coexistence of data services with the voice service however lies beyond the scopes of this patent and therefore no further mention will be given thereto. Another important and innovative result of the proposed method is represented by the correct discrimination of the FR- and HR-type components of the carried traffic of the underlay cell (Eq. 6.i and Eq. 6.1) taking into account the non-Poissonian overflow traffic component originating from the overlay cell (Eq. 6.h), and also the correct discrimination of the blocking probabilities for the two types of dual-rate and single-rate terminals and for the terminals which attempt to gain access first to the overlay cell and subordinately to the underlay cell (Eq. 6.r, Eq. 6.s and Eq. 6.t) and for the terminals that attempt to directly gain access to the underlay cell without passing through the overlay cell (Eq. 6.o, Eq. 6.p and Eq. 6.q). It is noted that the blocking probability for the terminals which attempt to gain access first to the overlay cell and subordinately to the underlay cell is considerably less than the blocking probability for the terminals which attempt to gain access directly to the underlay cell without passing through the overlay cell: this is one of the main reasons why the call requests are preferentially directed to the overlay cell.

An additional innovative result is the correct evaluation of the mean blocking probability of the underlay cell, or the grade of service of the underlay cell (Eq. 6.q), and the correct assessment of the average blocking probability of the entire underlay/overlay cell, or the grade of service of the underlay/overlay cell (Eq. 6.u). Eq. 6

If the network, through the enhanced preemption feature and having saturated its resources, anticipated the switching from an FR traffic channel to an HR traffic channel for one or two ongoing communications, respectively, so as to free-up a sub-slot or a slot within the underlay cell for a new incoming communication to the underlay/overlay cell, equations 6.o/6.p/6.r/6.s would only provide a rough approximation of the real blocking probability for the dual-rate and the single-rate terminals in so far as some states contemplated in the summation are not necessarily blocking. It is however possible to adapt such definitions, so as to take them properly into account, similarly to what is done in patent PCT/IT2008/000387. Together with the cell performance reported in Eq. 6, the proposed method also provides, as additional information, the number of time-slots N_eq that would necessarily have to be assigned to the voice service in case the HR traffic channels could no longer be utilized to satisfy, at the same level of offered traffic, the same grade of service requirements and, therefore, the underlay/overlay cell capacity requirements: for this purpose, Eq. 7 which follows is solved to determine the unknown

in which the first member shows the well-known Erlang B formula whereas the second member shows the result obtained from Eq. 6.u which was determined with the proposed method and which is a function, not only of the individual values of offered traffic to the underlay /overlay cell but also of the

average service duration of the overlay cell and of the underlay cell . the percentage of calls

originated by dual-rate terminals incoming to the underlay cell (P_DRUL) and to the overlay cell (P_DR_OL), the number of time-slots assigned to the voice service in the underlay cell (NU_L) and in the overlay cell

), the configuration of resources of the underlay cell (the threshold value x, enhanced preemption, etc.). The performance analysis method subject to this patent also anticipates an innovational criteria to reduce the dimensions of the system of equations to be solved. In fact, following the precise method and solving Eq. 4 or 5 for a hypothetical underlay/overlay network portion having 49 time-slots for the overlay cell and 49 time- slots for the underlay cell, a system of equations with 50³ = 125,000 unknowns would be obtained: the system matrix of Eq. 4 or 5 could therefore contain even millions of non-null elements. Under these conditions, the processing time, which is a function of the processing capacity of the CPU performing the calculations, could be on the order of minutes, comparable to the processing times of simulative methods. It would therefore seem advisable to attempt to reduce the unknowns of the system of equations shown in Eq. 4 or 5, for example reducing the number of possible states of the three-dimensional CTMC from which it derives. First of all it is noted that to conduct the performance analysis on the underlay/overlay cell, it suffices to know:

^■ the steady-state probabilities 6. a) and the overlay cell performance, which does not

depend on the underlay cell and which can therefore be determined using the well-known Erlang B formula, given that the overlay cell evolves as a one-dimensional CTMC with one service; ■ the steady-state probabilities (i,j,Noι). for each possible value of i and of/, in so far as they take into account the fact that the overlay cell is saturated and is therefore in a condition whereat it deviates each new attempted call to underlay cell;

^■ the steady-state probabilities of the underlay cel

according to the definition in Eq. 6.b. This innovational technique of reducing the states consists in grouping, for each possible value of (ij), y+1 states, in particular from the state (ijO) to the state (ij,y). Each grouping of states (ij.O÷y) essentially represents the probability that the underlay cell is in this state (ij) when there are up to y users in the overlay cell (cf. fig. 3). Eq. 4 can then be reduced to the form: Eq. 4.b

The number of equations can be reduced with respect to those of Eq. 4 as a function of y and the parameter γ.. By solving Eq. 4.b, values are determined for

which are a valid approximation of the

solutions of Eq. 4. In a completely analogous way, a system of reduced equations can also be determined for Eq. 5. In confonnity with the method, the approximated values of can be used in Eq. 6 so as to obtain all the

infoπnation necessary to carry out the performance analysis on the underlay/overlay cell considered. Thanks to this state reduction technique, the complexity of the problem, in terms of the number of equations to be solved, can be reduced from m

to

where the parameter

can be set so as to obtain a solution of a system such as Eq. 4.b with a lower (low z) or higher (high z) level of precision. The solution of the system of Eq. 4.b requires a "slow" processing time if z is high (high precision) or a "fast" processing time if z is low (lower precision).

It's necessary at this point to determine the optimum value of γ_z. Given that the compression of the states (ij.k) of the underlay cell is also reflected in the CTMC with regard only to the sole overlay cell (cf. fig. 4), which becomes a reduced one-dimensional CTMC in which the first y+1 states degenerate into a single state (O÷y), indicating the steady-state probabilities of the reduced CTMC of the overlay cell with , the following

conditions must be verified: Eq. S

■a)

._b)

The reduced CTMC which verifies this relation is shown in fig. 4: here it is simply necessary to determine the multiplication factor

" relative to the equivalent service rate between the state ( and the state (O÷y) of

the overlay cell so that Eq. 8 is verified, while the other arrival rates and service rates remain unchanged with respect to the original CTMC, given that all the conditions imposed by Eq. 8.b must be observed. This technique applies then for any grouping of states (ij.k) of the underlay cell except for those in which the number of users in the overlay cell is equal to the number of time-slots of that same cell, i.e., the states since the assumption that the evolvement of the underlay cell is independent of the overlay cell does

not hold for them. To determine the coefficient "y_z; " which will be used for each state (ij,k) of the underlay cell as "i" and "j" vary, with "k=y+l " being fixed, a recursive formulation is used based on the corresponding reduced one-dimensional CTMC relative to the overlay cell. In particular, the procedure begins regrouping all the states of the overlay cell excluding the last one, namely from O setting

z=l (therefore y = N_OL-1). It can be proved that the following equation is obtained: Eq. 9

Eq. 9 holds only if is non-null, contrariwise there is no overflow from the overlay cell and,

obviously, the network becomes a pair of cells which do not interact with each other and which therefore can be treated separately as individual cells. Note the solution of the system of equations 4.b after the first iteration with z = 1, which represents the maximum reduction of the states and the least precise of the results; this technique may conveniently be used to gradually obtain smaller state reductions, until the exact solution is obtained. In fact, in the subsequent iteration, with z = 2, a new reduced one-dimensional CTMC is created for the overlay cell, this time regrouping all of the states of its original CTMC except the last and the second- from-the-last, i.e., from and similarly the corresponding states of the CTMC relative to the

underlay/overlay cell are regrouped from

for each (ij). It can be proved by induction that the following formula is valid for determining the parameters γ_z useful for eq 4.b for each value of z;

Eq. 9 and Eq. 10 allow all the values useful for making any reduction of the states to be determined. It is

observed that the value of the coefficien

must obligatorily equal 1 (no reduction of the states, i.e., the exact solution): recursively applying Eq. 10 from z~2 to z = N_0L this result is in fact obtained, confirming the validity of this formulation. Due to this state reduction technique, the complexity of the problem, in terms of the number of system equations to be solved, can therefore be reduced from where the parameter "z" can be set so as to more or less rapidly

obtain a solution such as Eq. 4.b, though with a lower or higher level of precision, respectively. CASE 2 - Underlay cell with only one type of traffic channel

The method may be properly adapted also to case in which the overlay cell can assign FR and/or HR traffic channels whereas only FR traffic channels (or in general, only high-symbol-rate traffic channels) can be assigned to the underlay cell. It suffices to define each state of the underlay/overlay cell setting j=0 and representing the state k of the overlay cell with a number and a number j_0L, in which represents the

number of FR users served in the overlay cell, regardless whether they are equipped with single-rate or dual- rate terminals, being the number of HR users served in the overlay cell. The state of the underlay/overlay

cell is therefore defined by:

Having set the state of the underlay/overlay cell, the overall number of occupied time-slots in

the underlay cell is therefore equal to whereas the number of occupied time-slots in the overlay cell is

equal to and λ^*, are then determined for the overlay cell in a manner similar to the

previous Eq. 1, 2, and 3 and then a system of equations similar to Eq. 4 is created which, once determined, allows the steady-state probabilities of the underlay/overlay cell to be determined for this case, and from these values, the corresponding performance parameters using Eq. 6, for example. The use of the state-reduction technique would be inappropriate in this case because it would not allow the performance to be determined with an acceptable level of precision. CASE 3 — general case

Having introduced the state-reduction technique for the case of the underlay/overlay cell in which the overlay cell assigns only one type of traffic channels, the more complex case can be treated in which both the overlay and underlay cells are configured so as to assign FR and/or HR traffic channels, again with the threshold and/or with the enhanced preemption feature. Exactly as in the case previously dealt with wherein the overlay cell could not assign two type of traffic channels, there is a certain level of incoming traffic of each of the two overlay and underlay cells characterized by the corresponding percentage of dual-rate terminals Again it is emphasized that to correctly perform the analysis, the overflow

traffic from the overlay cell cannot be directly summed with the incoming traffic going directly to the underlay cell. It can be intuitively understood that handling the dimensioning problem or the performance analysis problem with a rigorous treatise would involve a CTMC having at four dimensions that inevitably would lengthen the processing time to solve a system of equations by a considerable amount.

First of all, the performance analysis of the overlay cell can be conducted, independently of the underlay cell, using the known method described in patent no. PCT/IT2008/000387: this is possible if the overlay cell operates independently of the underlay cell. In this way, the number of equations necessary to determine the performance parameters of the overlay cell is known and is equal to

whereas to determine the performance parameters of the underlay cell, a compromise solution can be adopted, attempting to reduce the number of possible underlay/overlay cell states: The solution obtained with this stratagem is close to the exact solution, which can be evaluated with the proposed method but in most cases this could require processing times comparable to those of methods based on simulations. It is in fact possible in this case to evaluate the performance of the underlay cell with satisfactory precision also taking into account the contribution of the non-Poissonian overflow traffic originating from the overlay cell. In conformity with the method, first, a number of equivalent servers of the overlay cell, which in general is a real quantity, is determined (cf. fig. 5) by Eq. 11: Eq. 11

in which the first member is the well-known Erlang B formula generalized to the case of a non-integer (real) number of servers while the second member is the average blocking probability of the overlay cell. In fact, once the perfonnance of the overlay cell is known - i.e., the steady-state probabilities, the blocking probability and the carried traffic components - the generic two-dimensional CTMC relative to the overlay cell may be converted, in compliance with the proposed method, into a one-dimensional queue equivalent to a non-integer number of servers with a single service (cf. fig. 5). After having carried out the performance analysis of the overlay cell using the optimal method, the unknown, i.e., the number of equivalent single- service servers N of the overlay cell is obtained from Eq. 11 given that the second member of Eq. 11 is

known and can be obtained from the "perfonnance analysis" method of patent PCT/IT2008/000387, assuming that the offered traffic of the overlay cell, the percentage P_DR

O_L of incoming dual-rate terminals of the overlay cell, the number of time-slots N_0L assigned to the voice service in the overlay cell, and its configuration (threshold value X_OL, enhanced preemption used or not used, etc.) are known. In conformity with the method, the two-dimensional CTMC relative to the evolvement of the overlay cell is equivalent to a new one-dimensional CTMC with a non-integer number servers which evolve as in Fig. 5, in which the following terms are used:

The term represents the integer portion of the number of equivalent servers N_eq0L of the overlay cell. The problem of analyzing the performance of the underlay cell is thus equivalent to that of determining the steady-state probabilities of a three-dimensional CTMC, of which a thorough description was given, which can also be handled through the state-reduction technique, generalized to the case of overlay cells with a real number of servers. With this innovational stratagem, the "equivalent" CTMC which describes the evolvement of the underlay/overlay cell is again based on a certain number of states defined by a triplet of indices (i, j, k), in which "k" represents the number of equivalent servers occupied in the overlay cell, this number k being less than or equal to regardless of the type of FR or HR traffic channel with which they are served, "i"

and "j" are again the FR and HR users of the underlay cell, respectively. To construct the equivalent three- dimensional CTMC it is necessary to redefine the arrival rates for the individual states of the CTMC, based on the new variable

i.e., the integer portion of the number of equivalent and single-service servers of the overlay cell, and as a function Of _L (Eq. 12). In conformity with the method, therefore the parameters

and are redefined with respect to the general triangular plane of the CTMC, which represents the evolvement of the underlay/overlay cell when both of the cells can assign FR-type and HR-type traffic channels and in which the influence of the overlay cell on the underlay cell has been reduced to "one- dimension."

Let N_eq-o_L be the number of equivalent servers of the overlay cell their integer portion, the

number of time-slots of the underlay cell the number of occupied resources in the underlay cell,

I_0L the arrival rate of the overlay cell, P

the average percentage of terminals, relative to the offered traffic of the overlay cell, which support the HR encoding, "k" the number of users served in the overlay cell without distinguishing between FR and

the arrival rate of the underlay cell, "x" the threshold of the DHRA for the underlay cell,

the average percentage of calls originated by terminals, relative to the offered traffic of the underlay cell, which support the HR encoding. It's assumed for simplicity that there are no particular constraints for the traffic component originating by handover from neighboring cells (PH_R ⁼0 and both for the incoming traffic of the overlay cell and for that incoming traffic of the underlay cell.

In compliance with the method, for each state (i,j,k) the following are defined:

k =

k

Obviously, Eq. 13 and 14 can be adapted accordingly also to take into account any constraints in the handover policy similarly to what was done for equations 1 and 2. Furthermore, they can be adapted for the general case of high-symbol-rate or low-symbol-rate traffic channels instead the FR and HR, respectively. Continuing as in Eq. 4, the flow-balance equations of the equivalent CTMC of the underlay/overlay cell are determined: Eq. 15

In this case also it is possible to take into account both the presence of the enhanced pre-emption feature in the underlay cell (whereas the overlay cell, at this point in the process, has already been analyzed completely and exactly using the method of patent no. PCT/IT2008/000387) and the handover policy. The corrections to be made are identical to those of the case of the underlay/overlay cell in which the overlay cell only cannot assign two types of traffic channels. In compliance with the method, all the values for

are determined from both Eq. 4 and from Eq. 15, solving the corresponding system of equations. It is thus possible to obtain information regarding the performance parameters of the underlay cell and of the underlay/overlay cell, based on the definitions reported in Eq. 6. In detail, the proposed method entails the following steps:

^■ determining the performance of the overlay cell with known methods (PCT/IT2008/000387) when the overlay cell can be treated as a single cell; ■ determining the exact steady-state probabilities of the overlay cell o jo and/or πoι( )\ these

also can be determined by known methods (PCT/IT2008/000387);

^■ if necessary, reducing the number of possible states of the underlay/overlay cell, representing the CTMC of the overlay cell as the equivalent CTMC with a real number of single-service servers;

^■ determining the steady-state probabilities of the underlay/overlay cell, including the steady-state probabilities of the underlay cell solving Eq. 15 for example;

• determining the performance of the underlay/overlay cell according to the definitions in Eq. 6. Due to the fact that the original problem has been converted from a four-dimensional CTMC, to an equivalent three-dimensional CTMC, though with a non-integer number of equivalent servers of the ove

rlay cell, a state- reduction technique similar to those described previously by Eq. 9 and by Eq. 10 can easily toe used. In this way, the complexity of the problem, in terms of number of system equations to be solved can be further reduced from of Eq. 15 to where the parameter

y " may be set so as to determine π values approximated by solving the following system:

Eq. 15.b

In fact, exactly as in the case of integer quantity of servers, the state-reduction technique of a CTMC having a real number of servers consists in grouping the network-portion states from (ij^'O) to (ij, y+1) for each (i,j). The states refer to the decimal part of the real number of equivalent servers of the overlay cell (i,j,ΔN_{eq m},0L) and those relative to the integer part ( ) of the number of equivalent servers of the overlay cell cannot

be grouped because they are different from all the others and also they are the only ones which take into account the overflow traffic originating from the overlay cell. As in the case of Eq. 4 and Eq. 4.b, a new system of equations is obtained, shown in Eq. 15.b, which presents a number of unknowns reduced with respect to the system of Eq. 15. By solving Eq. 15.b, the values are determined for which are a valid

approximation of the solutions of Eq. 15. The approximated values can be used again in Eq. 6 so as

to obtain all the information necessary to conduct the performance analysis on the underlay cell taking into account the influence of the overlay cell. It is necessary to determine the optimum value of γ. for Eq. 15.b. The compression of the states is reflected in this case in the equivalent one-dimensional CTMC relative to the overlay cell, in which the first y+1 states degenerate into a single state (O÷y). Indicating with π^* _0L(k) the steady-state probabilities of said reduced one-dimensional CTMC, the following conditions must be verified:

For this reduced CTMC, it's simply suffices to determine the coefficient y. of the equivalent service rate between the state (y+1) and the state (O÷y) so that the equation system 16 is verified. This technique applies for any grouping of the states of the CTMC with the exclusion of those, relative to the decimal part of the number of equivalent servers for the overlay cell, and the second-from-the-last, relative to its integer part. Continuing exactly as in Eq. 9 and Eq. 10, defining it can be proved that:

Eq. 17

As can be intuitively understood, a recursive formulation of the γ. values of Eq. 15.b is possible:

which together with Eq. 17 provides all the necessary information for determining the coefficients y_: useful for making any reduction of the states, from It is thus possible to determine the performance

of an underlay/overlay cell with a degree of precision that can be controlled through the parameter "z" of the state-reduction technique. Based on Eq. 6, it is therefore possible to determine all the information necessary to carry out the performance analysis of a underlay/overlay cell under the various operating conditions and configurations mentioned above. It's necessaiy to notice first of all that the procedure described up to now entails the solution of Eq. 4 or Eq. 4.b in the case of an underlay/overlay cell in which the overlay can assign only one type of traffic channels and the underlay can assign two types (FR and/or HR, for example) of traffic channels, whereas it entails the solving of Eq. 15 or Eq. 15.b in the case of an underlay/overlay cell in which both the overlay cell and the underlay cell can assign two types (FR and/or HR, for example) of traffic channels. The procedure (cf. fig. 6) requires that the following data being known:

- the characteristics of the incoming traffic to the overlay cell (2 U OL) and to the underlay cell (211UL), in particular:

^■ the arrival rate at the overlay cell

the arrival rate at the underlay cell λ_UL (which do not include the overflow component from the overlay cell), the average duration of occupation for a channel of the overlay cell τ_0L and the average duration of occupation for a channel of the underlay cell τ_UL. If a single τ value can be assumed for the average duration of occupation for a channel, both for the overlay cell and for the underlay cell, it suffices to know the offered traffic of the overlay cell and the offered traffic of the underlay cell '. the procedure ensures that an arbitrary

value is assigned to τ in order to determine the useful values of and of

^■ the average percentage of calls originated by dual-rate terminals P_DROL relative to the arrival rate of the overlay cell λo_L and the average percentage of calls originated by dual-rate terminals P_DRU_L relative to the arrival rate of the underlay cell λ_UL, or also, instead of such percentages, the probability that a terminal associated with the arrival rate λo_L of the overlay cell is a dual-rate terminal and the probability that a terminal associated with the arrival rate λu_L of the underlay cell is a dual-rate terminal;

^■ Optionally, if special constraints are set for traffic components originating by handover from neighboring cells, the percentages PHR, PS_RH or P_DRh are also required both for the arrival rate of the overlay cell λoi_ and for the arrival rate of the underlay cell λ_UL;

- An amount of resources of the overlay cell (212OL) and of the underlay cell (212UL), for example, the number of time-slots assigned to voice service to the overlay cell (N_OL) and the number of time-slots assigned to voice service to the underlay cell (NUL);

- the configuration (CONF) of the overlay cell and of the underlay cell, in particular:

■ the threshold value (XO_L) above which the network attempts to allocate the calls on Half-Rate-type traffic channels in the overlay cell (213OL);

■ the threshold value (X_1JL) above which the network attempts to allocate the calls on Half-Rate-type traffic channels in the underlay cell(213UL);

■ optionally, the activation or non-activation of the enhanced preemption feature in the overlay cell (214OL) and in the underlay cell (214UL); ■ optionally, the handover policy in the overlay cell (215OL) and in the underlay cell (215UL); in particular, if a continuity constraint is set for the FR-type traffic channels, the procedure also requires, as additional characteristics of the incoming traffic of the cells, the percentages P_SRh or directly the percentages PDRh, both for the incoming traffic of the overlay cell and for the incoming traffic of the underlay cell. If the continuity constraint is also set for the HR-type traffic channels, then the procedure also requires, as additional characteristics of the incoming traffic of the cells, the percentages PHR both for the incoming traffic of the overlay cell and for the incoming traffic of the underlay cell.

- The desired precision level of the performance parameters determined by the method (219). The method, for example, could anticipate the selection of one of the following four options: ■ Exact solution. Selecting this option, the performance parameters are determined solving the system of equations (such as Eq. 4) which allows the exact steady-state probabilities of the underlay/overlay cell and thus the exact values of the performance parameters of Eq. 6 to be determined;

^■ High-precision solution. Selecting this option, the performance parameters are determined solving the system of equations (such as Eq. 4.b or Eq. 15.b) which allows the approximated values of the steady-state probabilities of the underlay/overlay cell to be determined so that the performance parameters determined by Eq. 6 are affected by an error of less than 1% (1% tolerance). A maximum processing time can also be set (for example 60 sec.) so as to stop the procedure when the processing times of the method exceed said maximum time;

^■ Acceptable-precision solution. Selecting this option, the performance parameters are determined solving the system of equations (such as Eq. 4.b or Eq. 5.b) which requires processing times lower than the previous two options and that allows the approximated values of the steady-state probabilities of the underlay/overlay cell to be determined so that the performance values determined by Eq. 6 are affected by an error of less than 10% (10% tolerance). A maximum processing time can also be set (for example 60 sec.) so as to stop the procedure when the processing times of the method exceeds this maximum time; • Moderate-precision solution. Selecting this option, the perfoπnance parameters are determined solving a system of equations (such as Eq. 4.b or Eq. 15.b) setting the parameter "z" of the state- reduction technique to the minimum value (z=l) so that the processing times are minimal. In this way, without any particular guarantees regarding precision, approximated values of the steady-state probabilities of the underlay/overlay cell and, accordingly, the approximated values of the underlay/overlay cell performance parameters are determined from Eq. 6;

The possibility of providing two different values of the average duration of resource occupation in the underlay cell and in the overlay cell is an especially advantageous aspect because it is the only way to take into account the fact that the coverage area of the overlay cell and of the underlay cell are different, in particular one is contained within the other. In fact, the users served on the overlay cell, being mobile, are more likely to leave the communication channels of the overlay cell as compared to the users served on a communication channel of the underlay cell, holding the average conversation duration constant. Another especially innovational aspect with respect to the known art consists in the possibility of selecting the desired precision level of the performance parameters for the underlay/overlay cell. The other input data are instead already known from patent no. PCT/IT2008/000387 which are utilized advantageously in the proposed method for an underlay/overlay cell. The procedure described up to now is generically indicated hereafter as the "performance analysis" method. A few possible preferred embodiments of the computer system which allows the method described in this patent to be actually used are hereafter described. BEST WAY FOR CARRYING OUT THE INVENTION A computer system capable of actually implementing the method described in this patent includes an electronic computer equipped with a CPU, RAM memory units, hard disk units, an operating system, a keyboard, a monitor, etc. Said computer system is capable of allowing the dimensioning and the performance analysis of at least one telecommunication network portion, in particular of an underlay/overlay cell or of a number of time-slots of an underlay/overlay cell, based on modules or software procedures stored and processed by said electronic computer to implement the method according to the invention described in this document. A preferred embodiment of a software application (software module B_UL) is shown in fig. 6 which implements the steps of the method for the performance analysis of an underlay/overlay cell according to the invention. Block 210 of module BUL ensures that the input data previously described is requested. In particular, the blocks from 211 to 215 refer to underlay/overlay cell parameters while block 219 has parameters relative to the proposed method, in particular the desired precision level (for example one of the four possible options previously described) and the maximum processing time of the method (for example 60 sec). Block 220, of known type, ensures that the perfoπnance of the overlay cell is determined based on the input data provided, in particular the performance is determined using the Erlang B formula if the overlay assigns only one type of channels or using module B_L of patent no. PCT/IT2008/000387 . Block 230, of unknown type, ensures that a value is assigned to the parameter "z" of the state-reduction technique based on the desired precision level. In particular: if the "exact solution" option is selected, the maximum value is assigned to z (i.e., no reduction of the states); if the "high precision solution" option is selected, this means that the tolerated error must be less than 1 % and a first value is assigned to z, for example 1 or 2; if the "satisfactory-precision solution" option is selected, this means that the tolerated error must be less than 10% and a first value is assigned to z, for example 1 or 2; if the "moderate-precision solution" option is selected, a minimum value is assigned to z, 1 in particular. Block 230 also ensures that the value of the parameterγ is determined for each possible value of z. Block 240, of unknown type, ensures the possible values ofλi, λ₂ and if necessary λ^*; are determined based on the values of

U P etc. It also

ensures that the corresponding system matrix and the vector of the known teπns λ

are constructed based on the current value of z and Block 250, of known type, ensures that the system of

equations just created is solved and that the steady-state probabilities of the underlay/overlay cell are determined. The algebraic library UMFPACK, for example, can be used for said block 250. Block 260, of known type, ensures that the performance parameters of the underlay/overlay cell are determined based on Eq. 6 and that the number of equivalent time-slots is determined, for example, from Eq. 7 or from Eq. 11. Block 270, of unknown type, ensures that a verification is made regarding whether the obtained solution has an error less than the tolerated error. For example, it can check whether the difference between the grade of service set in the current iteration and the grade of service set in the previous iteration is less than the maximum error tolerated, in this case the procedure continues on to block 280, contrariwise the value of z is increased and the produced continues on with a new iteration. Block 270 could however pass directly to block 280 if the processing time exceeds the maximum value previously set in the initial phase (219), even if the performance parameters determined with the current value of z do not have the desired level of precision. If the "exact solution" option or the "moderate solution" option is selected, block 270 does not perform any verification or iteration and passes directly to block 280. Block 280, of known type, ensures that the output data, i.e., the performance parameters calculated by block 220 and by block 260, are communicated to the procedure that called up module BU_L or directly to a graphic interface configured to display said data.

Module can furthermore be used iteratively to obtain planning information both for an underlay/overlay cell not yet installed and for an existing underlay/overlay cell, or also to adapt an existing individual cell so that it can operate as an underlay/overlay cell. Based on module it is therefore possible to carry out:

^■ the dimensioning of the resources of an underlay/overlay cell. With this mode, first of all the number of time-slots are determined and from these, being generally known, within the scope of the GSM standard, any rules allowing signaling channels to be associated with traffic channels, the number of GSM carriers both of the underlay cell and of the overlay cell. Having been determined the number of carriers, it's possible to determine the overall occupied frequency bandwidth and the equipment best suited for the underlay/overlay cell " the choice of the best threshold value. This mode could operate together with the previous mode in order to determine the best configuration of the underlay/overlay cell.

■ the prediction of the performance parameters as the configuration of the relevant parameters of the network portion vary (for ex., the need or lack thereof to utilize the enhanced preemption feature, the best handover policy for each cell, etc.). Using this mode, it is possible, for example, to determine an estimate of the maximum traffic that can be carried by the underlay/overlay cell, i.e., to evaluate the capacity of said underlay/overlay cell: in particular, an estimate is made of the maximum traffic that can be carried by the underlay/overlay cell at a desired grade of service, being known the amount of resources, the configuration and the percentage of incoming dual-rate terminals of the cell.

^■ the estimate of the offered traffic and of the grade of service of the underlay/overlay cell, being known the amount of resources, the configuration and the traffic actually carried by the cell (the so- called sustained traffic) as well as the estimate of the percentages of incoming dual-rate terminals and incoming single-rate terminals of the cell.

The determination of this planning information may also be made with the aid of a software application. In general, a method of convergence towards the best solution is used according to methods well-known in the literature, for example the dichotomy method or the Newton-Rapson method. These methods, being well- known, will not be described in this document, also because, if applied correctly, they influence only the processing time, and not however the correctness of the final result. The applications of said module B_UL are therefore almost identical to those of the module B_L described in patent no. PCT/IT2008/000387. Refer to this patent for additional details and demonstrational embodiments. The module BUL also includes in fact the module B_L. It suffices, for example, to set the number of time-slots of the overlay cell to 0 and to consider the underlay cell as if it were a regular cell: in this case, the same results are obtained with both module B_UL and module BL. The method may be conveniently applied to an arbitrary number of underlay/overlay cells and regular cells; this number can also be on the order of thousands or multiples often thousands. For the sake of accelerating the processing times of the method, it's possible to print or to memorize, in tables, the values relative to the input data and to the output data of a software application that implements the described method. These tables, whether in digital format or printed out, can be utilized by the interpolation of such tabulated values in order to more rapidly carry out the performance analysis or the dimensioning of an underlay/overlay cell, with the advantage of not being forced to utilize the software nor to follow the entire processing step otherwise required by the software. 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. Moreover, all the details may be substituted by technically equivalent elements.

Claims

1. A method for analyzing the performance of at least one portion of a telecommunication system, including a first and a second network subportion capable of allocating communication-channel requests by mobile terminals, said first network subportion being able to sustain the corresponding communications in high and/or low-symbol-rate traffic channels, said second network subportion being able to sustain the corresponding communications in high and/or low-symbol-rate traffic channels, said method including the steps of: providing a first average number (λ_0L) of requests per unit time to said first network subportion, in a predetermined time interval; providing an average service duration of said communications in said first network subportion;

providing an amount and a resource configuration of said first network subportion; providing a first average percentage (PDR_OL) of calls originated by dual-rate mobile terminals, relative to said first average number (λ_0L.) of requests^ capable of supporting both high and low- symbol-rate traffic channels; determining the perfoπnance of said first network subportion based on said amount and on said configuration of resources, on said average number λou on said average duration and on said

first average percentage PDROL; characterized by the fact of comprising the further steps of: - providing a second average number (λ_UL) of requests per unit time to said second network subportion, in said predetermined time interval, said requests to said second network subportion not being included in said requests to said first network subportion; providing an average service duration of said communications in said second network

subportion; - providing an amount and a resource configuration of said second network subportion; providing a second average percentage of calls originated by dual-rate mobile terminals, relative to said second average number of requests, capable of supporting both high and low-

symbol-rate traffic channels; defining each state of said network portion by means of the number "k" of communications sustained in said first network subportion, the number "i" of communications sustained in high-symbol-rate communication channels and the number "j" of communications sustained in low-symbol-rate communication channels in said second network subportion; determining, for each state , the probability of selecting, in case of a new request, a low or also

a high-symbol-rate communication channel within said second network subportion

or also a high or a low-symbol-rate traffic channel within said first network subportion said probability of selection being based on said average numbers of requests _> on said amount and on said

resource configurations of said first network subportion, on said amount and said resource configurations of said second network subportion, on said average percentages of dual-rate terminals; determining, for each state a probability of said network portion being in said state, based

on said probability of selection, on said numbers "i," "j," and "k" and on said average service durations

determining the performance of said second network subportion and of said network portion based on the set of probabilities of said network portion being in each state

2. A method according to claim 1, characterized by the fact of comprising a step of reducing the number of the possible states (i,j,k) of said network portion which consists in comprising one or more of the further steps of:

- providing a desired precision level of performance determined by the method;

- providing a maximum processing time of the method;

- determining a number N_eqo_L of equivalent communication channels of said first network subportion;

- defining each of the possible states of said second network subportion with said number "i" and said number "j" of communications in said second network subportion and attributing, to said number

"k," a number of equivalent communication channels of said first network subportion, said attributed number "k" being less than or equal to said number "N_eqo_L;"

- grouping each of said states of said second network subportion starting from state (ijO) until

the state (ij,y), "y" being a number of states to be grouped; — ascertaining a number "y" of states to be grouped which allows said set of probabilities in said second network subportion, or said performance of said second network subportion or of said network portion to be determined, with said desired precision level, within said maximum processing time if necessary; said performance determination steps being also based on said desired precision level and on said maximum processing time.

3. A method according to claims 1 or 2, characterized by the fact that said amount of resources of a network subportion comprises a number (N_0L or NUL) of low- or high-symbol-rate communication channels assigned to a service requested by the users.

4. A method according to any one of claims from 1 to 3, characterized by the fact that said configuration of resources of a network subportion comprises the settings of a threshold value such a way that if

the occupied level of said resources is greater than or equal to said threshold value, a new request is preferentially allocated on a low-symbol-rate communication channel.

5. A method according to any one of the aforesaid claims, characterized by the fact of providing a first value of traffic offered for said first network subportion

and a second value of traffic offered for said second network subportion A instead of the individual values of said average numbers of requests

(λ_0L and λu_L) and of said average service durations

6. A method according to any one of the aforesaid claims, characterized by the feet that said configuration of resources of a network subportion comprises the possibility of imposing the transition from a high-symbol- rate communication channel to a low-symbol-rate communication channel for at least one ongoing communication in said network subportion when, in the presence of a new call request, said network subportion is congested.

7. A method according to claim 6, characterized by the feet of attributing to said number "i" of communications sustained in high-symbol-rate communication channels in said second network subportion, for each of the states of said network portion, the number and the number being the number

of communications sustained in high-symbol-rate communication channels with said dual-rate terminals and "i_SR" being the number of communications sustained in bigh-symbol-rate communication channels with single- rate terminals that do not support the low-symbol-rate traffic channel.

8. A method according to claim 7, characterized by the fact of attributing to said number "i" of communications sustained in high-symbol-rate communication channels in said second network subportion, for each of the states of said network portion, the value

9. A method according to any one or more of claims 6 or 7 or 8, characterized by the feet of comprising the additional step of determining, for each state of said network portion, a third probability of selecting a

low or high-symbol-rate communication channel in said first or in said second network subportion when said first or said second network subportion is congested, in case of a new incoming request, said steady-state probability being also based on said third probability of selection

10. A method according to any one of the aforesaid claims, characterized by the fact that said configuration of resources comprises the possibility of imposing the preservation of the type of communication channel for the component of said average number of requests which, subsequent to handover procedures, originate from neighbored-network portions.

11. A method according to any one of the aforesaid claims, characterized by the feet of providing several average terminal percentages having the capability of supporting the high and/or low-

symbol-rate communication channels in said predetermined time interval based on said configurations of resources, said first, second and third probabilities of selection (

) being also based on said percentages

12. A method according to any one of the aforesaid claims, characterized by the feet that said configuration of resources comprises furthermore:

- the possibility of preferentially allocating a communication channel in said first network subportion rather than in said second network subportion;

- the possibility of configuring said network portion as an underlay/overlay cell of a cellular telecommunication system and of configuring said first network subportion as an overlay cell (OL) and said second network subportion as an underlay cell (UL);

- the possibility that said first network subportion may operate on a primary or on a secondary frequency band and that said second network subportion may operate on a primary or on a secondary frequency band; - the possibility of allocating a communication channel in one of said first or of said second network subportion operating on a secondary frequency band only to users who are equipped with terminals capable of supporting said secondary frequency band (dual-band terminals), whereas any terminal is capable of supporting at least the primary frequency band.

13. A method according to claim 12 characterized by the fact of providing a percentage (P_DRDB) of dual-band terminals capable of supporting both frequency bands, primary and secondary, and of providing a probability

P_MA that said dual-band terminals does not make connection with the network subportion operating on the secondary frequency band.

14. A method according to any one of the aforesaid claims, characterized by the fact that said performance comprises one or more of the following parameters: - a grade of service of said resources of said first or of said second network subportion of the cellular telecommunication system; a grade of service of said resources of said network portion of the cellular telecommunication system

(GOS); the overall carried traffic and/or the overall carried traffic in low-symbol-rate communication channels and/or the overall carried traffic in high-symbol-rate communication channels, by said network portion of the telecommunication system, by said resources of said first network subportion and by said resources of said second network subportion of the telecommunication system; the offered traffic component not carried by said resources of said first network subportion (overflow traffic) or of said second network subportion of the telecommunication system; - the set of probabilities of occupying a certain number of communication channels of said resources of said first or of said second network subportion of the telecommunication system; the blocking probability for a service request to said second network subportion originating from dual-rate terminals; the blocking probability for a service request to said second network subportion originating from non-dual-rate (single-rate) terminals; the blocking probability for said dual-rate terminals in case of a service request forwarded to said first network subportion and, subordinately, to said second network subportion; the blocking probability for said single-rate terminals in case of a service request forwarded to said first network subportion and, subordinately, to said second network subportion.

15. A method according to any one or more of the aforesaid claims, characterized by the fact that said telecommunication system comprises a cellular telecommunication system in which the communication channels are formatted within time-slots in compliance with the TDMA or FDMA/TDMA technology.

16. A method according to one or more of the aforesaid claims, characterized by the fact that said network portion of the telecommunication system comprises an underlay/overlay cell of a cellular telecommunication system.

17. A method according to one or more of the aforesaid claims, characterized by the fact that said resources comprise a number of time-slots, a number of carriers, a fully-used radiofrequency bandwidth, a number of antennas, a number of transceivers, a set of A-bis interface links and a set of hardware apparatus and software with which said underlay cell and/or said overlay cell is equipped.

18. A method according to one or more of the aforesaid claims, characterized by the fact that said communication channels are also able to support the voice conversations vocal (Le., telephone calls) and that said service request by the users comprises telephony.

19. A method according to one or more of the aforesaid claims, characterized by the fact that:

- said high-symbol-rate communication channels comprise the full-rate traffic channels and said low-symbol-rate communication channels comprise the half-rate traffic channels; said high-symbol-rate communication channels comprise the half-rate-type traffic channels and said low-symbol-rate communication channels comprise the 8PSK-based traffic channels.

20. A computer system comprising a computer programmed to use the method according to any one or more of the aforesaid claims.

21. A software application comprising portions of software procedures (Bu₁,) which, when loaded or run in said computer system, implement the method according to any one or more of the aforesaid claims.

22. The set of values relative to the input data and to the output data of a software application according to claim 21, said set of values being in tabular format, the performance analysis or the dimensioning of the resources of said network portion of the telecommunication system being made by interpolation of the tabulated values.

23. 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 claims.