Modelling of the access part of a multiservice mobile network with service priorities
 Slawomir Hanczewski^{1}Email author,
 Maciej Stasiak^{1} and
 Piotr Zwierzykowski^{1}
https://doi.org/10.1186/s1363801504204
© Hanczewski et al. 2015
Received: 13 January 2015
Accepted: 1 July 2015
Published: 18 July 2015
Abstract
This paper presents a methodology for the modelling and optimization of multiservice radio access for universal mobile telecommunications system (UMTS) networks. The paper provides a description of the basis for modelling of a tandem pair: a wideband code division multiple access (WCDMA) interface and a Iub interface. The models involved in the study take into consideration a possibility of setting priorities to a number of selected traffic classes. Particular attention is given to the development of simple computational algorithms that would make it possible to determine the blocking probability for call streams with different priorities. The results of the analytical calculations are then compared with the results of simulation experiments, which confirms the high accuracy of the proposed analytical solutions.
Keywords
1 Introduction
Modern mobile networks service mixtures of different traffic streams with different quality requirements. Both the traffic that requires appropriate quality parameters (e.g., VoIP traffic, speech) and the traffic with lower requirements (e.g., www traffic) are serviced in shared network resources. Given that there are different requirements that impose different quality demands for services and users of the network, manufacturers of network devices have started to introduce appropriate functions and traffic control mechanisms to adjust their products to meet these challenges.
Mobile network users are more and more willing to pay whatever it costs for access to links that offer a higher sustainable data throughput. From a network operator’s perspective, the introduction of priorities for some selected groups of users is then very advantageous and profitable. A differentiation in the access to the network is required to be not only at the user level but also results from specific quality requirements of some services. This entails, in turn, the need for the introduction of appropriate quality of service (QoS) mechanisms in network devices. QoS mechanisms in the universal mobile telecommunications system (UMTS) network are available, for example, in the radio interface that is responsible for the highest degree of limitation imposed on network capacity. Such mechanisms are also available in the Iub interface, located between NodeB and radio network controller (RNC) [1–4]. For the purpose 3G network analysis, dimensioning, and optimization, it is then necessary to develop appropriate analytical models of these interfaces.
The literature of the subject abounds in the presentations of models of interfaces of mobile systems that give priority to a selected group of services [5–8] or to users [9, 10]. These models are essentially based on the model of the multiservice fullavailability group [11, 12]. In this paper, however, to model the wideband code division multiple access (WCDMA) interface, a model of a multiservice Erlang’s ideal grading is used [13, 14]. In addition, the paper proposes a model of the nonfullavailability group with priorities based on the approach that has been earlier adopted for the analysis of priorities in the fullavailability group [5, 6].
The nonfullavailability group is the socalled statedependent system [14, 15]. This dependence results from the particular structure of the system in which calls arriving at the input have access to a limited amount of resources, substantially lower than the total capacity of the system. Until the 1980s, nonfullavailability groups with singleservice traffic were used in electromechanical switching nodes of telecommunications networks. With the advent of electronic nodes, groups of this type ceased to be used in their direct form, though they were, and still are, used in analytical models of more complex systems, such as, for example, single and multiservice switching networks [16–18], network systems with reservation [19, 20], systems with traffic overflow [21–23], video on demand (VoD) systems [24, 25], or radio and Iub interfaces of the UMTS system [26–28]. One of the most extensive elaborations on nonfullavailability groups is provided in the [29]. This paper presents all of the most important methods of modelling singleservice nonfullavailability groups. Among different types of the nonfullavailability group, particular attention should be given to Erlang’s ideal grading, the structure of which and the first singleservice analytical model was presented by Erlang [30]. The first model of the ideal grading with multiservice traffic and identical value of the availability parameter for all classes of calls serviced by the group is proposed in [13]. Stasiak and Hanczewski [31] discuss a model of the group with multiservice traffic and a variable value of the availability parameter. This model is then expanded to include the possibility of performing calculations for noninteger vales of availability [31]. The most extensive description of multiservice nonfullavailability groups is provided in [14] in which different models of multiservice ideal nonfullavailability groups, defined for different types of call streams and different structures of groups, are presented.
The idea of the nonfullavailability group makes it possible to take into consideration the influence of interference from other cells in a given cell, since an increase in interference directly leads to a decrease in the availability of a given group. The relationship between the changes in availability and changes in the level of interference is discussed in [28, 32].
So far, the literature on the subject has been addressing exclusively models of single interfaces with priorities. Systems in which priorities have been simultaneously introduced to two interfaces, e.g., the radio interface and the Iub interface, have not been analyzed yet. This paper proposes a model of a system with priorities that enables the analysis of such systems to be performed. The mutual dependence between traffic serviced in both interfaces is taken into account by the application of the fixedpoint methodology [33, 34] that makes it possible to analyze the call an analysis of the call service in a number of systems simultaneously.
The paper is an overview of the subject in ten sections. Section 2 presents the architecture of the access part of the UMTS network. Sections 3 and 4 provide a description of the traffic representation in the Iub and the WCDMA interfaces. Sections 5 and 6 discuss analytical models of the Iub and the WCDMA interface, while Section 7 includes a description of a model of the system with priorities. Section 8 presents a model for setting up connections in a system that consists of a cascade of WCDMA and Iub interfaces. The following section, Section 9, provides an example illustrating the available possibilities of the application of the model in analyzing the UMTS system. Finally, the conclusions and considerations which emerge from the study and the results of the experiments are provided in the last section of the paper.
2 UMTS network architecture
A number of sectors can be run within one base station (usually from 3 to 6), whereas the number of cells that can operate within one sector can be as many as the carriers of a given operator (e.g., R99, high speed packet access (HSPA) 1carrier, HSPA dualcarrier, and UMTS900). Hence, if we assume that we consider only one carrier, then the number of cells added to a given base station ranges from 3 to 6. The number of cells that can be added to a single RNC actually depends on the producer and the type of license held by the operator. In the main, no more than 5000 cells can be added to one RNC, which means that one can get from about 800 to about 1600 base stations for three or six sectors, respectively.
It should be stressed, however, that both the number of sectors in a base station and the number of cells added to RNC can substantially differ depending on the solutions preferred by given producers of network devices for UMTS. In the UMTS network, priorities can be assigned to particular services. Priorities define the sequence of resource allocation. This sequence may result, in the case of services with lower priority, in a decrease in the amount of resources or may even enforce a termination of a service (in an instance when there are no sufficient resources to be allocated to services with higher priority). The decision of whether a priority is allocated or not is made by the network operator who defines its importance (significance) in the core network. Hence, the call service process of calls with different priorities is carried out both in the radio part as well as in the resources of Iub interfaces of the access part of the UMTS network. The execution of prioritization means that the traffic management mechanism implemented at the call admission control (CAC) and/or call congestion control (CCC) levels, which are usually executed in the RNC software, is being used. In practice, many operators execute the prioritization of services in such a way as to make it imperceptible to users, while the priorities assigned to different categories of users are visible. Generally, the available categories of users are labelled as platinum, gold, silver, and bronze, while each of the groups included is assigned appropriate service parameters, e.g., through the allocation of specific priorities [9, 10]. The process of defining priorities is executed at both the radio interface level and the Iub resource level.
3 Traffic representation in the Iub interface
Let us assume that an Iub interface is offered a mixture of different packet streams. Analytical traffic models are constructed based on the internal structure of the packet stream or the socalled call stream in which a packet stream with a variable bit rate is treated as a single call that is characterized by a constant bit rate and appropriate service time. The term “call” is then meant to be understood as a packet stream or its section, which is related to a given service [2, 35]. It has been proved, on the basis of simulation experiments and measurements carried out in networks, that thus defined calls can be described by the Poisson streams characteristics [2, 35, 36] in which variable bit rates of packet streams are replaced by constant bit rates called the equivalent bandwidth [37]. The equivalent bandwidth is determined depending on and in relation to the capacity of the system, the maximum and the average bit rate of the packet stream, the variance of the bit rate, packet delay, and other important and relevant parameters for a given service [38, 39].
where M is the number of call streams offered to the system.
where [λ _{ i }]_{ M } is the intensity of a Poisson call stream of class i (1≤i≤M) and [μ _{ i }]_{ M } is the average service intensity for call of class i.
4 Traffic representation in the WCDMA radio interface

W is the chip rate of the dispersing signal that defines the velocity at which the input signal is dispersed,

[v _{ i }]_{ M } is the activity coefficient that defines the percentage occupancy of a transmission channel occupied by a user of class i, and

E _{ b }/N _{0} is the ratio between the energy per one bit E _{ b } and the noise spectral density N _{0}.
where M is the number of call streams offered to the system.
where value 1 defines the theoretical capacity of an isolated radio interface for the uplink or the downlink.
The intensity of the offered traffic of a given class does not depend on the type of the interface and can be expressed by Formula 4. Observe that due to the nonlinear dependence between the noise load and bit rate (Eq. 5), the number of allocation units necessary for a connection of a given class to be set up will be different in the radio interface and in the Iub interface.
5 Model of the Iub interface
Formulas 9–10 have been derived on the basis of the analysis of the Markovian process taking place in FAG [11, 12]. If the system services only one call stream, then Formula 10 can be reduced in its essence to the socalled Erlang B formula.
6 Model of the WCDMA radio interface
where S is the number of adjacent (neighboring) cells to the access cell, N _{ i,k } is the average value of the number of serviced calls of class i in the neighboring cell with the index k (1≤k≤S), and N _{ i } is the average value of the number of serviced calls of class i in the access cell.
where ξ is the interference suppression coefficient, while δ is the average value of the coefficient adopted by a given operator of a mobile network worked out on the basis of measurements. It indicates the degree of interference reduction between the users of the same cell due to the application of channel codes based on orthogonal variable spreading factor (OVSF). It means that they can have a different dispersion coefficient, and their mutual correlation is zero [41]. The parameter V, just as in the previous case, defines the potential theoretical capacity of the isolated radio interface.
To model the occupancy distribution in the WCDMA radio interface, the multiservice model of Erlang’s ideal grading (EIG) can be used. Let us consider an EIG to which a mixture of call streams M with different bit rates is offered. The group is defined by the demands of individual call classes [t _{ i }]_{ M } (1≤i≤M) expressed in AUs, capacity V expressed in AUs, availability d also expressed in AUs, as well as the traffic intensities [A _{ i }]_{ M } (1≤i≤M) of individual call classes, expressed in Erlangs. In the case of the WCDMA interface, parameters [t _{ i }]_{ M }, and V are defined by Formulas 7–8, whereas parameter d—depending on the type of link—by Formulas 15 or 16. Traffic intensity for calls of particular classes is defined by Formula 4.

The number of inputs to a system g (called load groups) is equal to the number of the possible effective ways of the selection of d AUs from among all V AUs (two load groups differ from each other in at least one AU),

Each load group has access to the same number of d AUs of the group,

Traffic offered to each of the load groups is identical, and

The occupancy distribution in each of the load groups is identical.
where Ψ=n if (d−[t _{ i }]_{ M }+1)≤n≤d and Ψ=d if n>d.
7 Model of a system with priorities
In [5, 6], a methodology for modelling of FAG with priorities is developed. In the present section, this methodology will be expanded to include EIG and used to model interfaces in the access part of the UMTS network in which priorities have been introduced.
In Eq. 29, parameter [Y]_{2} defines the total traffic carried in a system that services two classes of calls, whereas [Y _{ i }]_{2} defines the carried traffic of class i in a system that services two classes of calls.
The exemplary algorithm that makes it possible to determine all blocking probabilities in EIG with priorities can be written in the form of algorithm ALG_EIG_P(A,t,V,d,M), presented below.
8 Model of setting up connections in the access part of UMTS

A—Traffic offered to the system under consideration:$$ \textbf{A}_{\text{}}=\left\{\left[A_{i\text{}}\right]_{M}: i \in\{1,2,...,M\}\right\}, $$(38)

c—Resources demanded by calls of individual classes:$$ \textbf{c}_{\text{}}=\{\left[c_{i\text{}}\right]_{M}: i \in\{1,2,...,M\}\}, $$(39)

SysX—Component system X (X ∈ {1,2}):$$ \textbf{SysX}=\left\{\textbf{A}_{\text{SysX}},\textbf{t}_{\text{SysX}},V_{\text{SysX}},M\right\}, $$(40)where:

A _{SysX}—Traffic offered to system SysX (the sequence of classes is enforced by the priority mechanism in the system):
$$ \textbf{A}_{\text{SysX}}=\left\{\left[A_{j,\text{SysX}}^{i}\right]_{M}: j \in \{1,2,...,M\}\right\}, $$(41) 
\(\left [A_{j,\text {SysX}}^{i}\right ]_{M}\)—Traffic of class i with priority j in system SysX,

t _{SysX}—Resources demanded by calls of individual classes expressed in allocation units determined in relation to the type of system SysX:$$ \textbf{t}_{\text{SysX}}=\left\{\left[t_{j,\text{SysX}}^{i}\right]_{M}: j \in \{1,2,...,M\}\right\}, $$(42)

\(\left [t_{j,\text {SysX}}^{i}\right ]_{M}\)—Resources demanded by calls of class i with priority j in system SysX, expressed in units for system SysX, and

V _{SysX}—The capacity of system SysX, expressed in units for this system.

where \(\left [E_{j,\text {Sys1}}^{i}\right ]_{M}\) and \(\left [E_{k,\mathrm {Sys2}}^{i}\right ]_{M}\) is the blocking probability for calls of the same class i, indexed differently in Sys1 (1≤j≤M) and in Sys2 (1≤k≤M).
The calculations of the probabilities in Eq. 45 are performed iteratively until the required level of a relative error has been reached. In each consecutive step, new intensities of effective traffic and the corresponding blocking probabilities are determined. The method for the determination of the blocking probability depends on the adopted model of the system, e.g., there is a choice of the FAG model for the Iub interface (Formulas 9–10) or the EIG model for the WCDMA interface (Formulas 17–22). In the case of the application of priorities in determining the blocking probability of individual call classes in composed (complex) systems (e.g., WCDMA and Iub interfaces), it is possible to use the model proposed in Section 7 and the algorithm ALG_EIG_P(A,t,d,V,M) worked out on its basis.
Given below is a simplified algorithm (ALG_FPM(Sys1, Sys2)) for the calculation of the blocking probability in the tandem of the two systems Sys1 and Sys2.
In the algorithm presented above, the following notation has been adopted: symbol \(\left [X_{j,\text {Sys1}}^{i}\right ]_{M}^{(l)}\) defines the value of the X parameter in the lth step of the iteration.
Let us now consider the sequence of calculations in a telecommunication system composed of the WCDMA interface and the Iub interface in tandem, assuming that in each interface, a mechanism has been introduced for the prioritization of M classes of calls. Another assumption is that the hierarchy of priorities in each of the interfaces can be different. This means that call classes offered to both interfaces are appropriately arranged (WCDMA interface 1≤j≤M, Iub interface 1≤k≤M). The calculations start with the determination of AU in each of the interfaces. Then, the sets of demands of the number of AUs by calls of particular classes t _{WCDMA} and t _{Iub} in respective interfaces are determined. The capacities and availabilities of the considered interfaces are also expressed in AUs. After the parameterization of the interfaces, on the basis of the fixedpoint methodology and the algorithm ALG_EIG_P(A,t,V,d, M) for each interface, it is possible to determine the blocking probability for calls of individual classes in the tandem of WCDMA and Iub. Given below is a simplified algorithm for the calculations of the blocking probability in the tandem.
9 Case study
The results of the analytical studies have been confirmed by the results of the simulation that was carried out based on an original simulation program developed by the authors. The simulator was implemented in the Python language, and it employed the event scheduling approach [43]. The simulation model, however, does not take into consideration all technological parameters for the UMTS system. For example, it takes into account neither the propagation model of the radio channel nor the mobility of users. The developed simulator is intended to model the traffic capacity of the system, and thus to model the system at the socalled call (flow or connection) level [38]. At this level, technological parameters are rather insignificant for the accuracy of mapping the system to be modelled [44]. In the simulation experiments presented in all included graphs, each point on the curve represents an average value of the blocking probability obtained in the fifth series of the simulation. The assumption was that in an individual simulation series, at least 10,000,000 calls of the class that required the highest number of allocation units for service were offered. The results of the simulation are presented in graphs in the form of marks with a 95 % confidence level determined and 5 % confidence interval on the basis of the Student’s tdistribution. In many instances, the values of the confidence intervals are almost included inside the marks that identify the average result of the simulation experiment for calls of a given traffic class.

A priority is assigned independently to calls of each service classes,

In the case of the lack of free resources, the arrival of a call with a higher priority can be followed by the termination of service for calls with a lower priority, and

Setting up a connection requires the simultaneous provision of free resources in the radio interface and in the Iub interface.
Analytical calculations were performed according to Algorithm 3, while the accuracy of the model was validated by the comparison of corresponding results with the results of simulation experiments.
The hierarchy of priorities was adopted to be identical in both interfaces under consideration as well as consistent with the indexing of call classes given above. The capacity of the radio interface in the uplink direction was 8000 AU, whereas the capacity of the Iub interface was 15,000 AU.
It can thus be assumed that after the introduction of priorities, the amount of resources available for calls of classes with higher priorities increases and, this way, the amount of resources for calls with lower priorities decreases. An increase or a decrease in the amount of available resources leads to an increase or a decrease in the value of the blocking probability for calls of appropriate traffic classes.
Figure 7 presents the results obtained for a system in which priorities were changed for classes 2 and 3. It is easily noticeable that despite a higher number of demanded allocation units, class 3 (data) is characterised by a lower blocking probability than class 2 (voice).
Accuracy of the model (Fig 6)
a  Class 2  Class 3  Class 4  

E _{2}(sim.)  E _{2} (calc.)  δ[%]  E _{3}(sim.)  E _{3} (calc.)  δ[%]  E _{4}(sim.)  E _{4} (calc.)  δ[%]  
0.5  0  0  0  0  0  0  1.41E −03  9.52E −04  32.7 
0.7  0  0  0  8.74E −05  1.15E −04  32  1.27E −0  9.75E −02  23.1 
0.9  0  0  0  5.90E −02  7.27E −02  23.1  7.86E −01  6.91E −01  12.2 
1.1  6.34E −04  4.92E −04  22.5  6.02E −01  7.13E −01  18.4  9.97E −01  8.97E −01  10 
The models and algorithms discussed in the article use the most effective approach to modeling multiservice systems that is based on the approximation of the service process that occurs in the system by an appropriate Markov chain. The occupancy distribution in a single multiservice system can be determined on the basis of appropriate recurrent formulas, e.g., [2, 11, 12, 14] that take the specificity of systems into consideration. Given the concurrent nature of the call service in two multiservice systems (radio interface and Iub interface), the article employs the fixed point methodology [42]. This method has already been used in earlier works of the authors (e.g., in [44, 46–50]) in order to take into account the concurrency of service processes that occur in different multiservice systems. The fixed point methodology is characterized by a high effectiveness, e.g., [42]. The decision to drop the application of this method would necessitate the consideration of a very complex Markov process that would correspond to the service process occurring concurrently in both systems. Such an approach would necessitate the use of far more complex mathematical models that, in practice, would impose limits on the analysis of systems reducing it to the analysis of systems with a very low capacity, much lower than the capacity of the systems considered in the article.
10 Conclusions
This paper presents a new analytical model of the part of the UMTS network in which a mechanism for services prioritization has been introduced. The proposed model involves a radio interface and an Iub interface. The paper proposes a new model of the nonfullavailability group with priorities that has been used to model the WCDMA interface. To model the Iub interface, in turn, a model of the fullavailability group with priorities that has been developed earlier is used. The mutual dependence between the serviced traffic in both interfaces is taken into account by the fixedpoint methodology. The model is then used to evaluate the blocking probability in an exemplary system. The results obtained in the study confirm a satisfactory accuracy of the model. This model can be used to analyze dimension and optimize multiservice mobile phone networks.
11 Endnote
^{a} In the functional notation the twoindex notation [X _{ i }]_{ r } has been adopted in which the internal index i defines the current index of a given parameter, while the external index, r, indicates the maximum value of index i, e.g., as in the notation [c _{ i }]_{ M }, where (1≤i≤M), the internal index defines the traffic class, whereas the external index M indicates the class with the highest index, which is equivalent to the number of all classes serviced in the system. Thus, the adopted notation will make further considerations more convenient.
Declarations
Acknowledgments
The presented work has been funded by the Polish Ministry of Science and Higher Education within the status activity task "Structure, analysis and design of modern switching system and communication networks" in 2015.
Authors’ Affiliations
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