In the last decade, mobile networks have experienced an enormous growth. Moreover, due to the increase in the number of services and in the required bandwidth, it is necessary to develop accurate models and resource management mechanisms. This work aims to be a contribution to the development of models for the study and evaluation of radio resource management in mobile cellular networks. More specifically, the aim has been directed to the study retrial models. These models are useful for the characterization of different aspects of the network operation, such as modelling human behaviour and the characterization of new services offered by communication networks. Traditionally, a retrial system has been defined as a system in which users that are blocked, seek for access after a timeout. This characteristic is typical of the human behaviour and therefore, it should not be ignored when modelling a communication system, since it can have a great impact on the performance parameters of the system —blocking probability, probability forced termination . . . —. Additionally, in mobile cellular networks, this effect can be found in the handovers due to the network structure and its characteristics. Thus, according to the GSM standard, for example, while the mobile is in the handover area —overlapped-area between the coverage of two or more cells—, and without the user’s perception, it can ask the destination cell for resources a limited number of times. A correct characterization of this retrial process improves the performance of the network, avoiding unnecessary forced termination sessions.

When modelling this type of systems, we have a structure characterized by two basic functional blocks: a main block which houses the set of servers, i.e., the system resources, plus a possible queue. On the other hand, there is a second block that houses the users who retry, usually called retrial orbit. Moreover, we consider the possibility that users are impatient and leave the system without being served. For the specific case of a monoservice cellular network, the system presents two orbits, one for new service requests and one for handovers, since the characteristics of these two types requests are different.

These systems can be characterized as a multidimensional continuous time Markov chain, CTMC. Dimensions represent the servers, or system resources, and the users in each of the retrial orbits of the system. In the case of studying systems with infinite population, we have systems in which the dimensions that represent the retrial orbits are infinite and moreover, they present state-dependent transitions in all dimensions. With these features it is impossible to solve the system in an exact way and it is necessary to use approximate models to obtain the state probabilities of the system. 

Throughout this work we have developed approximate models in order to improve the performance of those models found in the specialized literature. We have developed a model, called Finite Model, FM, that belongs to the Truncated models category. This category is based on replacing the initial infinite state space for a finite one. We have also developed the Model of state space Limitation, LM, and Homogenisation Models, HM1 and HM2, all of them are Generalized truncated models. In this case, we approach the initial infinity state space that can not be solved —it is impossible to calculate the state probabilities of the system—, for another infinite one, but with some characteristics that make possible to solve the system. 

Specifically, the LM model considers that the rate of retrials is infinite for certain states; on the other hand, models HM1 and HM2 are based on the homogenization of the state space from a given level of associated Quasi Birth and Death Process, QBD. The fact of keeping the infinite state space improves the accuracy of these models, compared to that obtained with models that use a finite state space. These models were compared, in a generic scenario, with the most popular models in the literature. Results show that FM gets better results in terms of accuracy than the other Truncated models compared. Obviously, Generalized truncated models get better results than Truncated models. We emphasize the use of the HM2 model, which gets a very good trade off between accuracy and computational cost. 

All these models are based on the calculation of the probabilities of state. Recently, however, an alternative approach to evaluate Markov processes, including those with an infinite state space, has appeared. It is called Extrapolation Value (VE). The main feature of this approach is that it considers the system as a Markov Decision Process, MDP. This solution has been adapted to retrial systems, obtaining an approximate model that is very versatile and it presents a very good performance, both in terms of accuracy and computational cost.

You may find other retrial systems that characterize a number of new applications such as VoIP or video conferencing services. These applications, in case of blocking, allow the user to retry the access with a lower number of resources requested. Thus, adaptive rate techniques have been developed to offer a greater or lesser quality according to the degree of congestion. Apart from these applications, we find those applications related to the transfer of electronic documents and that can be modelled as elastic traffic. In this work we have developed different mechanisms, working together with the admission control policy, to improve the efficiency of the network while ensuring a certain quality of service to the users of these applications. Specifically, a reserve policy has been developed, which gets a soft degradation in the performance of the rate adaptive flows when there is congestion in the system. Additionally, we can include a elastic traffic flow as best effort in order to utilize the resources that real-time users leave free, without affecting the quality of service obtained by the real time flow.