In the planning of modern cellular mobile communication systems, the impact of customer behavior has to be carefully taken into account. Two models dealing with the call retrial phenomenon are presented. The first model considers a base station with a finite customer population and repeated attempts. A Markov chain modeling is proposed, and an efficient recursive solution of the state probabilities is presented. The second model focuses on the use of the guard channel concept to prioritize the handover traffic. Again, the retrial phenomenon plays an important role. The influence of the repeated attempt effect on the quality of service experienced by the mobile customers is discussed by means of numerical results.

Modeling of customer retrial phenomenon in cellular mobile networks

Single server retrial queues with priority calls

A novel approximate technique is proposed for the estimation of call blocking probabilities in cellular mobile telephony networks where call blocking triggers customer retrials. The approximate analysis technique is based on Markovian models with state spaces whose cardinalities are proportional to the maximum number of calls that can be simultaneously in progress within cells. The accuracy of the approximate technique is assessed by comparison against results of detailed simulation experiments, results of a previously proposed Markovian analysis approach, and upper and lower bounds to the call blocking probability. Numerical results show that the proposed approximate technique is very accurate, in spite of the remarkably small state spaces of the Markovian models.

Efficient estimation of call blocking probabilities in cellular mobile telephony networks with customer retrials

Foreword Preface to the Second Edition Preface 1. Maximization, Minimization, and Motivation 2. Vectors and Matrices 3. Diagonalization and Canonical Forms for Symmetric Matrices 4. Reduction of General Symmetric Matrices to Diagonal Form 5. Constrained Maxima 6. Functions of Matrices 7. Variational Description of Characteristic Roots 8. Inequalities 9. Dynamic Programming 10. Matrices and Differential Equations 11. Explicit Solutions and Canonical Forms 12. Symmetric Function, Kronecker Products and Circulants 13. Stability Theory 14. Markoff Matrices and Probability Theory 15. Stochastic Matrices 16. Positive Matrices, Perron's Theorem, and Mathematical Economics 17. Control Processes 18. Invariant Imbedding 19. Numerical Inversion of the Laplace Transform and Tychonov Regularization Appendix A. Linear Equations and Rank Appendix B. The Quadratic Form of Selberg Appendix C. A Method of Hermite Appendix D. Moments and Quadratic Forms Index.

Introduction to Matrix Analysis. By Richard Bellman. 2nd Edition. Pp. xxiii, 403. £7·50. (McGraw-Hill.)

In the last twenty years the field of Markov-modulated fluid queues has received considerable attention. In these models a fluid reservoir receives and/or releases fluid at rates which depend on the actual state of a background Markov chain. In the first chapter of this thesis we give a short introduction on how the stationary distribution for such a model is usually found, as well as a literature overview on Markov-modulated and related uid queues. The rest of the thesis is concerned with �nding stationary distributions for some types of fluid models that have received little or no attention until now. The two main contributions are the following.
1. We focus on models in which the state space of the regulating Markov process is infinitely large, either denumerable or not. Regarding the first type, we mainly look into regulating processes that are of birth-death type. We present procedures to find the stationary distribution, using the theory of orthogonal polynomials. In the nondenumerable case, we look into simple systems of fluid queues, in which one fluid queue regulates the behaviour of another (one example being a fluid tandem queue).
2. We look into models in which the state of the fluid reservoir in quences the behaviour of the regulating process, so that the latter does not constitute a Markov process. We call suchlike systems feedback fluid queues, to emphasize the two-way dependence between fluid reservoir and regulating process.

/pdf/markov-modulated-and-feedback-fluid-queues-1iunes5rbv.pdf

Markov-modulated and feedback fluid queues

We consider anM/G/1 priority retrial queueing system with two types of calls which models a telephone switching system and a cellular mobile communication system. In the case that arriving calls are blocked due to the server being busy, type I calls are queued in a priority queue of finite capacityK whereas type II calls enter the retrial group in order to try service again after a random amount of time. In this paper we find the joint generating function of the numbers of calls in the priority queue and the retrial group in closed form. When λ1=0, it is shown that our results are consistent with the known results for a classical retrial queueing system.

M/G/1 retrial queueing systems with two types of calls and finite capacity

The authors consider a single server priority queueing system with two priority classes of customers. The work is motivated for performance analysis of multiplexing video and data in communication networks, where videos at cell level arrive according to a two-state Markov-modulated Poisson process (MMPP) and data arrive according to a Poisson process. With the supplementary variable method, the authors explicitly obtain the steady-state joint generating function of the queue lengths of each class. They also investigate the queue lengths of each class by a technique of Markov-modulated fluid flow (MMFF). In comparison with the MMPP model, the MMFF model provides computationally simple procedures and results. Numerical results show that performance measures obtained with the MMFF model are quite close to those with the MMPP model.

Priority queue with two-state Markov-modulated arrivals

We investigate a Markov modulated fluid queueing system with strict priority. The input process is composed of two fluid flows which are stored in buffer?1 and buffer?2, respectively. The rates of these fluid flows depend on the current state of a finite state Markov chain. Buffer?1 has full assignment of priority (=strict priority) for service and so buffer?2 is served at a residual service rate when buffer?1 is empty. We explicitly derive the stationary joint distribution of the two buffer contents in the system by a spectral decomposition method. In the case of a two?state Markov chain, the joint distribution is explicitly expressed in terms of the system parameters. Also the joint moments and tail distributions of the two buffer contents are obtained and some numerical examples are presented.

A Markov modulated fluid queueing system with strict priority

In broadband ISDN (B-ISDN) with ATM, various kinds of traffic such as video, data, and voice share the common transmission resources, i.e. they are multiplexed into one transmission stream. We consider a single server priority queueing system with two priority classes of customers. This work is motivated by the need for a performance analysis of video and data multiplexing in a communication network, where video at the cell level arrive according to a two-state Markov modulated Poisson process (MMPP) and data arrive according to a Poisson process. With the supplementary variable method, we explicitly obtain the steady-state joint generating function of the queue lengths of each class. We also investigate the queue lengths of each class by a technique of Markov modulated fluid flow (MMFF). In comparison with the MMPP model, the MMFF model provides computationally simple procedures and results. Moreover, numerical results show that performance measures obtained with the MMFF model are quite close to those with the MMPP model.

Ki Bong Choi

Papers

M/G/1 retrial queueing systems with two types of calls and finite capacity

Priority queue with two-state Markov-modulated arrivals

A Markov modulated fluid queueing system with strict priority

Priority queue with two state Markov modulated arrivals