Stability analysis and optimal control of multi-server wireless queueing systems

Abstract

In this thesis, we concentrate on the stability analysis and stochastic control of wireless queueing systems. The queueing systems considered in this thesis can be applied to model orthogonal resource allocation in wireless access and satellite communication networks. Most of the work in this area has focused on deriving the optimal server allocation policy (optimality with respect to various objective functions), while only a few papers characterize the stability region of the studied models in an explicit form. An explicit characterization of the stability region not only enables us to solve network utility optimization problems with incurring less queueing delay, but also can facilitate the performance evaluation of the proposed control policies in network stochastic control. In the first part of this thesis, we focus on the stability analysis of three specific queueing systems, namely multi-interface queueing system with a randomly connected server bank, system with random connectivities and multi-server single-interface queueing system with random For each system, the stability region of the system is characterized by a finite set of linear inequalities. More specifically, for each queueing model we derive the necessary and sufficient conditions for 'the stability of the system for general packet arrival processes. For stationary arrivals, it is shown that these conditions will characterize the network stability region. For each system, we also derived an upper bound, in a closed form expression, for the average queueing delay of the optimal policy. Thereafter, we generalize our analysis for the multi-queue system to a system with stationary M-ary channels (instead of independent binary channels) and derive a linear algebraic characterization of the stability region for this system. We further generalize the analysis for a fluid flow system and show that in this case, the stability region is determined by an infinite set of linear inequalities. However, by use of an example we show that depending on the channel distribution and the number of queues, we may be able to characterize the stability region by a finite set of non-linear inequalities instead of infinite number of linear inequalities. Finally, in the last part of the thesis we investigate the problem of delay-optimal server assignment in the single-interface queueing system for which we did the stability analysis in the previous part of the thesis. In particular, we consider the assignment of K identical servers to a set of N parallel queues in a time slotted queueing system with random connectivities. It has been previously proven that Maximum Weighted Matching (MWM) is a throughput-optimal server assignment policy for such queueing systems In this thesis, we prove that for, a symmetric system with i.i.d. Bernoulli packet arrivals and connectivities, MWM minimizes, in stochastic ordering sense, a broad range of cost functions of the queue lengths including total queue occupancy (or equivalently minimizes the average queueing delay). Then, we extend the model by considering imperfect services where it is assumed that the service of a scheduled packet fails randomly with a certain probability. We prove that the same policy is still optimal for the extended model. We also show that the results are still valid for more general connectivity and arrival processes, e.g., Poisson arrival process.