Analysis of finite queueing systems via structured markov Chain

Abstract

Finite queueing network is a useful tool in evaluating the performance of real-life systems which have finite capacity resources. The complexity associated with the blocking phenomena inherent to such systems with finite capacities, in general, makes the analysis difficult. The approximation methods, which are the only means available for large systems, are generally based on decomposition. In most of the decomposition approaches, each subsystem is a single queueing system. However, the configurational complexity of the system and/or the dependencies between subsystems seriously degrades the accuracy and the efficiency of the decomposition. This thesis presents an efficient method which yields the steady-state probabilities for the general two-node tandem queueing network and some of its variants which have the similar transition structures. Also, we propose a decomposition scheme for the finite-buffered fork/join queueing network, in which the simple fork or join networks can be the subsystems. By using the equivalence relations, such subsystems are evaluated by the algorithm for the two-node tandem queueing networks. First, focusing on repetitive-service(RS) blocking, we propose an aggregation scheme for the two-node tandem queueing network. Together with the recursive relations between the states, derived then is a reduced system of linear equations. Also, we propose an equivalence relation between the cyclic network and the tandem network with population size constraints, which makes it possible that three-node cyclic networks can be analyzed using the same line of approach. Second, we show that the proposed principle, the aggregation and the recursion, can be applied to some tandem networks with more general assumptions such as the ones with any commonly used blocking mechanism, with feedback, with multiple servers, and with more than two nodes. Also, we deal with the finite-buffered cutoff priority queue with reneging as an illustration that any queuei...