ANALYSIS OF OPEN FINITE QUEUEING NETWORKS (OPTIMIZATION, APPROXIMATIONS)

Interest in queueing networks and their solutions have flourished over the past two decades largely due to their potential applications in computer systems, communication networks, facilities planning, and flexible manufacturing systems. The majority of efficient computational techniques that have been developed deal mainly with unrestricted queueing networks because of their well-behaved mathematical characteristics. Since finite queueing networks are extremely complex for exact analysis, there is growing interest in their approximate analysis. The main thrust of this thesis addresses the development of approximation techniques for estimating the performance measures within these open finite queueing networks. The techniques which are based on expanding and then decomposing the networks with general interarrival and service time distributions. Small (n (LESSTHEQ) 3) as well as large (n > 3) open finite queueing networks are examined the results are validated by simulation. The second thrust of this thesis is concerned with the optimal routing of customers within open finite queueing networks. Not only is the problem complex because of its stochastic aspect, it is complex because of the multi-objective nature of the problem. A heuristic based on the k-th shortest path algorithm is divised to find the approximate Nondominated sets of routes with respect to the following two objectives: (1) Minimize average sojourn times in the network; (2) Minimize processing costs in the network. All the developed methodologies for analyzing open finite queueing networks are successfully tested on a large network representing a hypothetical manufacturing facility.