Approximation analysis for a multi-inflow tandem queueing model with blocking and unreliable servers

Abstract

This thesis considers a multi-inflow tandem queueing model with blocking and unreliable servers. This queueing model consists of two level queues. The first-level queues represent parallel single server (facility) finite queues and the second-level queues represent single server finite queues linked in series. The first-level queues are merged in the first queue of the second-level queues. The servers in this queueing model are subject to breakdown such that each breakdown is immediate repaired as it occurs. It is assumed that service times of each server, inter-breakdown times and repair times are all exponentially distributed, and that there are exogenous Poison arrivals to each queue of the first-level queues. An approximate algorithm is derived in the form of the marginal probability distribution of the numbers of units in each queue. The performance measures such as mean queue length and throughout are also formulated by use of the marginal distribution. The efficiency of the approximation procedure is examined through numerical examples.