الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
In this thesis , a mathematical analysis of general types queuing networks in developed. We focus in our study on models that have a direct application in engineering . More specifically , we consider models that are commonly used in the performance evaluation of manufacturing systems and computer communication networks . For general queuing networks like those considered here, it seems difficult to obtain the steady state distribution of the number of customers at various nodes of the network . Hence, we develop an approximate analysis based on constructing a linear program whose solution gives upper and lower bounds on the performance measures of interest .This idea was originally used by Kumar to study reentrant lines in a Markovian setting . In the present work, this technique is extended and fully investigated to include more general arrival stream and service time distributions .Moreover ,we develop a Mathematics program to automate the solution which opens the way for tackling large systems .
Two types of general queueing networks are considered : one with exponential interarrival times and Erlangian service times and the other with Erlangian interarrival times and exponential service times . By solving a linear program , upper and lower bounds on the expected number of customers in the network are calculated .The objective function is that performance measure . the constraints are derived by assuming stability and examining the consequence of a steady state for general quadratic forms . Many numerical examples are presented. Single node queueing systems are examined first where our bounds give the exact result for one example (M/Er /1) and very tight bounds for other (Er /M/1). It has been proved that for multiple nodes systems (networks) , the bounds are tight for a great range of load factors Erlangian distribution was chosen since one may approximate a general distribution (which has a coefficient of variation less than 1) with an Erlangian distribution. In addition , the same methodology applied here to deal with the Erlangian distribution may be used to deal with some other distributions which are constructed using the method of stages such as hyperexponential and Cox distribution . In fact , it seems that this methodology may be a fundamental step when dealing with general queueing systems .