APPROXIMATE AND EXACT SOLUTIONS FOR MULTIPLE CLASS QUEUEING NETWORK MODELS (PERFORMANCE, ANALYSIS, THROUGHPUT, BOUNDS)

TEEMU TAPANI KEROLA, Purdue University

Abstract

In recent years there has been significant interest in multiple class closed queueing network models. These models can be solved exactly if a certain set of assumptions apply. A general problem with all of these methods is that they often become too expensive in terms of processing time or memory requirements to use for networks with many job classes or for networks with moderate or large class populations. The work presented in this thesis is threefold: first, we develop the Composite Bound Method (CBM) that extends bottleneck analysis to multiple classes. If lower system throughput bounds for all classes are available, the CBM can use them to compute the composite upper throughput bounds and the composite lower system response time bounds. If zero is used for the lower throughput bounds, the CBM reduces to single class bottleneck analysis. The CBM can also be used for networks with delay servers and multiple server devices. We extend the theory of multiple class balanced job bounds to cover the networks mentioned above, so that the corresponding balanced job lower bounds can be used with the CBM. Second, we develop a new solution technique that reduces the complexity of finding the exact solution for a special type of network having balanced and unbalanced job classes. We can remove all balanced classes from the system, solve the reduced system exactly, and finally map the results back to the original network. Third, we develop a new approximation technique that is based on class aggregation. The Aggregate MVA aggregates all but one class together, solves the resulting two class system, and uses the performance measures of the one non-aggregated class as those of that class in the original network. The Iterative Aggregate method first makes an intelligent guess about the class throughputs, then uses these throughput estimates as the class aggregation factors for the Aggregate MVA. The Aggregate MVA is invoked once for each job class, resulting in new class throughput estimates. The whole process is repeated until the class throughputs converge. The method is empirically shown to give very good results, but unfortunately it does not converge for all networks. In general, its run time is greater than that of the Bard-Schweitzer algorithm, and about equal to that of the linearizer algorithm.

Degree

Ph.D.

Subject Area

Computer science

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