OPERATIONAL ANALYSIS OF QUEUEING PHENOMENA
Abstract
Operational analysis provides a framework for studying queueing phenomena during finite time periods. There are two sources of error in using operational formulas for performance prediction: parameter estimation error and assumption violation. This thesis investigates how these errors affect the estimates of performance quantities. Different operational assumptions are used to derive several formulas for the mean queue length and response time of an isolated service center. One formula is analogous to the stochastic Pollaczck-Khinchine formula for an M/G/1 queue. If the necessary assumptions are not satisfied, the formulas are only estimators. The error in each estimator is expressed in terms of the assumption errors. An analysis of the error expressions reveals a common term that can be used to detect ill-conditioned problems. A flow balance assumption is used in the derivation of many operational formulas. We demonstrate that violation of this assumption can lead to large errors in state occupancies. A flow balanced portion of an observation period can be used to approximate the state occupancies. The errors are shown to be no larger than the proportion of the observation period that is discarded.
Degree
Ph.D.
Subject Area
Computer science
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