Approximations for waiting times in queueing systems /
Queueing systems are commonly used in modeling manufacturing,
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| Format: | Thesis Book |
| Language: | English |
| Published: |
[Place of publication not identified] :
[publisher not identified] ;
1996.
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| Subjects: | |
| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=739668731&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | Queueing systems are commonly used in modeling manufacturing, telecommunications, and transportation systems. Waiting time is an important measure of effectiveness in these models. The objective of this dissertation is to devise easily computable and reasonably accurate approximations for the mean, variance, and distribution of steady state waiting times in single as well as multiple server queues. An easily implementable numerical approximation based on the Fredholm integral equations is developed to compute the waiting time distribution in a GI/G/1 queue. This numerical procedure is further refined to obtain very accurate estimates of the mean and variance of waiting times. Bounds, based on the first three moments of interarrival and service times, are derived on the variance of waiting times in GI/G/1 queue. These bounds are sharper whenever similar bounds are available in the literature. An Allen-Cunneen type approximation is proposed for the variance of waiting times in a GI/G/k queue. This approximation is expressed in terms of the first three moments of interarrival and service times. Computable approximations and bounds are derived for the tail probabilities of waiting times in a single server queue with stationary and ergodic interarrival and service times. These approximations are shown to be useful in estimating the overflow probabilities in a finite buffer batch arrival and batch service discrete time queue. |
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| Item Description: | Vita. "Major Subject: Industrial Engineering". |
| Physical Description: | xi, 75 leaves : illustrations ; 28 cm. Issued also on microfiche from University Microfilms Inc. |
| Bibliography: | Includes bibliographical references: pages 69-74. |