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Generalizing the Pollaczek-Khintchine Formula to Account for Arbitrary Work Removal

Published online by Cambridge University Press:  27 July 2009

Gautam Jain  and
Karl Sigman
Gautam Jain
Affiliation:
Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027
Karl Sigman
Affiliation:
Department of Industrial Engineering and Operations Research, Columbia University, New York, New York 10027
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Extract

Recently, a Pollaczek-Khintchine-like formulation for M/G/l queues with disasters has been obtained. A disaster is said to occur if a negative arrival causes all the customers (and therefore work) to depart from the system immediately. This study generalizes this result further, as it is shown to hold even when negative arrivals cause only part of the work to be demolished. In other words, an arbitrary amount of work, following a known distribution, is allowed to be removed at a negative event. Under these circumstances, a general approach for obtaining the Pollaczek–Khintchine Formula is proposed, which is then illustrated via several examples. Typically, it is seen that the formulainvolves certain parameters that are not explicitly known. The formula itself is made possible due to the number in system being geometric under preemptive last in-first out discipline.

Information

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 10 , Issue 4 , October 1996 , pp. 519 - 531
Copyright
Copyright © Cambridge University Press 1996

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