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The geometricity of the limiting distributions in queues and dams

Part of: Special processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

R. M. Phatarfod
R. M. Phatarfod*
Affiliation:
Monash University
*
∗ Postal address: Department of Mathematics, Monash University, Clayton, VIC 3168, Australia.
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Abstract

There are a number of cases in the theories of queues and dams where the limiting distribution of the pertinent processes is geometric with a modified initial term — herein called zero-modified geometric (ZMG). The paper gives a unified treatment of the various cases considered hitherto and some others by using a duality relation between random walks with impenetrable and with absorbing barriers, and deriving the probabilities of absorption by using Waldian identities. Thus the method enables us to distinguish between those cases where the limiting distribution would be ZMG and those where it would not.

Keywords

MOVING AVERAGE INPUTSEMI-MARKOV INPUTBOTTOMLESS DAMGI/M/1 QUEUEDUALITY OF RANDOM WALKSWALDIAN IDENTITIES

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60K30: Applications (congestion, allocation, storage, traffic, etc.) 60G40: Stopping times; optimal stopping problems; gambling theory 60G42: Martingales with discrete parameter
Type
Research Papers
Information
Journal of Applied Probability , Volume 30 , Issue 2 , June 1993 , pp. 438 - 445
Copyright
Copyright © Applied Probability Trust 1993 

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