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Some extensions of Takács's limit theorems

Published online by Cambridge University Press:  14 July 2016

D. N. Shanbhag
D. N. Shanbhag*
Affiliation:
University of Sheffield
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Abstract

In this paper, we establish that if an interarrival time exceeds a service time with a positive probability then the queueing system GI/G/s with a finite waiting room always has proper limiting distributions for its characteristics such as queue length, waiting time and the remaining service times of the customers being served. The result remains valid if we consider a GI/G/s system with bounded waiting times. A technique is also given to establish that for a system with Poisson arrivals the limiting distributions of the queueing characteristics at an epoch of arrival and at an arbitrary epoch are identical.

Keywords

GI/G/sRENEWAL THEOREMPOISSON ARRIVALSLIMIT THEOREMS
Type
Research Papers
Information
Journal of Applied Probability , Volume 11 , Issue 4 , December 1974 , pp. 752 - 761
Copyright
Copyright © Applied Probability Trust 1974 

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