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The probability of large queue lengths and waiting times in a heterogeneous multiserver queue II: Positive recurrence and logarithmic limits

Part of: Special processes Limit theorems Markov processes

Published online by Cambridge University Press:  01 July 2016

John S. Sadowsky
John S. Sadowsky*
Affiliation:
Arizona State University
*
* Postal address: Department of Electrical Engineering, Arizona State University, Tempe, AZ 85287–5706, USA.
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Abstract

We continue our investigation of the batch arrival-heterogeneous multiserver queue begun in Part I. In a general setting we prove the positive Harris recurrence of the system, and with no additional conditions we prove logarithmic tail limits for the stationary queue length and waiting time distributions.

Keywords

QUEUEING THEORYHARRIS RECURRENT MARKOV CHAINSFOSTER-LYAPUNOV THEORYMARKOV ADDITIVE PROCESSESRENEWAL THEORY

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60F10: Large deviations 60J05: Discrete-time Markov processes on general state spaces 60K15: Markov renewal processes, semi-Markov processes 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.)
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 27 , Issue 2 , June 1995 , pp. 567 - 583
Copyright
Copyright © Applied Probability Trust 1995 

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Footnotes

Supported by the National Science Foundation (NCR-9003007).

References

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