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A monotonicity result for a single-server loss system

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Xiuli Chao  and
Liyi Dai
Xiuli Chao*
Affiliation:
New Jersey Institute of Technology
Liyi Dai*
Affiliation:
Washington University
*
∗ Postal address: Department of Industrial and Manufacturing Engineering, New Jersey Institute of Technology, Newark, NJ 07102, USA.
∗∗ Postal address: Department of Systems Science and Mathematics, Washington University, St. Louis, MO 63130, USA.
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Abstract

We consider a family of M(t)/M(t)/1/1 loss systems with arrival and service intensities (λt (c), μt (c)) = (λct , μct ), where (λt , μt ) are governed by an irreducible Markov process with infinitesimal generator Q = (qij )m × m such that (λt , μt ) = (λi , μi ) when the Markov process is in state i. Based on matrix analysis we show that the blocking probability is decreasing in c in the interval [0, c ∗], where c ∗ = 1/maxi Σj ≠iqij /(λi + μi ). Two special cases are studied for which the result can be extended to all c. These results support Ross's conjecture that a more regular arrival (and service) process leads to a smaller blocking probability.

Keywords

NON-STATIONARY QUEUEBLOCKING PROBABILITYMATRIX ANALYSISROSS'S CONJECTURE

MSC classification

Primary: 60K25: Queueing theory

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 32 , Issue 4 , December 1995 , pp. 1112 - 1117
Copyright
Copyright © Applied Probability Trust 1995 

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