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Characterizing losses during busy periods in finite buffer systems

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Erol A. Peköz ,
Rhonda Righter  and
Cathy H. Xia
Erol A. Peköz*
Affiliation:
Boston University
Rhonda Righter*
Affiliation:
Santa Clara University
Cathy H. Xia*
Affiliation:
IBM
*
∗ Postal address: School of Management, Boston University, Boston, MA 02215, USA.
∗∗ Postal address: Department of Operations and Management Information Systems, Santa Clara University, Santa Clara, CA 95053, USA. Email address: rrighter@scu.edu
∗∗∗ Postal address: IBM T.J. Watson Research Center, PO Box 704, Yorktown, NY 10598, USA.
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Abstract

For multiple-server finite-buffer systems with batch Poisson arrivals, we explore how the distribution of the number of losses during a busy period changes with the buffer size and the initial number of customers. We show that when the arrival rate equals the maximal service rate (ρ = 1), as the buffer size increases the number of losses in a busy period increases in the convex sense, and when ρ > 1, as the buffer size increases the number of busy period losses increases in the increasing convex sense. Also, the number of busy period losses is stochastically increasing in the initial number of customers. A consequence of our results is that, when ρ = 1, the mean number of busy period losses equals the mean batch size of arrivals regardless of the buffer size. We show that this invariance does not extend to general arrival processes.

Keywords

Finite buffer systembusy period lossesMX/GI/1/n queue

MSC classification

Primary: 60K25: Queueing theory
Secondary: 90B22: Queues and service
Type
Short Communications
Information
Journal of Applied Probability , Volume 40 , Issue 1 , March 2003 , pp. 242 - 249
Copyright
Copyright © Applied Probability Trust 2003 

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Footnotes

Research supported by the Breetwor Fellowship of the Leavey School of Business of Santa Clara University.

References

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