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A monotonicity result for a G/GI/c queue with balking or reneging

Part of: Special processes

Published online by Cambridge University Press:  14 July 2016

Serhan Ziya ,
Hayriye Ayhan ,
Robert D. Foley  and
Erol Peköz
Serhan Ziya*
Affiliation:
University of North Carolina
Hayriye Ayhan*
Affiliation:
Georgia Institute of Technology
Robert D. Foley*
Affiliation:
Georgia Institute of Technology
Erol Peköz*
Affiliation:
Boston University
*
∗Postal address: Department of Statistics and Operations Research, University of North Carolina, CB# 3260, 213 Smith Building, Chapel Hill, NC 27599, USA. Email address: ziya@unc.edu
∗∗Postal address: H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, 765 Ferst Drive, Atlanta, GA 30332-0205, USA.
∗∗Postal address: H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, 765 Ferst Drive, Atlanta, GA 30332-0205, USA.
∗∗∗∗∗Postal address: School of Management, 595 Commonwealth Avenue, Boston, MA 02215, USA. Email address: pekoz@bu.edu
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Abstract

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In a G/GI/c loss system with balking, reneging, or limited waiting space, deleting some of the arriving customers can either increase or decrease the fraction of the remaining arrivals who get served, depending on how customers are deleted. We present a model in which the random deletion of arrivals independently and with some fixed probability can never decrease the fraction of the remaining arrivals who get served.

Keywords

Monotonicity in queuesbalkingrenegingloss systemcoupling

MSC classification

Primary: 60K25: Queueing theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 43 , Issue 4 , December 2006 , pp. 1201 - 1205
Copyright
© Applied Probability Trust 2006 

References

Sonderman, D. (1979). Comparing multi-server queues with finite waiting rooms. I: Same number of servers. Adv. Appl. Prob. 11, 439–447.Google Scholar