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How Nearly do Arriving Customers See Time-Average Behavior?

Part of: Special processes Stochastic processes Operations research and management science

Published online by Cambridge University Press:  14 July 2016

Erol A. Peköz ,
Sheldon M. Ross  and
Sridhar Seshadri
Erol A. Peköz*
Affiliation:
Boston University
Sheldon M. Ross*
Affiliation:
University of Southern California
Sridhar Seshadri*
Affiliation:
New York University
*
∗Postal address: Department of Operations and Technology Management, Boston University, 595 Commonwealth Avenue, Boston, MA 02215, USA. Email address: pekoz@bu.edu
∗∗Postal address: Department of Industrial and System Engineering, University of Southern California, Los Angeles, CA 90089, USA.
∗∗∗Current address: Department of Information, Risk, and Operations Management, McCombs School of Business, University of Texas at Austin, 1 University Station, B6500, Austin, TX 78712, USA.
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Abstract

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Customers arriving at a queue do not usually see its time-average behavior unless arrivals occur according to a Poisson process. In this article we study how nearly customers see time-average behavior. We give total variation error bounds for comparing the distance between the time- and customer-average distributions of a queueing system in terms of properties of the interarrival distribution. Some refinements are given for special cases and numerical computations are used to demonstrate the performance of the inequalities.

Keywords

PASTAarrivals that see time averagesarrival theorem

MSC classification

Secondary: 60K25: Queueing theory 90B22: Queues and service 60K05: Renewal theory 60G10: Stationary processes
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 4 , December 2008 , pp. 963 - 971
Copyright
Copyright © Applied Probability Trust 2008 

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