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Poisson traffic flow in a general feedback queue

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

Published online by Cambridge University Press:  14 July 2016

Erol A. Peköz  and
Nitindra Joglekar
Erol A. Peköz*
Affiliation:
Boston University
Nitindra Joglekar*
Affiliation:
Boston University
*
∗ Postal address: School of Management, Boston University, 595 Commonwealth Ave, Boston, MA 02215, USA.
∗ Postal address: School of Management, Boston University, 595 Commonwealth Ave, Boston, MA 02215, USA.
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Abstract

Consider a ·/G/k finite-buffer queue with a stationary ergodic arrival process and delayed customer feedback, where customers after service may repeatedly return to the back of the queue after an independent general feedback delay whose distribution has a continuous density function. We use coupling methods to show that, under some mild conditions, the feedback flow of customers returning to the back of the queue converges to a Poisson process as the feedback delay distribution is scaled up. This allows for easy waiting-time approximations in the setting of Poisson arrivals, and also gives a new coupling proof of a classic highway traffic result of Breiman (1963). We also consider the case of nonindependent feedback delays.

Keywords

Feedback queuePoisson convergencecoupling methods

MSC classification

Primary: 60K25: Queueing theory 90B22: Queues and service
Secondary: 60G55: Point processes 90B20: Traffic problems
Type
Short Communications
Information
Journal of Applied Probability , Volume 39 , Issue 3 , September 2002 , pp. 630 - 636
Copyright
Copyright © Applied Probability Trust 2002 

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