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Relating Time and Customer Averages for Queues Using ‘forward’ Coupling from the Past

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

Published online by Cambridge University Press:  14 July 2016

Erol A. Peköz  and
Sheldon M. Ross
Erol A. Peköz*
Affiliation:
Boston University
Sheldon M. Ross*
Affiliation:
University of Southern California
*
∗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.
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Abstract

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We give a new method for simulating the time average steady-state distribution of a continuous-time queueing system, by extending a ‘read-once’ or ‘forward’ version of the coupling from the past (CFTP) algorithm developed for discrete-time Markov chains. We then use this to give a new proof of the ‘Poisson arrivals see time averages’ (PASTA) property, and a new proof for why renewal arrivals see either stochastically smaller or larger congestion than the time average if interarrival times are respectively new better than used in expectation (NBUE) or new worse than used in expectation (NWUE).

Keywords

PASTAcoupling from the pastsimulationqueues

MSC classification

Secondary: 60K25: Queueing theory 68U20: Simulation 60J27: Continuous-time Markov processes on discrete state spaces 60J10: Markov chains (discrete-time Markov processes on discrete state spaces) 90B22: Queues and service
Type
Research Article
Information
Journal of Applied Probability , Volume 45 , Issue 2 , June 2008 , pp. 568 - 574
Copyright
Copyright © Applied Probability Trust 2008 

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