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User-Optimal State-Dependent Routeing in Parallel Tandem Queues with Loss

Part of: Operations research and management science Special processes

Published online by Cambridge University Press:  14 July 2016

Scott Spicer  and
Ilze Ziedins
Scott Spicer*
Affiliation:
The University of Auckland
Ilze Ziedins*
Affiliation:
The University of Auckland
*
∗ Postal address: Department of Statistics, The University of Auckland, Private Bag 92019, Auckland, New Zealand.
∗ Postal address: Department of Statistics, The University of Auckland, Private Bag 92019, Auckland, New Zealand.
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Abstract

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We consider a system of parallel, finite tandem queues with loss. Each tandem queue consists of two single-server queues in series, with capacities C1 and C2 and exponential service times with rates μ1 and μ2 for the first and second queues, respectively. Customers that arrive at a queue that is full are lost. Customers arriving at the system can choose which tandem queue to enter. We show that, for customers choosing a queue to maximise the probability of their reaching the destination (or minimise their individual loss probability), it will sometimes be optimal to choose queues with more customers already present and/or with greater residual service requirements (where preceding customers are further from their final destination).

Keywords

Parallel queuestandem queuesloss probabilityrouteinguser optimality

MSC classification

Primary: 90B15: Network models, stochastic
Secondary: 60K25: Queueing theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 43 , Issue 1 , March 2006 , pp. 274 - 281
Copyright
© Applied Probability Trust 2006 

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