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Multiple-server system with flexible arrivals

Part of: Special processes Operations research and management science

Published online by Cambridge University Press:  01 July 2016

Osman T. Akgun ,
Rhonda Righter  and
Ronald Wolff
Osman T. Akgun*
Affiliation:
University of California, Berkeley
Rhonda Righter*
Affiliation:
University of California, Berkeley
Ronald Wolff*
Affiliation:
University of California, Berkeley
*
∗ Postal address: Department of Industrial Engineering and Operations Research, 4141 Etcheverry Hall, Berkeley, CA 94720, USA.
∗ Postal address: Department of Industrial Engineering and Operations Research, 4141 Etcheverry Hall, Berkeley, CA 94720, USA.
∗ Postal address: Department of Industrial Engineering and Operations Research, 4141 Etcheverry Hall, Berkeley, CA 94720, USA.
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Abstract

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In many service, production, and traffic systems there are multiple types of customers requiring different types of ‘servers’, i.e. different services, products, or routes. Often, however, a proportion of the customers are flexible, i.e. they are willing to change their type in order to achieve faster service, and even if this proportion is small, it has the potential of achieving large performance gains. We generalize earlier results on the optimality of ‘join the shortest queue’ (JSQ) for flexible arrivals to the following: arbitrary arrivals where only a subset are flexible, multiple-server stations, and abandonments. Surprisingly, with abandonments, the optimality of JSQ for minimizing the number of customers in the system depends on the relative abandonment and service rates. We extend our model to finite buffers and resequencing. We assume exponential service. Our optimality results are very strong; we minimize the queue length process in the weak majorization sense.

Keywords

JSQmajorizationabandonmentfinite buffermultiple-server station

MSC classification

Primary: 90B22: Queues and service
Secondary: 60K25: Queueing theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 43 , Issue 4 , December 2011 , pp. 985 - 1004
Copyright
Copyright © Applied Probability Trust 2011 

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