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Kelly and Jackson networks with interchangeable, cooperative servers

Part of: Special processes

Published online by Cambridge University Press:  01 July 2021

Chia-Li Wang  and
Ronald W. Wolff
Chia-Li Wang*
Affiliation:
National Dong Hwa University
Ronald W. Wolff*
Affiliation:
University of California, Berkeley
*
*Postal address: Department of Applied Mathematics, National Dong Hwa University, Hualien 974, Taiwan, ROC. E-mail: [email protected]
**Postal address: Department of Industrial Engineering and Operations Research, University of California, Berkeley, CA 94720, USA.
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Abstract

In open Kelly and Jackson networks, servers are assigned to individual stations, serving customers only where they are assigned. We investigate the performance of modified networks where servers cooperate. A server who would be idle at the assigned station will serve customers at another station, speeding up service there. We assume interchangeable servers: the service rate of a server at a station depends only on the station, not the server. This gives work conservation, which is used in various ways. We investigate three levels of server cooperation, from full cooperation, where all servers are busy when there is work to do anywhere in the network, to one-way cooperation, where a server assigned to one station may assist a server at another, but not the converse. We obtain the same stability conditions for each level and, in a series of examples, obtain substantial performance improvement with server cooperation, even when stations before modification are moderately loaded.

Keywords

Stabilitypositive recurrentwork conservationinsensitivityflexible servers

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60K20: Applications of Markov renewal processes (reliability, queueing networks, etc.)
Type
Original Article
Information
Advances in Applied Probability , Volume 53 , Issue 2 , June 2021 , pp. 463 - 483
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Copyright
© The Author(s), 2021. Published by Cambridge University Press on behalf of Applied Probability Trust

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