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SERVER COORDINATION IN QUEUEING SYSTEMS: WHEN AND HOW?

Published online by Cambridge University Press:  20 April 2021

Junqi Hu Open the ORCID record for Junqi Hu [Opens in a new window] ,
Sigrún Andradóttir Open the ORCID record for Sigrún Andradóttir [Opens in a new window]  and
Hayriye Ayhan
Junqi Hu
Affiliation:
H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0205, USA E-mail: sa@gatech.edu
Sigrún Andradóttir
Affiliation:
H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0205, USA E-mail: sa@gatech.edu
Hayriye Ayhan
Affiliation:
H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0205, USA E-mail: sa@gatech.edu
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Abstract

Standard server assignment policies for multi-server queueing stations include the noncollaborative policy, where the servers work in parallel on different jobs; and the fully collaborative policy, where the servers work together on the same job. However, if each job can be decomposed into subtasks with no precedence relationships, then we consider a form of server coordination named task assignment where the servers work in parallel on different subtasks of the same job. We identify the task assignment policy that maximizes the long-run average throughput of a queueing station with finite internal buffers when blocked servers can be idled or reassigned to either replace or collaborate with other servers on unblocked subtasks. We then compare the server coordination policies and show that the task assignment is best when the servers are highly specialized; otherwise, the fully collaborative or noncollaborative policies are preferable depending on whether the synergy level among the servers is high or not. We also provide numerical results that quantify our previous comparison. Finally, we address buffer allocation in longer lines where there are precedence relationships between some of the tasks, and present numerical results that suggest our comparisons for one queueing station generalize to longer lines.

Keywords

applied probabilityoperations researchqueueing theory
Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 36 , Issue 3 , July 2022 , pp. 868 - 922
Copyright
Copyright © The Author(s), 2021. Published by Cambridge University Press

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