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Optimal bulking threshold of batch service queues

Part of:Special processesMarkov processes

Published online by Cambridge University Press:  22 June 2017

Yun Zeng and
Cathy Honghui Xia
Yun Zeng*
Affiliation:
The Ohio State University
Cathy Honghui Xia*
Affiliation:
The Ohio State University
*
* Postal address: Department of Integrated Systems Engineering, The Ohio State University, 1971 Neil Avenue, Columbus, OH 43210, USA.
* Postal address: Department of Integrated Systems Engineering, The Ohio State University, 1971 Neil Avenue, Columbus, OH 43210, USA.
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Abstract

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Batch service has a wide application in manufacturing, communication networks, and cloud computing. In batch service queues with limited resources, one critical issue is to properly schedule the service so as to ensure the quality of service. In this paper we consider an M/G[a,b]/1/N batch service queue with bulking threshold a, max service capacity b, and buffer capacity N, where N can be finite or infinite. Through renewal theory, busy period analysis and decomposition techniques, we demonstrate explicitly how the bulking threshold influences the system performance such as the mean waiting time and time-averaged number of loss customers in batch service queues. We then establish a necessary and sufficient condition on the optimal bulking threshold that minimizes the expected waiting time. Enabled by this condition, we propose a simple algorithm which guarantees to find the optimal threshold in polynomial time. The performance of the algorithm is also demonstrated by numerical examples.

Keywords

Batch serviceoptimal bulking thresholdqueueingPoisson arrival

MSC classification

Primary:60K25: Queueing theory
Secondary:60J10: Markov chains (discrete-time Markov processes on discrete state spaces)60K05: Renewal theory

Information

Type
Research Papers
Information
Journal of Applied Probability , Volume 54 , Issue 2 , June 2017, pp. 409 - 423
Copyright
Copyright © Applied Probability Trust 2017 

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