Informatics and Applications
2022, Volume 16, Issue 4, pp 34-41
OPTIMAL CONTROL OF A QUEUE-LENGTH DEPENDENT ADDITIONAL SERVER IN GI/M/1 QUEUE
Abstract
Consideration is given to a GI/M/1 queue in which there is an additional server available for serving customers from the queue. The additional server can be turned on and off depending on the current queue length.
The long-run total cost per unit time, equal to the difference between the paid amount for service and the losses due to the waiting of customers and additional server depreciation, is being optimized. The case of finite queue capacity is also considered in which the losses also account for lost customers. It is proved that the cost function considered is unimodal. Necessary and sufficient conditions are given for the existence of the decision point (queue length) at which application of the additional server is optimal. A simple algorithm for controlling the decision point, requiring only observations of the cost function value, is provided.
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[+] About this article
Title
OPTIMAL CONTROL OF A QUEUE-LENGTH DEPENDENT ADDITIONAL SERVER IN GI/M/1 QUEUE
Journal
Informatics and Applications
2022, Volume 16, Issue 4, pp 34-41
Cover Date
2022-12-30
DOI
10.14357/19922264220406
Print ISSN
1992-2264
Publisher
Institute of Informatics Problems, Russian Academy of Sciences
Additional Links
Key words
queuing system; redundancy; management; optimization
Authors
Ya. M. Agalarov 
Author Affiliations
Federal Research Center "Computer Science and Control" of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation
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