Cost optimization of an M/M/r queueing system with queue-dependent servers: genetic algorithm

Authors:
Jyh-Bin Ke;Jau-Chuan Ke;Chuen-Horng Lin
Affiliations:
National Chung-Hsing University, Taichung, Taiwan;National Taichung Institute of Technology, Taichung, Taiwan;National Taichung Institute of Technology, Taichung, Taiwan
Venue:
Proceedings of the 5th International Conference on Queueing Theory and Network Applications
Year:
2010

Citing 3
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Finite capacity M/M/r queueing system with queue-dependent servers

Computers & Mathematics with Applications

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Abstract

We consider an M/M/r queueing system with infinite capacity, in which the number of working servers changes depending on the queue length. The steady-state probability distributions and the expected number of customers in the system are derived, which are used to construct a cost function. In order to minimize the expected cost of the system, we use the genetic algorithm to find the best thresholds of queue length in activating servers and their corresponding service rate. Some illustrative examples are provided to demonstrate how the process of this algorithm works for the optimal management policy of the multi-server queueing system.