Optimization analysis for an infinite capacity queueing system with multiple queue-dependent servers: genetic algorithm

Abstract

This paper considers 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.

Keywords:

• cost
• genetic algorithm
• multiple heterogeneous servers
• optimization

2010 AMS Subject Classifications :

• 17D92
• 60K25
• 90B22
• 68M20
• 90C31

Acknowledgements

The authors gratefully acknowledge the constructive comments of editors and the anonymous reviewers.