On retrial queue with customer balking and feedback subject to server breakdowns

Abstract

Motivated by some real stochastic service systems, we study a feedback retrial queue with customer balking and unreliable servers (servers subject to breakdowns). A customer will either join a retrial orbit or balk if all servers are busy upon his arrival. After a service completion, the customer either leave the system or enter the retrial group again for additional service. The customer who is interrupted by the server failure will be served by another server if available; otherwise, he will be contacted later and treated as leaving the system. We use a quasi-birth-and-death process to analyze this system with almost all possible uncertain factors and derive major performance measures of the system. We also develop a cost function determining the optimal parameter settings of the system under the stability condition. Probabilistic Global Search Lausanne approach is employed in solving the optimization issue. The effects of parameters on performance measures of the system are examined numerically. Finally, we discuss the application of the model in the telephone medical consulting service system.

Keywords:

• Balking
• cost
• feedback
• matrix-analytical approach
• retrial queue

Acknowledgment

The authors thank the editor and anonymous referees for the valuable comments and suggestions, which significantly improved the quality of the paper.

Additional information

Funding

This research was supported by Natural Sciences and Engineering Research Council of Canada, under Grant No. RGPIN197319 of the corresponding author.