Performance measures of M/G/1 retrial queues with recurrent customers, breakdowns, and general delays

ABSTRACT

In this paper, an M/G/1 retrial system with two classes of customers: transit and recurrent customers is studied. After service completion, recurrent customers always return to the orbit and transit customers leave the system forever. The server is subject to breakdowns and delayed repairs. The customer whose service is interrupted stays in the service, waiting for delay and repair of the server. After repair this customer completes his service. The study of the system concerns the joint generating function of the server state and the queue length in steady state. Some performance measures of the system are then derived and some numerical results are presented to illustrate the effect of the system parameters on the developed performance measures.

Keywords:

• Breakdown
• general delay times
• general retrial times
• repair times
• supplementary variable method
• transit and recurrent customers.

MATHEMATICS SUBJECT CLASSIFICATION:

• 90B22
• 60K25
• 68M20