An M/G/1 retrial queue with balking customers and Bernoulli working vacation interruption

Abstract

In this paper, an M/G/1 retrial queue with general retrial times and Bernoulli working vacation interruption is considered. If the server is busy, an arriving customer either enters an orbit with probability q ($0<q\le 1$) or balks (does not enter) with probability $1-q$. During a working vacation period, if there are customers in the system at a service completion instant, the vacation either is interrupted with probability p ($0\le p\le 1$) or continues with probability $1-p$. By applying the supplementary variable technique, we obtain the steady state joint distribution of the server and the number of customers in the orbit. Various interesting performance measures are also derived. Finally, some numerical examples and cost optimization analysis are presented.

Keywords:

• Retrial
• working vacation
• Bernoulli vacation interruption
• balking

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by the National Natural Science Foundation of China [No. 11301306]; the Natural Science Foundation of Anhui Higher Education Institutions [No. KJ2014ZD21].