Performance analysis of single server non-Markovian retrial queue with working vacation and constant retrial policy (Q2874630)

The paper under review studies an \(\mathrm{M}/\mathrm{G}/1\) retrial queueing system with working vacation and constant retrial policy. Customers arrive according to Poisson input with rate \(\lambda\). If at the arrival time the server is busy, then the customer joins the orbit to repeat his/her request later; otherwise, if the server is free it starts to serve the customer immediately. Customers in the orbit apply for a service one by one with exponentially distributed time and a constant retrial rate \(\gamma\). The working vacation of the single-server occurs at the departure times when there are no customers in the orbit. During the vacation time the service rate of the server (the reciprocal of the expected service time) is changed, it is \(\mu_b\) when the server is not at vacation, and it is \(\mu_v\) when the server is at vacation, \(\mu_v<\mu_b\). A vacation duration is exponentially distributed with parameter \(\eta\). After completing the vacation, the server stays idle until a new arrival from the outside or orbit. The paper derives the steady states distribution of retrial customers.