An M/G/1 Retrial Queue with a Single Vacation Scheme and General Retrial Times

摘要

Let us consider a service facility where a single server provides some service. It could be a plumber looking after repair and maintenance of the plumbing work in the apartment complexes situated near the shop or could be an electrician or a painter. Requests for service arrive in accordance with a Poisson process. When the server is away with the service of a customer, any other requests for service can be recorded and the customer cannot wait in a queue but has to leave and try for service after some time. The server after completion of the work on hand decides to take a break before attending to the next chore. This is an example of a retrial queue in which the server takes a vacation after the completion of each service. Motivated by this example, we have studied an M/G/1 retrial queue with server vacations. In this paper, we assume that the retrial times are generally distributed and that the retrial policy is constant. We have derived probability generating functions of the system size and the orbit size. We have investigated the conditions under which the steady state exists. Some useful performance measures are also obtained. Numerical examples are provided to illustrate the sensitivity of the performance measures to changes in the parameters of the system.