Renewal input (a, c, b) policy queue with multiple vacations and change over times

Abstract

This paper analyses a renewal input multiple vacations queue with change over times under (a, c, b) policy. The service and vacation times are exponentially distributed. The server begins service if there are at least c units in the queue and the service takes place in batches with a minimum of size a and a maximum of size b (a ≤ c ≤ b). At service completion instant, if the queue size is less than c but not less than a secondary limit a, the server continues to serve and takes vacation if the queue size is less than a – 1. The server is in change over period whenever the queue size is a – 1 at service completion instant and c – 1 at vacation completion instant. The steady state queue length distributions at both arbitrary and pre-arrival epochs are obtained and an optimal cost policy is presented with some numerical experiences for some particular values of the parameters using genetic algorithm.