Algorithmic approach to Markovian multi-server retrial queues with vacations

There are many practical situations that have both features of customer retrials and server vacations. The vacation policy is characterized by the vacation startup rules and vacation termination rules. The queueing system with retrials and vacations has been described in variety of ways according to the vacation rules and retrial policies such as constant retrial policy and linear retrial policy and analyzed for each specific model. In this paper, we model the Markovian multi-server queues with customers’ retrials and vacations with level dependent quasi-birth-and-death (LDQBD) process in a unified manner and present an algorithmic approach to compute the performance measures of the system.