BULK ARRIVAL RETRIAL QUEUE WITH FLUCTUATING MODES OF SERVICE, IMMEDIATE FEEDBACK, SERVER VACATION AND ORBITAL SEARCH

This paper deals with single server retrial queue with fluctuating modes of service. Server provides M modes of service with different service rates.  At the arrival epoch of a batch, if the server is idle, then one customer enters for service and others join the orbit. Otherwise all the customers join the orbit. After completion of service, the unsatisfied customers opt for re-service. At the completion epoch of each service, the server takes a single Bernoulli vacation. After vacation completion the server may search for customer in the orbit. The supplementary variables corresponding to retrial time, service time and vacation time are incorporated to determine the queue size distribution. The mean number of customers in the orbit, the mean number of customers in the system and system probabilities are obtained. Finally the stochastic decomposition law is verified. The analytical results are validated with the help of numerical illustrations.