Abstract
The present study deals with the performance analysis of a single server queues with state dependent arrival rates in batches. It is considerable that the units join the system for essential and optional services available in the system. The server can avail the at most m-vacations under randomised vacations policy. The system is analysed by using the supplementary variable technique with the assumptions of probability reasoning for study the steady state behaviour of the system and to obtain various performance indices of queue size distribution. The maximum entropy principle is used to find the approximate results of performance measures and comparative study of exact and approximate waiting times of the units is discussed. The numerical illustration is also carried out to facilitate the minimum cost for optimal parameters and validate the other results of the system.
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