Abstract
The present investigation deals with the single server stochastic model of queueing system, wherein the arrivals of units are in batches and follow Poisson process with state dependent arrival rates. There is a provision of two stages of heterogeneous service with arbitrary distributed different service time. The server may take optional vacation after the completion of the both stages of service of each unit. The server may fail at any instant of service and requires repair. The transient and steady state behaviours of the queue length distribution are studied by using the Laplace transform and probability generating function along with supplementary variable-based methodology, to obtain the performance measures of the system. Some particular cases are discussed by setting the parameters. The maximum entropy principle is applied to find the approximate system state probabilities. The numerical illustrations are also considered to validate the analytical results.
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