Maximum entropy analysis of unreliable MX/ (G1, G2)/1 queue with Bernoulli vacation schedule
Abstract
This paper examines the steady state behavior of unreliable server in a batch arrival queue with two phases of heterogeneous service along with Bernoulli schedule. The server provides two kinds of services in succession, the first stage service (FSS) followed by second stage service (SSS). As soon as both services are completed, the server may take a vacation or may continue staying in the system. The server may break down during the service; the failure and repair times are assumed to follow a general distribution. By using the maximum entropy method (MEM), the approximate formulae for the probability distributions of the number of customers in the system have been derived, which are further used to obtain various system performance measures. A comparative analysis between approximate results established and exact results has also been performed. It is noticed that the maximum entropy approach provides reasonably good approximate solutions for practical purpose.
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