Abstract
This paper deals with state dependent M/E k /1 queueing system with server breakdown and working vacation. As soon as the system becomes empty, the server leaves the system and takes vacation for random duration during which it may perform ancillary duty and is called on working vacation. It is assumed that the server may breakdown when it is busy. The vacation duration and the life time of server are exponentially distributed. Both service times in a working vacation and in a busy period are assumed to be Erlangian distributed. Once server starts the service, he continues until all jobs are served. The Chapman Kolmogorov equations are constructed in order to obtain the steady state probability distribution of the number of jobs in the system. The probability generating function is employed to obtain the average queue length and other system characteristics. Numerical experiment is performed to validate the analytical results. The sensitivity analysis has been done to examine the effect of different parameters.
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