A two server Poisson queue with state dependent hybrid service discipline with variant breakdown
Keywords:
Markovian queue, Homogeneous mode of service, Heterogeneous mode of service, Variant breakdown, Repair, Time independent solution, System measuresAbstract
A Poisson queue with two servers and with system breakdown has been
considered in this paper. In addition, the servers are in homogeneous mode
upto serving of N customers. After which the servers changed to heterogeneous
mode. If the system is busy failure may occur to the system. As in the case
of service policy, in a similar way two different breakdown policies are assumed.
At the instant of breakdown, if there are N or less than N customers in the
system the system is completely shutdown. Otherwise, the servers provides service
with different service rates. The number of arrivals and the number of service
completions follows different Poisson distributions. The interbreakdown periods
follows negative exponential distributions. Immediately the repair process takes
place. The repair periods are random variables, follows negative exponential
distribution. This model is defined and the time independent solutions are
derived. Also some system performance measures are obtained. To show the
practical applicability of the model some numerical illustrations are provided.
The corresponding cost model is defined and analyzed.
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