Abstract
We consider a multiple vacation queueing system in which a vacation following a busy period has a different distribution from a vacation that is taken without serving at least one customer. For ease of analysis it is assumed that the service times are exponentially distributed and the two vacation types are also exponentially distributed but with different means. The steady-state solution is obtained.
Highlights
A vacation queueing system is one in which a server may become unavailable for a random period of time from a primary service center
Server vacations are useful for those systems in which the server wishes to utilize his idle time for different purposes, and this makes the queueing model be applicable to a variety of real world stochastic service systems
We have considered an interesting class of multiple vacation queueing systems in which two types of vacations are encountered
Summary
A vacation queueing system is one in which a server may become unavailable for a random period of time from a primary service center. The server can come back to the normal working level before the vacation ends They obtained the steady-state distributions for the number of customers in the system at arrival epochs and waiting time for an arbitrary customer using the matrixgeometric solution method. If he returns from a break and there is no waiting customer, he goes back on another break whose length has another distribution This time can be used to attend to other duties at the station and usually has a shorter mean duration than the coffee/personal break. The practical application of this model is that durations of vacations taken after a nonzero busy period can be longer than those that are taken when the server did not serve any customer prior to the vacation in order to give the server a sufficient time to rest following some hectic busy period.
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