Transient Behavior of an M or M or 1 or N Queue with Vacation and Waiting Server
This paper studies the analysis of an M or M or 1 or N vacation queue and waiting server for the transient case. The server starts vacation whenever he becomes free after a busy period. After the completion of vacation period, the server comes back to the system. At that time, if no customer waits in the system for service, he activates a timer and stays idle in the system. If at least one customer arrives before the server's timer expires, the server immediately starts the service. If the timer expires before the arrival of a customer, the server immediately takes another vacation after the timer expires. Using generating function, the transient probabilities for the system size are derived explicitly. The average and variance of system size are also computed in time t. Further, numerical simulations are carried out to visualize the influence of parameters.
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