Abstract
This paper studies an M/M/1 queuing model with server vacation and customers impatient in which the server activates a timer T whenever he returns from his vacation to an empty system and waits idle. This type of situation occurs most commonly in many real life situations as a human behavior. The time-dependent system size probabilities are derived explicitly in terms of modified Bessel functions and confluent hyper geometric functions. Also the time-dependent mean and variance are obtained analytically. Finally, some numerical illustrations are presented.
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