*Department of Mathematics, BIT Campus, Anna University, Tiruchirappalli, Tamilnadu, India
**Department of Mathematics, St. Anne's College of Engineering and Technology, Panruti, Tamilnadu, India
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.
M/M/1 queue, vacation, impatience, waiting server timer, Continued fraction, modified Bessel function, Confluent hyper geometric functions
