Stationary tail asymptotics of a tandem queue with feedback |
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Authors: | Jiashan Tang Yiqiang Q Zhao |
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Institution: | (1) College of Mathematics and Physics, Nanjing University of Posts and Telecommunications, Nanjing, Jiangsu, 210003, People’s Republic of China;(2) School of Mathematics and Statistics, Carleton University, Ottawa, ON, K1S 5B6, Canada |
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Abstract: | Motivated by applications in manufacturing systems and computer networks, in this paper, we consider a tandem queue with feedback.
In this model, the i.i.d. interarrival times and the i.i.d. service times are both exponential and independent. Upon completion
of a service at the second station, the customer either leaves the system with probability p or goes back, together with all customers currently waiting in the second queue, to the first queue with probability 1−p. For any fixed number of customers in one queue (either queue 1 or queue 2), using newly developed methods we study properties
of the exactly geometric tail asymptotics as the number of customers in the other queue increases to infinity. We hope that
this work can serve as a demonstration of how to deal with a block generating function of GI/M/1 type, and an illustration
of how the boundary behaviour can affect the tail decay rate. |
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Keywords: | Tandem queue Feedback Tail asymptotics α -positivity Geometric decay |
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