Tail asymptotics of the waiting time and the busy period for the {{\varvec{M/G/1/K}}} queues with subexponential service times |
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Authors: | Bin Liu Jinting Wang Yiqiang Q Zhao |
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Institution: | 1. Department of Mathematics, University of Northern Iowa, Cedar Falls, IA, 50614-0506, USA 2. Department of Mathematics, Beijing Jiaotong University, 100044, Beijing, China 3. School of Mathematics and Statistics, Carleton University, Ottawa, ON, K1S 5B6, Canada
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Abstract: | We study the asymptotic behavior of the tail probabilities of the waiting time and the busy period for the $M/G/1/K$ queues with subexponential service times under three different service disciplines: FCFS, LCFS, and ROS. Under the FCFS discipline, the result on the waiting time is proved for the more general $GI/G/1/K$ queue with subexponential service times and lighter interarrival times. Using the well-known Laplace–Stieltjes transform (LST) expressions for the probability distribution of the busy period of the $M/G/1/K$ queue, we decompose the busy period into a sum of a random number of independent random variables. The result is used to obtain the tail asymptotics for the waiting time distributions under the LCFS and ROS disciplines. |
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