Tail Asymptotics for the Queue Size Distribution in an M/G/1 Retrial Queue

Journal of Applied Probability - Tập 44 Số 4 - Trang 1111-1118 - 2007
Jerim Kim1, Bara Kim2, Sung‐Seok Ko3
1Korea University
2Department of Mathematics
3Konkuk University

Tóm tắt

We consider an M/G/1 retrial queue, where the service time distribution has a finite exponential moment. We show that the tail of the queue size distribution is asymptotically given by a geometric function multiplied by a power function. The result is obtained by investigating analytic properties of probability generating functions for the queue size and the server state.

Từ khóa


Tài liệu tham khảo

10.1287/moor.1030.0083

10.1007/s11134-006-5223-1

10.1081/STM-120034127

10.1017/S0001867800000677

Kim J. and Kim B. (2007). Regularly varying tail of the waiting time distribution in M/G/1 retrial queue. Submitted.

10.1017/S002190020004081X

10.1007/978-1-4899-2977-8

10.1023/A:1011045621441

10.1016/S0895-7177(99)00129-6

10.1111/j.1467-9574.1984.tb01094.x

Abate, 1997, Asymptotics for M/G/1 low-priority waiting-time tail probabilities, Queueing Systems, 26, 69, 10.1023/A:1019168821588

Tijms, 1987, Stochastic Modelling and Analysis: A Computational Approach

10.1287/opre.43.5.885

10.1007/BF02564721

Choi, 2000, Sharp result on convergence rate for the distribution of GI/M/1/K queues as K tends to infinity, J. Appl. Prob., 37, 1010, 10.1239/jap/1014843080

10.1111/j.1467-9574.2006.00312.x

10.1017/S0001867800013380