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On berry–esseen rate for queue length of the GI/G/K system in heavy traffic

Published online by Cambridge University Press:  14 July 2016

Xing Jin*
Affiliation:
Anhui University
*
Postal address: Department of Mathematics, Anhui University, Hefei City, Anhui Province, People's Republic of China.

Abstract

This paper provides Berry–Esseen rate of limit theorem concerning the number of customers in a GI/G/K queueing system observed at arrival epochs for traffic intensity ρ > 1. The main method employed involves establishing several equalities about waiting time and queue length.

Type
Research Papers
Copyright
Copyright © Applied Probability Trust 1988 

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References

[1] Chow, Y. S. and Teicher, H. (1978) Probability Theory. Springer-Verlag, Berlin.Google Scholar
[2] Xing, Jin (1986) On the Berry–Esseen type theorems of GI/G/K system. To appear.Google Scholar
[3] Xing, Jin and Rongxing, Wang (1986) On Berry–Esseen rate for the waiting time of GI/G/1 system in heavy traffic. Acta Math. Sinica 29, 651657.Google Scholar
[4] Kennedy, D. P. (1972) Rates of convergence for queue in heavy traffic, I. Adv. Appl. Prob. 4, 357391.Google Scholar
[5] Nagaev, S. V. (1970) On the speed of convergence in a boundary problem, I and II. Theory Prob. Appl. 15, 179199; 419441.Google Scholar
[6] Petrov, P. P. (1975) Sums of Independent Random Variables. Springer-Verlag, Berlin.Google Scholar
[7] Sawyer, S. (1972) Rates of convergence for some functionals in probability. Ann. Math. Statist. 43, 273284.Google Scholar