Asymptotic Analysis of Loss Probabilities in GI/M/m/n Queueing Systems as n Increases to Infinity

Abstract

The paper studies asymptotic behavior of the loss probability for the GI/M/m/n queueing system as n increases to infinity. The approach of the paper is based on applications of classic results of Takács [24] and the Tauberian theorem with remainder of Postnikov [17] associated with the recurrence relation of convolution type. The main result of the paper is associated with asymptotic behavior of the loss probability. Specifically it is shown that in some cases (precisely described in the paper) where the load of the system approaches 1 from the left and n increases to infinity, the loss probability of the GI/M/m/n queue becomes asymptotically independent of the parameter m.

Key Words:

• Asymptotic analysis
• GI/M/m/n queueing system
• loss probabilities
• Tauberian theorem with remainder

Additional information

Notes on contributors

Vyacheslav M. Abramov

Vyacheslav M. Abramov Tadzhik State University (Dushanbe, Tadzhikistan) in 1977. During the period 1977–1992 he worked at the Research Institute of Economics under the Tadzhikistan State Planning Committee (GosPlan). In 1992 he repatriated to Israel and during 1994–2001 worked in software companies of Israel as a software engineer and algorithms developer. In 2002–2005 he was an assistant and lecturer in Judea and Samaria College, Tel Aviv University and Holon Institute of Technology. In 2004 he received a PhD degree from Tel Aviv University, and since 2005 has been working at School of Mathematical Sciences of Monash University (Australia). The scientific interests of him are mainly focused on the theory and application of queueing systems. He is an author of a monograph and various papers published in Journal of Applied Probability, Annals of Operations Research, Queueing Systems, SIAM Journal on Applied Mathematics and other journals.