Estimating the loss probability under heavy traffic conditions

Authors:
Chia-Hung Wang;Hsing Paul Luh
Affiliations:
College of Management, National Chiao Tung University, No. 1001, Ta Hsueh Road, Hsinchu 30010, Taiwan, ROC;Department of Mathematical Sciences, National Chengchi University, No. 64, Sec. 2, ZhiNan Road, Wen-Shan District, Taipei 11605, Taiwan, ROC
Venue:
Computers & Mathematics with Applications
Year:
2012

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Abstract

This paper studies a multiple-server queueing model under the assumptions of renewal arrival processes and limited buffer size. An approximation for the loss probability and the asymptotic behavior are studied under the heavy traffic conditions. We present an asymptotic analysis of the loss probability when both the arrival rate and number of servers approach infinity. In illustrative examples, the loss probabilities are estimated with heavy traffic under three common distributions of inter-arrival times: exponential, deterministic and Erlang-r distributions, respectively.