Estimating the Loss Probability under Heavy Traffic Conditions

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.