Waiting-Time Asymptotics for the M/G/2 Queue with Heterogeneous Servers.

摘要

This paper considers a heterogeneous M/G/2 queue. The service times at server 1 are exponentially distributed, and at server 2 they have a general distribution B(dot). The authors present an exact analysis of the queue length and waiting time distribution in case B(dot) has a rational Laplace-Stieltjes transform. When B(dot) is regularly varying at infinity of index-v, the authors determine the tail behavior of the waiting time distribution. This tail is shown to be semi-exponential if the arrival rate is lower than the service rate of the exponential server, and regularly varying at infinity of index 1-v if the arrival rate is higher than that service rate.