Waiting-time asymptotics for the M/G/2 queue with heterogeneous servers

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(.). We present an exact analysis of the queue length and waiting time distribution in case B(·) has a rational Laplace-Stieltjes transform. When B(·) is regularly varying at infinity of index -\nu, we determine the tail behaviour of the waiting time distribution. This tail is shown to be semiexponential if the arrival rate is lower than the service rate of the exponential server, and regularly varying at infinity of index 1 - \nu if the arrival rate is higher than that service rate.