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 - v, we 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.
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