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 semi-exponential 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.
m/g/2 queue heterogeneous servers queue length waiting time tail behaviour slowly varying function regularly varying distribution semi-exponential distribution