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

@article{Boxma2002WaitingTimeAF,
  title={Waiting-Time Asymptotics for the M/G/2 Queue with Heterogeneous Servers},
  author={Onno J. Boxma and Q. Deng and A. P. Zwart},
  journal={Queueing Systems},
  year={2002},
  volume={40},
  pages={5-31}
}
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 −ν, 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… 
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