M/G/∞ tandem queues

We consider a series of queues with Poisson input. Each queueing system contains an infinite number of service channels. The service times in each channel have a general distribution. For this M/G∞ tandem model we obtain the joint time-dependent distribution of queue length and residual service times at each queue. This leads to an expression for the joint stationary distribution of the number of customers in various queues at the arrival epochs of a tagged customer at those queues.