Summary: (Blank Abstract)

Jackson's Theorem is concerned only with networks of single-server queues having exponentially distributed service times. The theorem states that the steady state queue occupancy distribution is the product of the individual queue distributions when each queue is treated as an independent, M/M/1 queue with the appropriate arrival rate. For this reason, networks of single server queues with exponential service times and Poisson arrival rates from the "outside world" are called product-form or separable queueing networks.

The BCMP Theorem takes this idea much farther. It proves a
similar result for a much larger class of queueing networks. In
particular, queues are not constrained to have exponentially
distributed service rates, although if the service time
distribution for a queue in not exponential, the queue can have
only one of three queueing disciplines *not*
including FCFS.

Assume a computer network consists of

- FCFS with class-independent exponentially distributed service time
- PS (processor sharing)
- IS (infinite server)
- LCFSPR (last come first served preemptive resume)

Also assume that routing of jobs among queues is state-independent. That is, jobs are routed among the queues according to fixed probabilities (which may be different for different classes of jobs) and not based on the number of jobs in the queues.

Then the steady state probability distribution