Definition of A BCMP Network
A network of m interconnected queues is known as a BCMP network if each of the queues is of one of the following four types:
- FCFS discipline where all customers have the same negative exponential service time distribution. The service rate can be state dependent, so write for the service rate when the queue length is j.
- Processor sharing queues
- Infinite server queues
- LCFS with pre-emptive resume (work is not lost)
In the final three cases, service time distributions must have rational Laplace transforms. This means the Laplace transform must be of the form
Also, the following conditions must be met.
- external arrivals to node i (if any) form a Poisson process,
- a customer completing service at queue i will either move to some new queue j with (fixed) probability or leave the system with probability, which is non-zero for some subset of the queues.
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