A nonblocking algorithm for the distributed simulation of FCFS queueing networks with irreducible Markovian routing

We consider the distributed simulation of queueing networks of FCFS servers with infinite buffers, and irreducible Markovian routing. We first show that for either the conservative or optimistic synchronization protocols the simulation of such networks can prematurely block owing to event buffer exhaustion. Buffer exhaustion can occur in the simulator, whether or not the simulator is stable, and, unlike simulators of feedforward networks, cannot be prevented by interprocessor flow control alone. We propose a simple technique (which we call compactification), which, when used in conjunction with interprocessor flow control, prevents buffer exhaustion. This leads to a general algorithm, for both conservative and optimistic synchronization, that allows one to simulate the queueing network within the finite amount of memory available at each processor. For each algorithm presented, we also provide the proof that it cannot get deadlocked owing to buffer exhaustion.