Product form approximations for queueing networks with multiple servers and blocking

It is shown that the equilibrium-state probabilities for this type of blocking queuing network have an approximate product-form solution, which is based on normalizing the infeasible states that violate station capacities. To obtain the throughput values, a state-space transformation is introduced. This concept is based on finding a nonblocking network with an appropriate total number of jobs of which the number of feasible states is equal or approximately equal to the number of feasible states in the blocking queuing network. This guarantees that the Markov processes describing the evolution networks over time have approximately the same structure, so the throughputs of both systems are approximately equal. The approximations are validated by executing several examples and comparing them with simulation results