Bounding blocking probabilities and throughput in queueing networks with buffer capacity constraints

We propose a new technique for upper and lower bounding the throughput and blocking probabilities in queueing networks with buuer capacity constraints, i.e, some buuers in the network have nite capacity. By studying the evolution of multinomials of the state of the system in its assumed steady state, we obtain constraints on the possible behavior of the system. Using these constraints, we obtain linear programs whose values upper and lower bound the performance measures of interest, namely throughputs or blocking probabilities. The main advantages of this new technique are that the computational complexity does not increase with the size of the nite buuers and that the technique is applicable to systems in which some buuers have innnite capacity. The technique is demonstrated on examples taken from both manufacturing systems and communication networks. As a special case, for the M/M/s/s queue, we establish the asymptotic exactness of the bounds, i.e, that the bounds on the blocking probability asymptotically approach the exact value as the degree of the multinomials considered is increased to innnity.