Joint optimisation of buffers and network population for closed finite queueing systems

The buffer allocation problem for closed finite queueing networks is a nonlinear integer programming problem which is -Hard. A queueing network decomposition methodology based upon a mean value analysis algorithm is coupled with a nonlinear sequential quadratic programming algorithm to compute the simultaneous optimal buffer allocations and network population via a branch-and-bound scheme for various network topologies. The joint optimisation problem is essentially multi-objective where the decision variable on the population will be treated as a constraint linking the buffer allocation and the throughput which is to be maximised. The fact that the optimisation problem is a concave programming problem assists in the search for an optimal solution. The material handling or transportation system for transferring the finite customer population between the nodes in the network is also examined. Extensive numerical results demonstrate the efficacy of the optimisation methodology.