Post-processing improvements in multi-objective optimization of general single-server finite queueing networks.

Abstract

An alternative mathematical programming formulation is considered for a mixed-integer optimization problem

in queueing networks. The sum of the blocking probabilities of a general service time, single server, and the finite, acyclic queueing network is minimized, and so are the total buffer sizes and the overall service rates. A multi-objective genetic algorithm (MOGA) and a particle swarm optimization (MOPSO) algorithm are combined to solve this difficult stochastic problem. The derived algorithm produces a set of efficient solutions for multiple objectives in the objective function. The implementation of the optimization algorithms is dependent on the generalized expansion method (GEM), a classical tool used to evaluate the performance of finite queueing networks. We carried out a set of computational experiments to attest to the efficacy and efficiency of the proposed approach. In addition, we present a comparative analysis of the solutions before and after post-processing. Insights obtained from the study of complex queue networks may assist the planning of these types of queueing networks.