Buffer and throughput trade-offs in M/ G/1/ K queueing networks: A bi-criteria approach

Abstract

The optimal design of real-life systems modeled as finite queueing networks is a difficult stochastic optimization problem. Besides being non-linear and including integer variables, different objectives often conflict with each other. For example, one conflicting pair of objectives includes first minimizing the overall number of buffers and then maximizing throughput. In this paper, we present an original methodology to solve a buffer allocation and throughput trade-off problem in single server general queueing networks. An approximation of the complete set of all best solutions, known as the Pareto optimal or non-inferior set, is derived by a special version of a multi-objective genetic algorithm (MOGA). The applied MOGA proves to be suitable for the stochastic trade-off problem. A comprehensive set of computational results attest to the efficiency and efficacy of the proposed methodology. We were able to show from a medium-sized mixed network that the squared coefficient of service time variation plays an important role in buffer allocation, which indicates the importance of using a general service model. Moreover, after the analysis of the solutions in the decision variable space, we confirm that the buffer allocation is highly dependent on the target throughput, which sometimes can be sacrificed in favor of using fewer of the usually expensive buffer spaces.