Optimal static distribution of prioritized customers to heterogeneous parallel servers

The main aim of this paper is to present a model for distributing prioritized customers to heterogeneous parallel servers. A queueing optimization model is proposed in the form of a nonlinear programming problem having linear constraints, so that the average mean response time taken over all job requests is minimized. A solution procedure is developed by employing the convexity of the performance objective. A distribution system is illustrated to demonstrate the applicability of the model. In addition, the model is extended to the case of class-dependent policies.