Queuing Models To Balance Systems With Excess Supply

Abstract

Many manufacturing and service activities can be modeled using queuing theory. The optimization of the long-run solution to imbalances between supply and demand is very important to established businesses. This paper presents a family of queuing models that minimize the expected total cost incurred when restoring equilibrium to a stochastic system that has become unstable due to changes in the environmental parameters affecting its behavior. Analytical expressions for the expected total cost in terms of a policy parameter are derived from which numerically-savvy users can obtain the policy that minimizes the expected total cost. To determine the model parameters that most affect the optimal policy and to facilitate the determination of near-optimal policies, exact solutions were found for a large number of scenarios and then used to fit a regression model. The resulting regression equation can be used by practitioners to find policy parameters that approximately minimize the expected total cost due to imbalances in supply and demand.