Computing Optimal Server-Vacation Policies

Abstract

Abstract The server-vacation model describes many situations in complex manufacturing or communications environments in which a central “server” (such as a robot, materials handling system, or switch) must “service” several different classes of “customers.” The customers compete with each other for the attention of the server, and while the server is handling one class, it appears to be on “vacation” to the others. Management frequently can set operating policies by dynamically changing priorities among the waiting customers to determine who gets served next under different circumstances. This paper describes how to apply the Poisson input, single-server vacation model to derive optimal operating or control policies in these situations. A principal observation is that the determination of an optimal policy can be formulated as a linear program. Hence optimal policies will generally be of the simple switchpoint or retarded switchpoint (hysteretic) types. Moreover, since linear programming codes are widely available, the implementation of these methods and the post-optimality analysis of solutions are relatively straightforward. Additional informationNotes on contributorsWILLIAM G. MARCHAL Prepared while this author was on sabbatical leave from the University of Toledo. Handled by the Applied Probability/Stochastic Processes Department.