Scheduling of Generalized Cambridge Rings

A Generalized Cambridge Ring is a queueing system that can be used as an approximate model of some material handling systems used in modern factories. It consists of one or more vehicles that carry cargo from origins to destinations around a loop, with queues forming when cargo temporarily exceeds the capacity of the system. For some Generalized Cambridge Rings that satisfy the usual traffic conditions for stability, it is demonstrated that some nonidling scheduling polices are unstable. A good scheduling policy will increase the efficiency of these systems by reducing waiting times and by therefore also reducing work in process (WIP). Simple heuristic policies are developed which provide substantial improvements over the commonly used first-in-first-out (FIFO) policy. Variances are incorporated into previously developed fluid models that used only means to produce a more accurate partially discrete fluid mean-variance model, which is used to further reduce waiting times. Optimal policies are obtained for some simple special cases, and simulations are used to compare policies in more general cases. The methods developed may be applicable to other queueing systems.