Discrete event systems with real-time constraints: a distributed algorithm for optimal resource sharing

Consideration is given to the problem of resource sharing in a class of systems where requests for service are subject to a real-time constraint on their waiting times. A job is lost if its waiting time exceeds a given deadline, and the objective is to minimize the overall loss probability for the system. At each resource, a controller is given local state information in the form of a queue length, and a threshold-based transfer policy for jobs is used, i.e. a job is transferred to another resource if the local queue length exceeds some value. The authors develop a distributed algorithm where each resource controls its own threshold and job flows to other resources. The algorithm requires sensitivity information with respect to both thresholds and flows. Sensitivity with respect to thresholds can be obtained online by means of an augmented system approach. Issues related to the algorithm properties are also discussed, and simulation results are included to illustrate the use of the distributed algorithm