Real-Time Stochastic Processing Networks with Concurrent Resource Requirements

TL;DR

This paper investigates real-time stochastic processing networks with concurrent resource requirements, providing feasibility conditions and optimal scheduling policies for systems with one or two resources, including a reduction method for two-resource systems.

Contribution

It introduces a reduction method for two-resource systems and derives sharp feasibility conditions and optimal policies for such systems, extending previous single-resource results.

Findings

Feasibility conditions are established for single-resource systems.

A reduction method transforms two-resource systems into equivalent single-resource systems.

Feasibility-optimal scheduling policies are developed for both system types.

Abstract

Stochastic Processing Networks (SPNs) can be used to model communication networks, manufacturing systems, service systems, etc. We consider a real-time SPN where tasks generate jobs with strict deadlines according to their traffic patterns. Each job requires the concurrent usage of some resources to be processed. The processing time of a job may be stochastic, and may not be known until the job completes. Finally, each task may require that some portion of its tasks to be completed on time. In this paper, we study the problem of verifying whether it is feasible to fulfill the requirements of tasks, and of designing scheduling policies that actually fulfill the requirements. We first address these problems for systems where there is only one resource. Such systems are analog to ones studied in a previous work, and, similar to the previous work, we can develop sharp conditions for feasibility and scheduling policy that is feasibility-optimal. We then study systems with two resources where there are jobs that require both resources to be processed. We show that there is a reduction method that turns systems with two resources into equivalent single-resource systems. Based on this method, we can also derive sharp feasibility conditions and feasibility-optimal scheduling policies for systems with two resources.