Multiclass Queueing Systems in Heavy Traffic: An Asymptotic Approach Based on Distributional and Conservation Laws

Operations Research · 1997 · Volume 45 · Issue 3

Abstract

We propose a new approach to analyze multiclass queueing systems in heavy traffic based on what we consider as fundamental laws in queueing systems, namely distributional and conservation laws. Methodologically, we extend the distributional laws from single class queueing systems to multiple classes and combine them with conservation laws to find the heavy traffic behavior of the following systems: (a) ∑ GI / G /1 queue under FIFO, (b) ∑ GI / G /1 queue with priorities, (c) Polling systems with general arrival distributions. Compared with traditional heavy traffic analysis via Brownian processes, our approach gives new insight to the asymptotics used, solves systems that traditional heavy traffic theory has not fully addressed, and, more importantly, leads to closed form answers, which compared to simulation are very accurate even for moderate traffic.

Keywords

queues/limit theorems, multiclass queueing systems in heavy traffic, queues/cyclic, priority, multiclass priority and polling systems

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