Analysis of Markovian Arrivals and Service with Applications to Intermittent Overload

TL;DR

This paper introduces a novel analytical framework for Markovian Arrival and Service systems, providing explicit bounds on mean queue length under fluctuating rates, especially during overload conditions, with tight results in heavy traffic.

Contribution

It develops a new framework based on relative arrivals and completions to analyze the MAMS system, deriving bounds that are tight in heavy traffic and for two-level arrivals.

Findings

Derived explicit bounds for mean queue length in MAMS systems.

Framework captures transient effects of fluctuating rates on queue length.

Bounds are tight in heavy traffic and for two-level overload scenarios.

Abstract

In many important real-world queueing settings, arrival and service rates fluctuate over time. We consider the MAMS system, where the arrival and service rates each vary according to an arbitrary finite-state Markov chain, allowing intermittent overload to be modeled. This model has been extensively studied, and we derive results matching those found in the literature via a somewhat novel framework. We derive a characterization of mean queue length in the MAMS system, with explicit bounds for all arrival and service chains at all loads, using our new framework. Our bounds are tight in heavy traffic. We prove even stronger bounds for the important special case of two-level arrivals with intermittent overload. Our framework is based around the concepts of relative arrivals and relative completions, which have previously been used in studying the MAMS system, under different names. These quantities allow us to tractably capture the transient correlational effect of the arrival and service processes on the mean queue length.