Optimum Monitoring and Job Assignment with Multiple Markov Machines

TL;DR

This paper develops optimal sampling and job assignment strategies for Markov Machines, which process jobs with exponential times, using new metrics to improve system monitoring and request allocation.

Contribution

It introduces optimal sampling schemes and new metrics for monitoring multiple heterogeneous Markov Machines in job processing systems.

Findings

Optimal sampling rate allocation schemes for multiple MMs.

Introduction of false acceptance and rejection ratios as evaluation metrics.

Enhanced job assignment strategies based on system state tracking.

Abstract

We study a class of systems termed Markov Machines (MM) which process job requests with exponential service times. Assuming a Poison job arrival process, these MMs oscillate between two states, free and busy. We consider the problem of sampling the states of these MMs so as to track their states, subject to a total sampling budget, with the goal of allocating external job requests effectively to them. For this purpose, we leverage the $\textit{binary freshness metric}$ to quantify the quality of our ability to track the states of the MMs, and introduce two new metrics termed $\textit{false acceptance ratio}$ (FAR) and $\textit{false rejection ratio}$ (FRR) to evaluate the effectiveness of our job assignment strategy. We provide optimal sampling rate allocation schemes for jointly monitoring a system of $N$ heterogeneous MMs.