Exact Analysis of the Age of Information in the Multi-Source M/GI/1 Queueing System

TL;DR

This paper provides an exact analytical formula for the age of information in a multi-source M/GI/1 queueing system, resolving a long-standing open problem and enabling precise performance evaluation.

Contribution

It derives a simple explicit formula for the stationary distribution and mean of AoI in the multi-source M/GI/1 queue, using the double Laplace transform of the workload.

Findings

Explicit formula for AoI distribution and mean

Utilizes double Laplace transform of workload

Addresses a long-standing open problem in queue analysis

Abstract

We consider a situation that multiple monitoring applications (each with a different sensor-monitor pair) compete for a common service resource such as a communication link. Each sensor reports the latest state of its own time-varying information source to its corresponding monitor, incurring queueing and processing delays at the shared resource. The primary performance metric of interest is the age of information (AoI) of each sensor-monitor pair, which is defined as the elapsed time from the generation of the information currently displayed on the monitor. Although the multi-source first-come first-served (FCFS) M/GI/1 queue is one of the most fundamental model to describe such competing sensors, its exact analysis has been an open problem for years. In this paper, we show that the Laplace-Stieltjes transform (LST) of the stationary distribution of the AoI in this model, as well as the mean AoI, is given by a simple explicit formula, utilizing the double Laplace transform of the transient workload in the M/GI/1 queue.