Multi-Source M/G/1/1 Queues with Probabilistic Preemption

TL;DR

This paper analyzes a multi-source M/G/1/1 queueing system with probabilistic preemption, deriving age of information metrics and demonstrating the policy's effectiveness through numerical results.

Contribution

It introduces a novel probabilistic preemption policy for multi-source M/G/1/1 queues and derives explicit MGFs for AoI and PAoI.

Findings

Derived MGFs for AoI and PAoI for each source.

Numerical results show the policy improves information freshness.

The policy effectively manages packet replacement in the system.

Abstract

We consider a multi-source status update system consisting of multiple independent sources, a single server, and a single sink. Each source generates packets according to a Poisson process, and packets are served according to a general service time distribution. The system has a capacity of one packet, i.e., no waiting buffer, and is modeled as a multi-source M/G/1/1 queueing system. We introduce a probabilistically preemptive packet management policy, under which an existing packet from the same source in the system is replaced by an arriving packet with a fixed probability. We derive the moment generating functions (MGFs) of the age of information (AoI) and peak AoI (PAoI) for each source under this policy. Numerical results demonstrate the effectiveness of the proposed packet management policy.