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

2025-12-02

AI Summary

This paper investigates age-of-information (AoI) and peak AoI (PAoI) analysis in multi-source status-updating systems under the M/G/1/1 queueing model with no waiting buffer. To overcome the freshness limitation inherent in conventional non-preemptive policies, we propose a source-aware probabilistic preemption scheduling mechanism: newly arriving packets preempt the currently served packet with a source-dependent probability. We derive, for the first time, closed-form moment-generating functions (MGFs) of AoI and PAoI for each source in a multi-source M/G/1/1 system, enabling fine-grained characterization of timeliness. The theoretical analysis assumes Poisson arrivals and general service times. Numerical results demonstrate that the proposed scheme significantly reduces both average AoI and tail-age risk, thereby enhancing freshness guarantees for heterogeneous information sources.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Multiagent Systems: Mechanism Design
• Knowledge Representation and Reasoning: Preferences

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Web Mining and Content Analysis: Content-based information diffusion
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

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.

Problem

• Analyzes multi-source M/G/1/1 queue with probabilistic preemption policy
• Derives age of information metrics under probabilistic packet replacement
• Evaluates packet management effectiveness for status update systems

Innovation

• Probabilistic preemption policy for packet replacement
• M/G/1/1 queue model with no waiting buffer
• Deriving age of information moment generating functions