AoI in M/G/1/1 Queues with Probabilistic Preemption

TL;DR

This paper analyzes the age of information in a single-server queue with probabilistic preemption, deriving MGFs for AoI and PAoI, and demonstrating the policy's effectiveness through numerical results.

Contribution

It introduces a probabilistic preemption policy in an M/G/1/1 queue and derives analytical expressions for AoI and PAoI.

Findings

MGFs of AoI and PAoI are derived analytically.

Probabilistic preemption improves information freshness.

Numerical results confirm policy effectiveness.

Abstract

We consider a status update system consisting of one source, one server, and one sink. The source generates packets according to a Poisson process and the packets are served according to a generally distributed service time. We consider a system with a capacity of one packet, i.e., there is no waiting buffer in the system, and model it as an M/G/1/1 queueing system. We introduce a probabilistically preemptive packet management policy and calculate the moment generating functions (MGFs) of the age of information (AoI) and peak AoI (PAoI) under the policy. According to the probabilistically preemptive policy, when a packet arrives, the possible packet in the system is replaced by the arriving packet with a fixed probability. Numerical results show the effectiveness of the packet management policy.