[Paper Review] Age-of-Information in the Presence of Error

Kun Chen, Longbo Huang|arXiv (Cornell University)|May 2, 2016

Age of Information Optimization10 references17 citations

TL;DR

This paper derives exact analytical expressions for peak age-of-information (PAoI) in an M/M/1 queueing system with packet delivery errors, evaluating LCFS and retransmission-based scheduling policies. It shows that both LCFS and retransmission strategies significantly reduce PAoI under high channel utilization and error rates, outperforming FCFS and packet management schemes.

ABSTRACT

We consider the peak age-of-information (PAoI) in an M/M/1 queueing system with packet delivery error, i.e., update packets can get lost during transmissions to their destination. We focus on two types of policies, one is to adopt Last-Come-First-Served (LCFS) scheduling, and the other is to utilize retransmissions, i.e., keep transmitting the most recent packet. Both policies can effectively avoid the queueing delay of a busy channel and ensure a small PAoI. Exact PAoI expressions under both policies with different error probabilities are derived, including First-Come-First-Served (FCFS), LCFS with preemptive priority, LCFS with non-preemptive priority, Retransmission with preemptive priority, and Retransmission with non-preemptive priority. Numerical results obtained from analysis and simulation are presented to validate our results.

Motivation & Objective

• To analyze the impact of packet delivery errors on age-of-information (AoI) in queueing systems.
• To evaluate scheduling policies—LCFS and retransmission—under error-prone transmissions.
• To derive exact PAoI expressions for LCFS with preemptive/non-preemptive priority and retransmission with/without preemption.
• To compare the performance of these policies against FCFS and packet management schemes under varying error rates and channel loads.

Proposed method

• Models an M/M/1 queue with independent packet loss probability p upon service completion.
• Derives PAoI using embedded Markov chains and renewal reward theory, analyzing steady-state behavior.
• Computes expected waiting times and service durations under different scheduling rules, incorporating loss probability.
• Uses conditional expectations to model inter-arrival and service times, accounting for retransmissions and preemption.
• Applies renewal theory to compute the expected time between successful updates, leading to PAoI expressions.
• Validates analytical results via simulation across multiple error regimes (p = 0.1, 0.5, 1) and load conditions (ρ = λ/μ).

Experimental results

Research questions

• RQ1 How does packet delivery error affect the peak age-of-information (PAoI) in an M/M/1 queue?
• RQ2 How do LCFS and retransmission-based scheduling policies compare to FCFS in terms of PAoI under error conditions?
• RQ3 What is the exact analytical expression for PAoI under LCFS with preemptive and non-preemptive priority?
• RQ4 How does retransmission with or without preemption influence PAoI when delivery is unreliable?
• RQ5 In what scenarios do LCFS and retransmission policies outperform traditional FCFS and packet management schemes?

Key findings

• LCFS with preemptive priority achieves lower PAoI than FCFS, especially under high channel utilization and error rates.
• Retransmission with non-preemptive priority suffers performance degradation when error rates are low due to blocking of newer updates.
• PAoI for LCFS non-preemptive and retransmission non-preemptive policies is derived as $ A_P^{LCFS,non} = \frac{1}{\mu} + \frac{1}{\lambda + p\mu} + \frac{1}{\lambda} + \frac{1}{p\mu} $, with exact closed-form expressions.
• Numerical results confirm perfect match between analytical derivations and simulations across all policies and error levels.
• Under high packet loss (p = 0.1), retransmission policies reduce PAoI significantly compared to LCFS and FCFS, demonstrating robustness to errors.
• LCFS policies maintain low PAoI even when packet management schemes fail due to lack of deliveries, confirming their resilience to loss.