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Optimizing Peak Age of Information in MEC Systems: Computing Preemption and Non-preemption

Jianhang Zhu, Jie Gong

TL;DR

The paper tackles minimizing average PAoI in MEC-enabled status-update systems by jointly considering transmission and computation delays under generate-at-will sources. It establishes that in the non-preemptive case, fixed-threshold policies are optimal, while in the preemptive case with exponential computation times, a transmission-aware threshold policy is optimal. Key insights include that preemption is not always superior and that optimal thresholds rise with longer transmission relative to computation time in preemptive settings but fall in non-preemptive ones. Numerical results corroborate the theory across exponential and Pareto distributions, providing practical guidelines for MEC scheduling to maintain information freshness. This work advances understanding of how to design efficient update policies in MEC systems with coupled transmission and computation resources.

Abstract

The freshness of information in real-time monitoring systems has received increasing attention, with Age of Information (AoI) emerging as a novel metric for measuring information freshness. In many applications, update packets need to be computed before being delivered to a destination. Mobile edge computing (MEC) is a promising approach for efficiently accomplishing the computing process, where the transmission process and computation process are coupled, jointly affecting freshness. In this paper, we aim to minimize the average peak AoI (PAoI) in an MEC system. We consider the generate-at-will source model and study when to generate a new update in two edge server setups: 1) computing preemption, where the packet in the computing process will be preempted by the newly arrived one, and 2) non-preemption, where the newly arrived packet will wait in the queue until the current one completes computing. We prove that the fixed threshold policy is optimal in a non-preemptive system for arbitrary transmission time and computation time distributions. In a preemptive system, we show that the transmission-aware threshold policy is optimal when the computing time follows an exponential distribution. Our numerical simulation results not only validate the theoretical findings but also demonstrate that: 1) in our problem, preemptive systems are not always superior to non-preemptive systems, even with exponential distribution, and 2) as the ratio of the mean transmission time to the mean computation time increases, the optimal threshold increases in preemptive systems but decreases in non-preemptive systems.

Optimizing Peak Age of Information in MEC Systems: Computing Preemption and Non-preemption

TL;DR

The paper tackles minimizing average PAoI in MEC-enabled status-update systems by jointly considering transmission and computation delays under generate-at-will sources. It establishes that in the non-preemptive case, fixed-threshold policies are optimal, while in the preemptive case with exponential computation times, a transmission-aware threshold policy is optimal. Key insights include that preemption is not always superior and that optimal thresholds rise with longer transmission relative to computation time in preemptive settings but fall in non-preemptive ones. Numerical results corroborate the theory across exponential and Pareto distributions, providing practical guidelines for MEC scheduling to maintain information freshness. This work advances understanding of how to design efficient update policies in MEC systems with coupled transmission and computation resources.

Abstract

The freshness of information in real-time monitoring systems has received increasing attention, with Age of Information (AoI) emerging as a novel metric for measuring information freshness. In many applications, update packets need to be computed before being delivered to a destination. Mobile edge computing (MEC) is a promising approach for efficiently accomplishing the computing process, where the transmission process and computation process are coupled, jointly affecting freshness. In this paper, we aim to minimize the average peak AoI (PAoI) in an MEC system. We consider the generate-at-will source model and study when to generate a new update in two edge server setups: 1) computing preemption, where the packet in the computing process will be preempted by the newly arrived one, and 2) non-preemption, where the newly arrived packet will wait in the queue until the current one completes computing. We prove that the fixed threshold policy is optimal in a non-preemptive system for arbitrary transmission time and computation time distributions. In a preemptive system, we show that the transmission-aware threshold policy is optimal when the computing time follows an exponential distribution. Our numerical simulation results not only validate the theoretical findings but also demonstrate that: 1) in our problem, preemptive systems are not always superior to non-preemptive systems, even with exponential distribution, and 2) as the ratio of the mean transmission time to the mean computation time increases, the optimal threshold increases in preemptive systems but decreases in non-preemptive systems.
Paper Structure (31 sections, 11 theorems, 63 equations, 10 figures, 2 algorithms)

This paper contains 31 sections, 11 theorems, 63 equations, 10 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Main Results
  4. System Model And Problem Formulation
  5. System Model
  6. Problem Formulation
  7. The Non-Preemption Case
  8. The Optimality of Continuous Working Policies
  9. The Optimality of Randomized Threshold Policies
  10. The Optimality of Fixed Threshold Policies
  11. Special Cases
  12. Exponentially Distributed Computation Time
  13. Exponentially Distributed Transmission Time
  14. The Service Preemption Case
  15. The Optimality of Continuous Working Policies
  16. ...and 16 more sections

Key Result

Lemma 1

In the optimal policy for the case $\omega\equiv \text{wop}$, the source submits a new packet before or immediately when the old packet is delivered to the destination, which means $S_k\le D_{k-1}$ for all $k=1,2,\cdots$.

Figures (10)

  • Figure 1: Status update system with MEC.
  • Figure 2: Age curve in two systems.
  • Figure 3: Average PAoI vs. $\theta$ under the fixed threshold policy with exponential transmission and computation time for different $\mathbb{E}[T]:\mathbb{E}[C]$ in the non-preemptive system.
  • Figure 4: Average PAoI vs. $\beta$ under the transmission-aware threshold policy with exponential transmission and computation time for different $\mathbb{E}[T]:\mathbb{E}[C]$ in the service preemptive system.
  • Figure 5: Average PAoI achieved by different policies under exponential transmission and computation time with varying $\frac{\mathbb{E}[T]}{\mathbb{E}[C]}$ in two systems.
  • ...and 5 more figures

Theorems & Definitions (22)

  • Lemma 1
  • proof
  • Corollary 1
  • Definition 1: Continuous Working Policy
  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Proposition 1
  • proof
  • ...and 12 more