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Randomized Scheduling for Periodic Multi-Source Systems with PAoI Violation Guarantees

Kuan-Yu Lin, Wei-Lun Lu, Yu-Pin Hsu, Yu-Chih Huang

TL;DR

This work addresses statistical timeliness guarantees for periodic multi-source status updates by introducing a randomized scheduling framework that yields PAoI violation guarantees without relying on saturated or synchronized traffic. It derives tractable upper bounds in two regimes via $\text{Wallenius}$ noncentral hypergeometric and geometric models, enabling efficient design of heterogenous PAoI targets. Two low-complexity schedulers, Randomized-L and Randomized-S, are proposed to meet individual source requirements, with simulations validating bound accuracy and practical feasibility. The findings demonstrate that randomized scheduling can provide robust PAoI guarantees across a wide range of configurations, supporting timely information in multi-source networks.

Abstract

We study peak Age of Information (PAoI) violation guarantee in a periodic multi-source status update system. The system is served by a shared base station, which requires scheduling. Our main contribution is a randomized scheduling framework that targets heterogeneous PAoI requirements. To that end, we derive numerically trackable upper bounds on the PAoI violation probability in two traffic regimes (long and short period) by leveraging the multivariate noncentral hypergeometric Wallenius distribution and the geometric distribution, respectively. Guided by these bounds, we design two low-complexity randomized scheduling schemes that meet diverse PAoI violation probability targets without the traffic assumption. Simulations validate the bounds and demonstrate feasible operation across a wide range of configurations.

Randomized Scheduling for Periodic Multi-Source Systems with PAoI Violation Guarantees

TL;DR

This work addresses statistical timeliness guarantees for periodic multi-source status updates by introducing a randomized scheduling framework that yields PAoI violation guarantees without relying on saturated or synchronized traffic. It derives tractable upper bounds in two regimes via noncentral hypergeometric and geometric models, enabling efficient design of heterogenous PAoI targets. Two low-complexity schedulers, Randomized-L and Randomized-S, are proposed to meet individual source requirements, with simulations validating bound accuracy and practical feasibility. The findings demonstrate that randomized scheduling can provide robust PAoI guarantees across a wide range of configurations, supporting timely information in multi-source networks.

Abstract

We study peak Age of Information (PAoI) violation guarantee in a periodic multi-source status update system. The system is served by a shared base station, which requires scheduling. Our main contribution is a randomized scheduling framework that targets heterogeneous PAoI requirements. To that end, we derive numerically trackable upper bounds on the PAoI violation probability in two traffic regimes (long and short period) by leveraging the multivariate noncentral hypergeometric Wallenius distribution and the geometric distribution, respectively. Guided by these bounds, we design two low-complexity randomized scheduling schemes that meet diverse PAoI violation probability targets without the traffic assumption. Simulations validate the bounds and demonstrate feasible operation across a wide range of configurations.

Paper Structure

This paper contains 19 sections, 8 theorems, 37 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Randomized Scheduling Policy & PAoI Analysis
  3. Randomized Scheduling Policy
  4. PAoI Analysis
  5. PAoI Analysis for Long Sampling Period Case
  6. PAoI Analysis for Short Sampling Period Case
  7. Randomized Scheduling Weight Design
  8. Randomized-L Scheduling Weight Design
  9. Randomized-S Scheduling Weight Design
  10. Simulation Results
  11. Conclusion
  12. Proof of Lemma \ref{['lemma:W_i(k)']}
  13. Proof of Lemma \ref{['lemma:peak age long']}
  14. Proof of Theorem \ref{['thm:UB_long_sampling_delay_case']}
  15. Proof of Corollary \ref{['coro:asym_decay_rate_rand_policy_long_sampling_delay']}
  16. ...and 4 more sections

Key Result

Lemma 1

The waiting time of update $(i,k)$ can be expressed by that of the previous update $(i,k-1)$, i.e., where $I_{i}(k-1)$ represents the number of preempted packets for source $i$ between update $(i,k-1)$ and $(i,k)$; $N_{i}(k-1)$ accounts for the total idle time of the BS from the start of transmitting update $(i,k-1)$ to the start of transmitting update $(i,k)$; $T_i(k-1)$ accounts for the total b

Figures (2)

  • Figure 1: Achievable region of our randomized policy under different scenarios
  • Figure 2: PAoI violation probability under different scenarios

Theorems & Definitions (8)

  • Lemma 1
  • Lemma 2
  • Theorem 1
  • Corollary 1
  • Lemma 3
  • Theorem 2
  • Corollary 2
  • Lemma 4