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Optimizing Age of Information without Knowing the Age of Information

Zhuoyi Zhao, Igor Kadota

TL;DR

This work tackles minimizing the Age of Information (AoI) in a multi-user wireless network when the base station has no, or imperfect, knowledge ofAoI and source timestamps due to unreliable and delayed links. It derives a lower bound on achievable AoI, presents an Optimal Randomized Policy for general renewal packet-generation processes, and develops MMSE estimators for AoI and system times. Building on these estimators, the authors introduce a Max-Weight policy that provably bounds performance and remains effective under no AoI knowledge, as demonstrated by simulations where MW with estimation outperforms the optimal randomized approach. The results show practical viability for AoI-aware scheduling in networks with delayed feedback and unreliable channels, highlighting that estimation-based MW strategies can closely match, or exceed, policies that rely on perfect timestamp information.

Abstract

Consider a network where a wireless base station (BS) connects multiple source-destination pairs. Packets from each source are generated according to a renewal process and are enqueued in a single-packet queue that stores only the freshest packet. The BS decides, at each time slot, which sources to schedule. Selected sources transmit their packet to the BS via unreliable links. Successfully received packets are forwarded to corresponding destinations. The connection between the BS and destinations is assumed unreliable and delayed. Information freshness is captured by the Age of Information (AoI) metric. The objective of the scheduling decisions is leveraging the delayed and unreliable AoI knowledge to keep the information fresh. In this paper, we derive a lower bound on the achievable AoI by any scheduling policy. Then, we develop an optimal randomized policy for any packet generation processes. Next, we develop minimum mean square error estimators of the AoI and system times, and a Max-Weight Policy that leverages these estimators. We evaluate the AoI of the Optimal Randomized Policy and the Max-Weight Policy both analytically and through simulations. The numerical results suggest that the Max-Weight Policy with estimation outperforms the Optimal Randomized Policy even when the BS has no AoI knowledge.

Optimizing Age of Information without Knowing the Age of Information

TL;DR

This work tackles minimizing the Age of Information (AoI) in a multi-user wireless network when the base station has no, or imperfect, knowledge ofAoI and source timestamps due to unreliable and delayed links. It derives a lower bound on achievable AoI, presents an Optimal Randomized Policy for general renewal packet-generation processes, and develops MMSE estimators for AoI and system times. Building on these estimators, the authors introduce a Max-Weight policy that provably bounds performance and remains effective under no AoI knowledge, as demonstrated by simulations where MW with estimation outperforms the optimal randomized approach. The results show practical viability for AoI-aware scheduling in networks with delayed feedback and unreliable channels, highlighting that estimation-based MW strategies can closely match, or exceed, policies that rely on perfect timestamp information.

Abstract

Consider a network where a wireless base station (BS) connects multiple source-destination pairs. Packets from each source are generated according to a renewal process and are enqueued in a single-packet queue that stores only the freshest packet. The BS decides, at each time slot, which sources to schedule. Selected sources transmit their packet to the BS via unreliable links. Successfully received packets are forwarded to corresponding destinations. The connection between the BS and destinations is assumed unreliable and delayed. Information freshness is captured by the Age of Information (AoI) metric. The objective of the scheduling decisions is leveraging the delayed and unreliable AoI knowledge to keep the information fresh. In this paper, we derive a lower bound on the achievable AoI by any scheduling policy. Then, we develop an optimal randomized policy for any packet generation processes. Next, we develop minimum mean square error estimators of the AoI and system times, and a Max-Weight Policy that leverages these estimators. We evaluate the AoI of the Optimal Randomized Policy and the Max-Weight Policy both analytically and through simulations. The numerical results suggest that the Max-Weight Policy with estimation outperforms the Optimal Randomized Policy even when the BS has no AoI knowledge.
Paper Structure (12 sections, 4 theorems, 35 equations, 5 figures, 4 algorithms)

This paper contains 12 sections, 4 theorems, 35 equations, 5 figures, 4 algorithms.

Table of Contents

  1. Introduction
  2. Network Model
  3. Age of Information at the Destinations
  4. Observable Network State at the Base Station
  5. Lower Bound on the achievable EWSAoI
  6. Randomized Scheduling Policy
  7. MMSE Estimation of AoI and System Times
  8. PMF of Packet Generation
  9. MMSE Estimators
  10. Max-Weight Policy with Estimation
  11. Simulation Results
  12. Final Remarks

Key Result

Theorem 2

For any given network model with parameters $\{N,K,\alpha_i,p_i^S,p_i^D,\lambda_i,\theta_i\}$ and any renewal packet generation processes at the sources with PMF $f_i(x)=\mathbb{P}(X_i = x)$, the lower bound on the AoI minimization problem in EWSAoIexpression, namely $L_B \leq \mathbb{E}[J^\pi],\for where $q_i^{L_B}$ yields from Algorithm 1.

Figures (5)

  • Figure 1: Network with $N$ source-destination pairs sharing time-sensitive information via a wireless base station (BS). The BS selects $K$ sources at every decision time $t$. Each selected source $i$ transmits a packet to the BS through a wireless channel with reliability $p_i^S$. The BS forwards all successfully received packets to their corresponding destinations through a heterogeneous multi-hop network with transmission reliability $p_i^D$, transmission delay $\theta_i$, and feedback delay $\omega_i$. The delayed feedback informs the BS whether or not the packet was successfully received by the destination.
  • Figure 2: Illustration of the history of transmission outcomes. The BS keeps track of the indices of the time slots in which successful packet transmissions occurred. These slots are part of the BS observation $\mathbb{O}(t)$ in \ref{['eq:observation']} that enables the BS to estimate AoI and system times.
  • Figure 3: Simulation results of networks with varying expected inter-generation periods $\mathbb{E}[X_i]$ with $N = 8,K = 2,$, $\boldsymbol{\alpha}=[4, 3, 2, 1, 5, 4, 1, 2]$, $p^S_i = i/N, \forall i$, $p^D_i = 0.8, \forall i$ and $\theta_i=5, \forall i$. The inter-generation period follows uniform distributions in (a), geometric distributions in (b), and is constant in (c).
  • Figure 4: Simulation results of networks with varying channel reliabilities with $N = 8, K = 2$, $\boldsymbol{\alpha}=[4, 3, 2, 1, 5, 4, 1, 2]$, $X_i \sim U[2,4]$ and $\theta_i=5, \forall i$. The channel reliabilities $p^D_i$ in (a) is given by $p^D_i = 0.8, \forall i$, and the channel reliabilities $p^S_i$ in (b) is given by $p^S_i = 0.8, \forall i$.
  • Figure 5: Simulation results of networks with varying transmission delay $\theta_i$ with $N = 8, K = 2$, $\boldsymbol{\alpha}=[4, 3, 2, 1, 5, 4, 1, 2]$, $X_i \sim U[2,4]$ , $p^S_i = i/N, \forall i$, $p^D_i = 0.8, \forall i$ and $\theta_i=5, \forall i$.

Theorems & Definitions (13)

  • Remark 1
  • Theorem 2
  • proof
  • Proposition 3
  • proof
  • Theorem 4
  • proof
  • Remark 5
  • Remark 6
  • Theorem 7
  • ...and 3 more