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Age and Value of Information Optimization for Systems with Multi-Class Updates

Ahmed Arafa, Roy D. Yates

TL;DR

This work addresses optimizing information freshness and value in a multi-class update system with blocking. It develops a stationary, class-dependent threshold policy for starting processing, derived via the Dinkelbach fractional programming framework, and shows a unique parameter $ heta^*$ that minimizes a convex combination of long-term AoI and negative VoI. The optimal policy assigns class-specific minimum inter-update times $ar{y}_i( heta)$ and uses a simple threshold rule ${ W}_i=[ar{y}_i( heta)-{ Y}_i]^+$, with $ heta^*$ found by solving $p( heta^*)=0$ using bisection. The approach is illustrated by a hyperexponential service example, revealing how decay rates, class values, and arrival rate $\lambda$ shape the AoI–VoI tradeoff and the benefits of generating updates under a threshold policy.

Abstract

Received samples of a stochastic process are processed by a server for delivery as updates to a monitor. Each sample belongs to a class that specifies a distribution for its processing time and a function that describes how the value of the processed update decays with age at the monitor. The class of a sample is identified when the processed update is delivered. The server implements a form of M/G/1/1 blocking queue; samples arriving at a busy server are discarded and samples arriving at an idle server are subject to an admission policy that depends on the age and class of the prior delivered update. For the delivered updates, we characterize the average age of information (AoI) and average value of information (VoI). We derive the optimal stationary policy that minimizes the convex combination of the AoI and (negative) VoI. It is shown that the policy has a threshold structure, in which a new sample is allowed to arrive to the server only if the previous update's age and value difference surpasses a certain threshold that depends on the specifics of the value function and system statistics.

Age and Value of Information Optimization for Systems with Multi-Class Updates

TL;DR

This work addresses optimizing information freshness and value in a multi-class update system with blocking. It develops a stationary, class-dependent threshold policy for starting processing, derived via the Dinkelbach fractional programming framework, and shows a unique parameter that minimizes a convex combination of long-term AoI and negative VoI. The optimal policy assigns class-specific minimum inter-update times and uses a simple threshold rule , with found by solving using bisection. The approach is illustrated by a hyperexponential service example, revealing how decay rates, class values, and arrival rate shape the AoI–VoI tradeoff and the benefits of generating updates under a threshold policy.

Abstract

Received samples of a stochastic process are processed by a server for delivery as updates to a monitor. Each sample belongs to a class that specifies a distribution for its processing time and a function that describes how the value of the processed update decays with age at the monitor. The class of a sample is identified when the processed update is delivered. The server implements a form of M/G/1/1 blocking queue; samples arriving at a busy server are discarded and samples arriving at an idle server are subject to an admission policy that depends on the age and class of the prior delivered update. For the delivered updates, we characterize the average age of information (AoI) and average value of information (VoI). We derive the optimal stationary policy that minimizes the convex combination of the AoI and (negative) VoI. It is shown that the policy has a threshold structure, in which a new sample is allowed to arrive to the server only if the previous update's age and value difference surpasses a certain threshold that depends on the specifics of the value function and system statistics.
Paper Structure (10 sections, 1 theorem, 42 equations, 4 figures)

This paper contains 10 sections, 1 theorem, 42 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. Notation
  4. System Model
  5. Problem Formulation and Objective
  6. Main Result
  7. Solution Summary
  8. Discussion
  9. Examples: Hyperexponential Service
  10. Derivation of Theorem \ref{['thm:opt-wait']}

Key Result

Theorem 1

The optimal waiting policy of problem (eqn:opt_gen-main) is given by the class-dependent threshold policy in (eqn:summary:opt-wait), with the class $i$ threshold $\bar{y}_{i}(\theta)$ in (eqn:summary:eq_yj). The value $\theta=\theta^*$ given by the unique solution of $p(\theta^*)=0$ in (eqn:opt_gen-

Figures (4)

  • Figure 1: Sample paths of age $\Delta(t)$ and exponentially decaying value $V(t)$.
  • Figure 2: Examples of (a) the threshold function $h_i(t)$ and (b) the corresponding inverses $h_i^{-1}(\tau)$. The minimum $h_i(0)=-\beta\phi_i$ occurs at $t=0$ and $h_i(t)\to(1-\beta)t$ as $t\to\infty$.
  • Figure 3: AoI vs. VoI tradeoff for a two class system with hyperexponential service: $[p_1,p_2]=[0.5,0.5]$, $[\nu_1, \nu_2]= [100,1]$, $[\alpha_1, \alpha_2]= [0.1,1]$ and $[\mu_1,\mu_2]=[0.1,1]$ (solid lines) or $[\mu_1,\mu_2]=[1,0.1]$ (dotted lines).
  • Figure 4: AoI vs. VoI tradeoff for a two class system with hyperexponential service: $[p_1,p_2]=[0.5,0.5]$, $[\nu_1, \nu_2]= [100,1]$, $[\mu_1,\mu_2]=[1,1]$ and $[\alpha_1, \alpha_2]= [0.1,0.1]$ (solid lines) or $[\alpha_1,\alpha_2]=[0.05,0.05]$ (dotted lines).

Theorems & Definitions (1)

  • Theorem 1