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Utilizing the Perceived Age to Maximize Freshness in Query-Based Update Systems

Sahan Liyanaarachchi, Sennur Ulukus, Nail Akar

TL;DR

The paper addresses maximizing mean binary freshness (MBF) in query-based monitoring of a finite-state CTMC under generic forward and backward delays by relaxing exponential-delay and instantaneous-feedback assumptions. It develops a semi-Markov decision process (SMDP) framework to derive waiting-based sampling policies and demonstrates that threshold-like policies can be optimal under certain delay-distribution conditions. The authors propose multiple policy classes—state-independent, delay-independent, greedy, and the fully optimal joint state-delay policy—each enabling policy iteration to compute solutions, with rigorous analysis and Dinkelbach linearization for the fractional objective. Numerical results show substantial MBF gains over zero-wait and constant-wait baselines across various delay configurations, highlighting the practical impact for pull-based remote monitoring and resource management scenarios where query and reply delays are non-negligible.

Abstract

Query-based sampling has become an increasingly popular technique for monitoring Markov sources in pull-based update systems. However, most of the contemporary literature on this assumes an exponential distribution for query delay and often relies on the assumption that the feedback or replies to the queries are instantaneous. In this work, we relax both of these assumptions and find optimal sampling policies for monitoring continuous-time Markov chains (CTMC) under generic delay distributions. In particular, we show that one can obtain significant gains in terms of mean binary freshness (MBF) by employing a waiting based strategy for query-based sampling.

Utilizing the Perceived Age to Maximize Freshness in Query-Based Update Systems

TL;DR

The paper addresses maximizing mean binary freshness (MBF) in query-based monitoring of a finite-state CTMC under generic forward and backward delays by relaxing exponential-delay and instantaneous-feedback assumptions. It develops a semi-Markov decision process (SMDP) framework to derive waiting-based sampling policies and demonstrates that threshold-like policies can be optimal under certain delay-distribution conditions. The authors propose multiple policy classes—state-independent, delay-independent, greedy, and the fully optimal joint state-delay policy—each enabling policy iteration to compute solutions, with rigorous analysis and Dinkelbach linearization for the fractional objective. Numerical results show substantial MBF gains over zero-wait and constant-wait baselines across various delay configurations, highlighting the practical impact for pull-based remote monitoring and resource management scenarios where query and reply delays are non-negligible.

Abstract

Query-based sampling has become an increasingly popular technique for monitoring Markov sources in pull-based update systems. However, most of the contemporary literature on this assumes an exponential distribution for query delay and often relies on the assumption that the feedback or replies to the queries are instantaneous. In this work, we relax both of these assumptions and find optimal sampling policies for monitoring continuous-time Markov chains (CTMC) under generic delay distributions. In particular, we show that one can obtain significant gains in terms of mean binary freshness (MBF) by employing a waiting based strategy for query-based sampling.
Paper Structure (17 sections, 7 theorems, 28 equations, 4 figures)

This paper contains 17 sections, 7 theorems, 28 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. System model
  4. Mean Binary Freshness
  5. Waiting Policies
  6. State-Independent Waiting Policy
  7. Delay-Independent Waiting Policy
  8. Greedy Waiting Policy
  9. Optimal Waiting Policies
  10. Numerical Results
  11. Conclusion
  12. Proof of Theorem \ref{['thrm:fresh_gen']}
  13. Proof of Corollary \ref{['cor:fresh_gen']}
  14. Proof of Lemma \ref{['lem:state_ind']}
  15. Proof of Theorem \ref{['thrm:state_ind_wait']}
  16. ...and 2 more sections

Key Result

Theorem 1

The MBF under a stationary waiting policy is , where $X$ is a discrete random variable over the states $\mathcal{S}$ with probability mass function $\bm\phi=\{\phi_1,\phi_2,\dots,\phi_S\}$ and $D'$ is an independent copy of $D$. Further, $\phi_i$ is the unique solution that satisfies the following equations, where $\tilde{P}_{i,j}=\int_D\int_YP_{i,j}(d+W(i,d)+y)\,\dd{F^Y(y)}\,\dd{F^D(d)}$.

Figures (4)

  • Figure 1: System model.
  • Figure 2: Variation of mean binary freshness for a binary CTMC with $\alpha=1$, $\beta=0.1$, $Y=0$ and $D=\{0,d_1\}$ with probabilities $\{0.5,0.5\}$.
  • Figure 3: Variation of mean binary freshness for a binary CTMC with $\alpha=0.6$, $\beta=0.4$, $Y=0$ and $D=\{0,d_1\}$ with probabilities $\{0.5,0.5\}$.
  • Figure 4: Variation of mean binary freshness for a binary CTMC with $\alpha=1$, $\beta=0.1$, $Y= \{0.3,0.5,1\}$ with probabilities $\{0.3,0.3,0.4\}$ and $D=\{0,d_1\}$ with probabilities $\{0.5,0.5\}$.

Theorems & Definitions (10)

  • Theorem 1
  • Corollary 1
  • Lemma 1
  • Corollary 2
  • Theorem 2
  • Corollary 3
  • Remark 1
  • Remark 2
  • Theorem 3
  • Remark 3