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Status Updating with Time Stamp Errors

Md Nurul Absar Siddiky, Ahmed Arafa

TL;DR

This work addresses timeliness-credibility in multi-process status updates where time-stamp errors depend on server activity. It formulates a sleep-wake scheduling optimization to balance AoI and timestamp credibility, deriving a threshold-wait policy for a single process via a Dinkelbach-based approach and proposing two scalable multi-process policies: round-robin with threshold-waiting and asymmetric zero-waiting. Numerical results show the optimal policy depends on system parameters, particularly server recovery rates, and highlight trade-offs between timeliness and data credibility. The findings offer practical scheduling guidelines for reliable AoI in networks with timestamp manipulation or degradation, informing energy-saving and reliability strategies in IoT and control applications.

Abstract

A status updating system is considered in which multiple processes are sampled and transmitted through a shared channel. Each process has its dedicated server that processes its samples before time stamping them for transmission. Time stamps, however, are prone to errors, and hence the status updates received may not be credible. Our setting models the time stamp error rate as a function of the servers' busy times. Hence, to reduce errors and enhance credibility, servers need to process samples on a relatively prolonged schedule. This, however, deteriorates timeliness, which is captured through the age of information (AoI) metric. An optimization problem is formulated whose goal to characterize the optimal processes' schedule and sampling instances to achieve the optimal trade-off between timeliness and credibility. The problem is first solved for a single process setting, where it is shown that a threshold-based sleep-wake schedule is optimal, in which the server wakes up and is allowed to process newly incoming samples only if the AoI surpasses a certain threshold that depends on the required timeliness-credibility trade-off. Such insights are then extended to the multi-process setting, where two main scheduling and sleep-wake policies, namely round-robin scheduling with threshold-waiting and asymmetric scheduling with zero-waiting, are introduced and analyzed.

Status Updating with Time Stamp Errors

TL;DR

This work addresses timeliness-credibility in multi-process status updates where time-stamp errors depend on server activity. It formulates a sleep-wake scheduling optimization to balance AoI and timestamp credibility, deriving a threshold-wait policy for a single process via a Dinkelbach-based approach and proposing two scalable multi-process policies: round-robin with threshold-waiting and asymmetric zero-waiting. Numerical results show the optimal policy depends on system parameters, particularly server recovery rates, and highlight trade-offs between timeliness and data credibility. The findings offer practical scheduling guidelines for reliable AoI in networks with timestamp manipulation or degradation, informing energy-saving and reliability strategies in IoT and control applications.

Abstract

A status updating system is considered in which multiple processes are sampled and transmitted through a shared channel. Each process has its dedicated server that processes its samples before time stamping them for transmission. Time stamps, however, are prone to errors, and hence the status updates received may not be credible. Our setting models the time stamp error rate as a function of the servers' busy times. Hence, to reduce errors and enhance credibility, servers need to process samples on a relatively prolonged schedule. This, however, deteriorates timeliness, which is captured through the age of information (AoI) metric. An optimization problem is formulated whose goal to characterize the optimal processes' schedule and sampling instances to achieve the optimal trade-off between timeliness and credibility. The problem is first solved for a single process setting, where it is shown that a threshold-based sleep-wake schedule is optimal, in which the server wakes up and is allowed to process newly incoming samples only if the AoI surpasses a certain threshold that depends on the required timeliness-credibility trade-off. Such insights are then extended to the multi-process setting, where two main scheduling and sleep-wake policies, namely round-robin scheduling with threshold-waiting and asymmetric scheduling with zero-waiting, are introduced and analyzed.

Paper Structure

This paper contains 8 sections, 1 theorem, 29 equations, 5 figures.

Table of Contents

  1. Introduction
  2. System Model and Problem Formulation
  3. The Single Process Setting
  4. The Multi-Process Setting
  5. Round-Robin Scheduling with Threshold-Waiting
  6. Asymmetric Scheduling with Zero-Waiting
  7. Numerical Results
  8. Conclusion

Key Result

Theorem 1

The optimal solution of problem opt_sgl-tau is given by a threshold-waiting policy $\omega^*(\cdot)=[\xi^*-\cdot]^+$. The threshold $\xi^*$ is given by $\theta^*-\frac{1}{\lambda}-\mu_Y$, provided that the credibility constraint is satisfied. Otherwise, it is given by the solution of eq_thrshld-equl

Figures (5)

  • Figure 1: System model: process $k$'s $i$th sample arrives at time $S_{k,i}$, yet is time-stamped as $S_{k,i}^\prime$ by its server.
  • Figure 2: Example AoI evolution at the destination for $K=2$ processes ($1$ in blue; $2$ in red). Filled circles denote true time stamps and crosses denote received (erroneous) time stamps.
  • Figure 3: Single process AoI vs. time-stamp error for different recovery rate $\alpha$ values.
  • Figure 4: Two processes sum AoI vs. sum time stamp error for different process 1 recovery rate $\alpha_1$ values.
  • Figure 5: Optimal AS policy behavior: $(m_1^*,m_2^*)$ vs. $\alpha_1$.

Theorems & Definitions (1)

  • Theorem 1