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Timely and Energy-Efficient Multi-Step Update Processing

Vishakha Ramani, Ivan Seskar, Roy D. Yates

TL;DR

This paper addresses how to minimize Age of Information (AoI) for updates that require two sequential computations in edge-enabled systems, comparing series (tandem) and parallel processing under a total power budget. It develops a power–speed model with a dynamic power law, formulates an optimization using PWPA to relate service rates to energy, and employs Stochastic Hybrid Systems (SHS) to derive AoI expressions for multiple two-server configurations, including preemptive and non-preemptive series and several parallel policies (P-SSS, P-CAF, P-SIU). A key finding is that the optimal second-step rate should be as large as allowed by the power constraint, with the optimal ratio $\rho^* = \mu_1/\mu_2$ typically not exceeding 1; parallel schemes generally achieve better AoI than series, and step 2 is faster than step 1 for energy-efficient timeliness. These results offer practical guidance for energy-aware timing in edge/offloading systems and suggest future directions such as extending to general service time distributions and dynamic rate-control policies.

Abstract

This work explores systems where source updates require multiple sequential processing steps. We model and analyze the Age of Information (AoI) performance of various system designs under both parallel and series server setups. In parallel setups, each processor executes all computation steps with multiple processors working in parallel, while in series setups, each processor performs a specific step in sequence. In practice, processing faster is better in terms of age but it also consumes more power. We identify the occurrence of wasted power in these setups, which arises when processing efforts do not lead to a reduction in age. This happens when a fresher update finishes first in parallel servers or when a server preempts processing due to a fresher update from preceding server in series setups. To address this age-power trade-off, we formulate and solve an optimization problem to determine the optimal service rates for each processing step under a given power budget. We focus on a special case where updates require two computational steps.

Timely and Energy-Efficient Multi-Step Update Processing

TL;DR

This paper addresses how to minimize Age of Information (AoI) for updates that require two sequential computations in edge-enabled systems, comparing series (tandem) and parallel processing under a total power budget. It develops a power–speed model with a dynamic power law, formulates an optimization using PWPA to relate service rates to energy, and employs Stochastic Hybrid Systems (SHS) to derive AoI expressions for multiple two-server configurations, including preemptive and non-preemptive series and several parallel policies (P-SSS, P-CAF, P-SIU). A key finding is that the optimal second-step rate should be as large as allowed by the power constraint, with the optimal ratio typically not exceeding 1; parallel schemes generally achieve better AoI than series, and step 2 is faster than step 1 for energy-efficient timeliness. These results offer practical guidance for energy-aware timing in edge/offloading systems and suggest future directions such as extending to general service time distributions and dynamic rate-control policies.

Abstract

This work explores systems where source updates require multiple sequential processing steps. We model and analyze the Age of Information (AoI) performance of various system designs under both parallel and series server setups. In parallel setups, each processor executes all computation steps with multiple processors working in parallel, while in series setups, each processor performs a specific step in sequence. In practice, processing faster is better in terms of age but it also consumes more power. We identify the occurrence of wasted power in these setups, which arises when processing efforts do not lead to a reduction in age. This happens when a fresher update finishes first in parallel servers or when a server preempts processing due to a fresher update from preceding server in series setups. To address this age-power trade-off, we formulate and solve an optimization problem to determine the optimal service rates for each processing step under a given power budget. We focus on a special case where updates require two computational steps.

Paper Structure

This paper contains 22 sections, 1 theorem, 70 equations, 10 figures.

Table of Contents

  1. Introduction
  2. AoI and Multi-Step Processing Systems
  3. Age-Power Trade-off
  4. Paper Outline and Main Contributions
  5. Related Work
  6. System Model Overview
  7. Power Consumption Model
  8. Processing Speed and Power Consumption
  9. Problem Formulation
  10. SHS Overview
  11. Problem Formulation: Servers in Series
  12. M/M/1*
  13. M/M/1/2*
  14. M/M/1/1
  15. Synchronous Sequential Service (SSS)
  16. ...and 7 more sections

Key Result

Theorem 1

yates2018ToIT If the discrete-state Markov chain $q(t)\in\mathcal{Q}=\{*\}{0,\ldots,M}$ is ergodic with stationary distribution $\bar{\text{\boldmath{$\pi$}}}=[]>0$ and there exists a non-negative vector $\bar{\mathbf{v}}=[]$ such that then the average age vector is $\mathop{\mathrm{E}}\nolimits[[]]{\mathbf{x}}\!=\!{ \lim_{t\rightarrow\infty}}\mathop{\mathrm{E}}\nolimits[[]]{\mathbf{x}(t)}\!=\! \

Figures (10)

  • Figure 1: Processors in series for source update processing. Processor $i$ is responsible for computation step $i$.
  • Figure 2: Parallel processors setup for source update processing. Each processor executes all $n$ computation steps.
  • Figure 3: The SHS transition/reset maps and Markov chain corresponding to M/M/$1$/$2^*$ model.
  • Figure 4: The SHS transition/reset maps and Markov chain corresponding to Model $M/M/1/1$.
  • Figure 5: The SHS transition/reset maps and Markov chain for synchronous sequential servers.
  • ...and 5 more figures

Theorems & Definitions (1)

  • Theorem 1