Timely CPU Scheduling for Computation-intensive Status Updates

TL;DR

The paper addresses minimizing the long-term age of information (AoI) in computation-heavy status updates by jointly optimizing CPU sleep/wake decisions and dynamic CPU speed under an average power constraint. It casts the problem as a constrained semi-Markov decision process with an uncountable state space and a fractional objective, then employs Dinkelbach's fractional programming to transform it into an average-cost SMDP. A four-loop, value-iteration-based algorithm with Generalized Benders decomposition and dual updates is developed, and the authors prove convergence to an optimal stationary policy, along with structural results for both predictable (PTS) and unpredictable (UTS) task-size cases. Numerical results show significant AoI reductions (up to about 50–55%) and energy savings, especially under tighter power constraints and higher task-size variance, validating the practical impact of joint AoI-aware CPU scheduling. The work provides a foundational framework for energy-aware, AoI-minimizing computation in mobile and edge settings, with clear avenues for extending to queues, multiple servers, and exogenous arrival processes.

Abstract

The proliferation of mobile devices and real-time status updating applications has motivated the optimization of data freshness in the context of age of information (AoI). Meanwhile, increasing computational demands have inspired research on CPU scheduling. Since prior CPU scheduling strategies have ignored data freshness and prior age-minimization strategies have considered only constant CPU speed, we formulate the first CPU scheduling problem as a constrained semi-Markov decision process (SMDP) problem with uncountable space, which aims to minimize the long-term average age of information, subject to an average CPU power constraint. We optimize strategies that specify when the CPU sleeps and adapt the CPU speed (clock frequency) during the execution of update-processing tasks. We consider the age-minimal CPU scheduling problem for both predictable task size (PTS) and unpredictable task size (UTS) cases, where the task size is realized at the start (PTS) or at the completion (UTS) of the task, respectively. To address the non-convex objective, we employ Dinkelbach's fractional programming method to transform our problem into an average cost SMDP. We develop a value-iteration-based algorithm and prove its convergence to obtain optimal policies and structural results for both the PTS and UTS systems. Compared to constant CPU speed, numerical results show that our proposed scheme can reduce the AoI by 50\% or more, with increasing benefits under tighter power constraints. Further, for a given AoI target, the age-minimal CPU scheduling policy can reduce the energy consumption by 50\% or more, with greater AoI reductions when the task size distribution exhibits higher variance.

Figures (8)

• Figure 1: The system model of age-minimal CPU scheduling.
• Figure 2: Age of information $\Delta(t)$ evolution in time.
• Figure 3: Age of information $\Delta(t)$ evolution in time and the time-slot for batch demand $X_{n}$ is realized at the beginning of task $n+1$ and after the completion of task $n+1$.
• Figure 4: Illustrative examples of convex $R^*(y)$ and non-convex $R^*(y)$ in the PTS system.
• Figure 5: Numerical evaluations of the optimal policy with (a) $b=2$, (b) $b=3$ and (c) $b=5$ batches under $\bar{P}=3$ in PTS case. The region between the two red dashed lines represents the support of the stationary distribution of state $y$.

Theorems & Definitions (15)

• Theorem 1: Stationarity
• Lemma 1: PTS Lemma
• Lemma 2
• Theorem 2
• Theorem 3
• Lemma 3: Differentiability of Optimal Value Function
• Corollary 1: Optimal Structure for PTS
• Proposition 1
• Proposition 2
• Corollary 2