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Age-of-Information vs. Value-of-Information Scheduling for Cellular Networked Control Systems
Onur Ayan, Mikhail Vilgelm, Markus Klügel, Sandra Hirche, Wolfgang Kellerer
TL;DR
Networked control systems need scheduling metrics that account for both information freshness and uncertainty evolution under constrained wireless communication. The paper models Value-of-Information as a function of Age-of-Information and system parameters, then compares centralized AoI- and VoI-based schedulers. Simulations show that prioritizing higher-VoI transmissions reduces uncertainty and improves control performance relative to maintaining equal freshness across subsystems.
Problem
Wireless networked control systems contain heterogeneous loops whose uncertainty evolves with system dynamics, raising whether freshness alone adequately guides scheduling under constrained communication.
Method
The paper formulates VoI as uncertainty reduction based on AoI and system parameters, then designs centralized AoI- and VoI-based schedulers for a cellular two-hop NCS.
Results
Prioritizing higher-VoI transmissions reduces estimation error and network-induced error more than regular or equally fresh updates, although VoI can sacrifice information freshness and fairness.
Takeaways & Limitations
AoI alone does not capture all networked control-loop requirements, while VoI-based prioritization provides lower uncertainty and better control performance in the studied setting.
Takeaways & Limitations
The analysis assumes uniformly distributed subsystem timing and equal channel qualities among loops, distinguishing uplink- and downlink-bottleneck cases.
Abstract
from arXiv · showhide
Age-of-Information (AoI) is a recently introduced metric for network operation with sensor applications which quantifies the freshness of data. In the context of networked control systems (NCSs), we compare the worth of the AoI metric with the value-of-information (VoI) metric, which is related to the uncertainty reduction in stochastic processes. First, we show that the uncertainty propagates non-linearly over time depending on system dynamics. Next, we define the value of a new update of the process of interest as a function of AoI and system parameters of the NCSs. We use the aggregated update value as a utility for the centralized scheduling problem in a cellular NCS composed of multiple heterogeneous control loops. By conducting a simulative analysis, we show that prioritizing transmissions with higher VoI improves performance of the NCSs compared with providing fair data freshness to all sub-systems equally.
1 INTRODUCTION
Industrial networked control systems use wireless communication for applications such as monitoring, control, and tele-robotics, but constrained and interference-prone channels make prioritization and scheduling necessary. This paper compares freshness-based and uncertainty-based scheduling metrics for heterogeneous control loops sharing a cellular network.
- Industrial applications such as remote monitoring, control, and tele-robotics are major use cases motivating wireless networked control systems.
- Wireless spectrum constraints and interference effects motivate prioritization and efficient scheduling for networked control systems.
- 5G machine-type communications support diverse applications whose distinct requirements call for tailored communication solutions.
- Prior work commonly optimizes resource-constrained networked control systems using stationary or control-agnostic policies, while cross-layer metrics can improve scheduling.
- The paper asks whether Age-of-Information or Value-of-Information is more suitable for scheduling multiple control loops sharing the same network.
- The studied cellular system uses a centralized scheduler to coordinate communication for multiple heterogeneous stochastic control systems over a resource-constrained two-hop network.
2 SCENARIO AND PROBLEM STATEMENT
The paper models multiple heterogeneous LTI control loops sharing a resource-constrained cellular network, where centralized scheduling determines which sensor updates traverse uplink and downlink resources. It represents controller knowledge through packet reception, estimation, AoI, and a link-based VoI metric tied to network-induced estimation error.
- System and network model: Each subsystem contains a plant, sensor, and controller, with the controller and plant co-located while the sensor communicates remotely.The cellular network connects all sensors and controllers through a common base station.
- System and network model: Packets generated periodically at sensors are stored until transmission, while centralized uplink and downlink decisions select which subsystem packets use finite resource sets.Each scheduled transmission consumes one resource and is received without packet loss at the end of the slot.
- State estimation: The controller’s state observation is represented by a reception indicator: δ_i[k_i] = 1 when the current state arrives, and δ_i[k_i] = 0 when it is dropped or waiting in the network.A Kalman-like estimator compensates for packet drops and delays using the controller’s available information set.
- Age and information state: AoI measures elapsed control steps since the latest received state, evolves linearly with control steps, and need not increase linearly with transmission time.Successful downlink reception extends the controller’s information set with the newly received observation.
- Value of information: For a stable scalar plant with A_1 = 0.75, expected estimation error converges to a finite value even as AoI becomes infinitely large.This behavior contrasts with the dependence of uncertainty propagation on plant dynamics illustrated for multiple scalar plants.
- Value of information: The link-based VoI metric measures uncertainty reduction from a receiver’s information set after successful uplink or downlink transmission.Network-induced estimation error is defined as the difference between the true state and the recursively computed state estimate.
3 JOINT SCHEDULING DESIGN
The paper designs joint uplink/downlink schedulers that prioritize transmissions using AoI or VoI under resource constraints, then uses greedy per-link VoI scheduling because global optimization is computationally expensive. The resulting VoI-based upper bound outperforms optimal AoI scheduling in the reported analysis.
- Scheduler design: The centralized scheduler prioritizes control sub-systems using AoI or VoI and jointly designs uplink and downlink decisions.Equal channel qualities permit separate uplink- and downlink-bottleneck cases; when uplink resources bottleneck, received uplink transmissions are forwarded immediately, whereas downlink bottlenecks require joint scheduling.
- AoI scheduling: With equal successful-transmission probabilities, greedy scheduling is age-optimal for a single hop and can be extended to the two-hop setting.The construction matches transmissions across hops according to the bottleneck: downlink schedules can repeat prior uplink schedules, or uplink schedules can fetch values one step before downlink transmission.
- AoI scheduling: The two-hop AoI construction avoids artificially increasing age by forwarding uplink data directly or fetching downlink data one step earlier, depending on the bottleneck.In both cases, optimal scheduling decisions are needed for only one hop.
- VoI scheduling: The proposed application-aware scheduler values uplink and downlink packets from their hop-specific AoI while minimizing expected quadratic network-induced error.The scheduler jointly allocates resources on both hops.
- VoI scheduling: Because the full scheduling problem is combinatorial and not polynomial-time solvable, the paper uses separate greedy solutions that maximize transmitted VoI on each link.The global optimum is computationally expensive and considered out of scope for dynamic schedulers.
- Evaluation: The VoI-based solution provides an upper bound for the optimal cost and outperforms optimal AoI scheduling in the reported analysis.The comparison concerns the network scheduling objective under the two-hop resource-constrained setting.
4 NUMERICAL EVALUATION
The simulations compare AoI- and VoI-based centralized schedulers across heterogeneous control loops, varying network size and UL/DL resources. VoI reduces integrated control error more effectively, but can sacrifice freshness for less valuable or dominated loops.
- Simulation setup: The study simulates heterogeneous scalar LTI sub-systems with four plant classes, varying total sub-systems and UL resources while fixing RDL = 3.Performance is measured using average AoI per loop and Integrated Absolute Error per loop.
- Scaling with network size: For AoI scheduling, average age increases linearly with N, with a higher slope when resources decrease from three per hop to one per hop.The scheduler treats plant types equally, making staleness proportional to network load and available resources.
- Scaling with network size: VoI scheduling causes a drastic increase in average AoI after N = 20 for RUL = RDL = 1 and after N = 80 for RUL = RDL = 3.From N = 40 and N = 100 onward, respectively, average AoI goes to infinity in these configurations.
- Scaling with network size: Plants with Ai = 0.75 never transmit under VoI scheduling because they are dominated by non-converging plants with Ai ≥1.Their uncertainty contribution converges, whereas higher-dynamics plants remain non-converging.
- Error performance: VoI scheduling outperforms AoI scheduling on Integrated Absolute Error, and the performance gap expands as resource inadequacy increases.The paper attributes this advantage to the non-linear growth of network-induced error with age.
- UL/DL sensitivity: For N = 20, both schedulers perform similarly, and adding uplink resources beyond RUL = 3 has no effect because all loops receive sufficient transmission opportunities.Reducing uplink resources decreases both performance indicators through lower throughput.
- UL/DL sensitivity: With N = 120, increasing RUL from 1 toward 9 produces a converging decrease in Σe, while average AoI becomes finite again for RUL ∈{6, 9}.The VoI scheduler benefits from additional uplink resources by evaluating packet content and prioritizing more valuable information.
5 RELATED WORK
Related work contrasts application-agnostic freshness scheduling with control-aware cross-layer approaches. The paper builds on VoI’s non-linear behavior to define a more application-specific scheduling metric.
- Control-aware scheduling: Prior NCS scheduling work often optimizes steady-state behavior under expected resource constraints while abstracting network behavior as control-agnostic.The paper identifies varying wireless channels, control-loop trade-offs, and multiple-loop coexistence as additional scheduling concerns.
- AoI and VoI: AoI introduced a uniform notion of information freshness for application-layer scheduling across multiple users and applications.The paper distinguishes this uniform freshness measure from application-dependent uncertainty evolution.
- AoI and VoI: Building on prior work defining VoI’s non-linear behavior, this paper defines VoI as a function of AoI and system parameters.This extends cross-layer scheduling toward application-specific control requirements.
6 CONCLUSIONS
The conclusion finds that AoI alone does not capture the requirements of two-hop networked control loops. Scheduling by VoI reduces estimation error more effectively than providing regular updates to every subsystem.
- Main conclusion: AoI captures information freshness but not the application-dependent evolution of uncertainty in networked control systems.The paper formulates estimation error as a function of AoI and application-specific system parameters.
- Main conclusion: Using VoI as the scheduling metric leads to lower estimation error in the stochastic process than providing regular updates to each sub-system.The conclusion is based on the paper’s simulative comparison of scheduling policies.
A PROOF OF LEMMA 1
The proof begins from positive age Δ_i[k_i] and establishes the stated lemma condition through the corresponding equation.
- Proof setup: The proof assumes Δ_i[k_i] > 0 and uses equation (11) as the starting condition for Lemma 1.The supplied passage introduces the proof but does not state its subsequent algebraic steps.
B PROOF OF LEMMA 2
The proof of Lemma 2 evaluates an expected quadratic error under positive age difference, using noise covariance and a standard quadratic-norm identity.
- The proof assumes ∆i[ki] > 0 before evaluating the expected error expression.
- Noise vectors are treated as independent and therefore uncorrelated in the first algebraic step.
- The quadratic-norm expectation is rewritten as a mean term plus tr(AC), yielding a trace expression involving the noise covariance matrix.