⚡ electrical engineering

Circulatory Load-sharing Redundancy for Resource Single Point of Failure in Automated Manufacturing Systems Using Petri Nets

This paper proposes a Petri net-based circular load-sharing redundancy technique that enhances the resilience of automated manufacturing systems to single resource failures by dynamically redistributing tasks among neighboring resources in a circle, thereby achieving high recovery efficiency without requiring additional backup resources or operational loss.

Original authors: Ebrahim A. Alzalab, Adeeb A. Ahmed, Haithm M. Al-Gunid, Sadiq Ghalib

Published 2026-08-31

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CC BY 4.0

Original authors: Ebrahim A. Alzalab, Adeeb A. Ahmed, Haithm M. Al-Gunid, Sadiq Ghalib

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Modern factories rely on automated systems that move parts, assemble components, and package goods with incredible speed. These machines work in a tightly coordinated rhythm, where one robot hands a piece to another, which then passes it to a machine for processing. The entire operation depends on every single component doing its job. If one robot breaks down or a sensor fails, the flow can stop completely. This is not just a minor inconvenience; a halted production line means lost time, wasted materials, and significant financial damage. For decades, engineers have tried to solve this by adding backup machines. If the main robot fails, a spare one takes over. However, buying and installing extra hardware for every single machine is expensive, and managing the switch between them can create its own complex problems, sometimes causing the system to freeze entirely.

A team of researchers has proposed a different way to handle these breakdowns, one that avoids the need for extra spare parts. Instead of adding new machines, they suggest arranging the existing unreliable robots in a circle. In this setup, each robot is responsible for its own work, but it also stands ready to take over the job of its neighbor if that neighbor stops working. If the first robot fails, the second one steps in. If the second fails, the third takes over, and so on, until the circle closes back on the first. This method, called circular load-sharing redundancy, allows the system to keep running even when a part breaks, without requiring any additional hardware or complicated layers of control. The researchers tested this idea using a computer model of a factory floor to see if it could truly keep the production line moving.

The study focuses on a specific type of automated system known as a manufacturing cell, where multiple robots and machines share resources to process parts. The researchers used a mathematical tool called a Petri net to map out exactly how these systems behave. Think of a Petri net as a detailed flowchart that tracks the movement of tokens, which represent the parts being made, through the various stages of production. This tool allows engineers to predict where the system might get stuck, a state known as a deadlock, where no part can move forward because every machine is waiting for another. In a standard factory model without any backup plan, if a single critical robot fails, the entire system grinds to a halt. The tokens representing the parts get stuck, and production stops completely.

To test their new circular idea, the researchers built a digital model of a factory with four robots and two machines. They arranged the four robots in a loop, where each one acts as a backup for the one before it. They then simulated a scenario where one of the robots suddenly stopped working. In the traditional model with no redundancy, the failure caused the system to stop immediately, resulting in zero recovery of the production process. However, when they applied the circular arrangement, the system reacted differently. As soon as the first robot failed, the model automatically shifted the tasks intended for that broken robot to the next robot in the circle. The second robot picked up the extra work, and the production line continued to move.

The results of the simulation were striking. When the researchers introduced a failure in the middle of a run, the system with the circular backup plan was able to recover 90.5 percent of its normal output. This means that even with one robot down, the factory kept producing the vast majority of its parts. The researchers noted that there was a small cost to this resilience. During normal operation, when no robots were broken, the system with the circular plan produced slightly fewer parts per hour than a standard system without any redundancy features. The output dropped from an average of 9.3 parts to 7.7 parts. This decrease is due to the slight overhead of managing the backup logic, but the researchers argue that losing about 17 percent of normal speed is a fair trade-off for the ability to keep running at 90 percent capacity when a failure occurs.

The study also looked at the complexity of the system. The circular method added a few extra steps to the computer model, increasing the number of transitions the system had to track, but it did so without needing any new physical machines. The researchers found that the system remained stable and did not get stuck in deadlocks, even when a robot failed. They proved mathematically that as long as only one robot fails at a time, the system will always be able to find a way to move the parts forward. This is a significant improvement over previous methods that relied on dedicated backup machines, which are costly, or hierarchical systems, which can be difficult to analyze and prone to their own errors.

The researchers are careful to point out the limits of their findings. Their simulations assumed that only one robot would fail at any given moment. They did not test what would happen if two or more robots broke down simultaneously, as that would require a more complex arrangement. They also noted that the current model uses random choices for certain actions, and a more deterministic approach might improve the speed further. Despite these limitations, the work demonstrates a clear path forward for making automated factories more resilient. By simply rethinking how existing machines are connected and how they support one another, it is possible to build systems that can withstand breakdowns without the heavy expense of buying extra equipment. The study concludes that this circular approach offers a practical, efficient way to keep manufacturing lines moving in the face of inevitable mechanical failures.

Technical Summary: Circulatory Load-sharing Redundancy for Resource Single Point of Failure in Automated Manufacturing Systems Using Petri Nets

Problem Statement
Automated Manufacturing Systems (AMS) are highly susceptible to resource failures (e.g., robots, machines, sensors), which can halt entire production lines, causing significant financial loss and downtime. While Petri nets have been extensively used to model and control Discrete Event Systems (DES) for deadlock avoidance in reliable environments, the presence of unreliable resources complicates these control strategies. Existing fault-tolerant approaches, such as Load-Sharing Redundant Resources (LSRR), typically rely on dedicated backup resources or hierarchical switching mechanisms. These methods incur high hardware costs, increase logic design complexity, and introduce issues like priority inversion and control overhead. Furthermore, extending dedicated backup schemes to systems with multiple unreliable resources requires a one-to-one backup ratio, which is economically prohibitive. The specific problem addressed is how to achieve fault tolerance for multiple unreliable resources in an AMS without adding dedicated backup hardware or complex hierarchical structures, while maintaining system liveness and boundedness.

Methodology
The paper proposes a Circular Load-Sharing Redundancy Recovery (C-LSRR) technique. The core methodology involves the following components:

Circular Arrangement: Unreliable resources ( $R = \{r_1, r_2, ..., r_n\}$ ) are arranged in a circular topology ( $r_1 \to r_2 \to ... \to r_n \to r_1$ ). In this configuration, each resource $r_i$ is backed up by its immediate successor $r_{i+1}$ (with $r_1$ serving as the backup for $r_n$ ).
Petri Net Modeling (US3PR to C-LSRR): The system is modeled using an extension of the S3PR (System of Simple Sequential Processes with Resources) class, known as US3PR (Unreliable S3PR). The proposed C-LSRR model introduces a circular switch subnet without inhibitor arcs.
- Failure/Repair Subnets: For each unreliable resource $r_i$ , a local failure/repair subnet is added, consisting of a failure place ( $fail_i$ ), a failure transition ( $t_{fail, r_i}$ ), and a repair transition ( $t_{rep, r_i}$ ).
- Transition Duplication: For every transition $t$ in the original net that consumes resource $r_i$ , a duplicate transition $t^{(i)}$ is created. This duplicate transition consumes the backup resource $r_{i+1}$ and requires a token in $fail_i$ to fire.
- Operation Logic: Under normal conditions, tokens reside in the resource places, enabling original transitions. Upon failure, a token moves to $fail_i$ , disabling original transitions and enabling duplicate transitions, which redirect the workload to the next resource in the circle. Upon repair, the token returns to the resource place, restoring normal operation.
Supervisory Control (TGAL): To ensure the system remains live (deadlock-free) and bounded under both normal and degraded (single failure) conditions, the Think Globally, Act Locally (TGAL) algorithm is employed.
- A supervisor is synthesized for the nominal mode (all resources working).
- Separate supervisors are synthesized for each degraded mode (single resource failure), where the failed resource and its backup are effectively treated as a pooled capacity.
- These supervisors are consolidated into a single controller by removing redundant monitors (place invariants).

Key Contributions
The paper outlines five primary contributions:

Circular Redundancy Mechanism: A novel redundancy scheme for handling multiple unreliable resources that requires no additional backup hardware or hierarchical layers, relying instead on mutual backup among existing resources.
Inhibitor-Free Petri Net Model: A formal Petri net model utilizing a circular switch subnet that manages failure and repair transitions without the use of inhibitor arcs, thereby saving computational resources.
Formal Verification: Sketch proofs and definitions establishing that the resulting C-LSRR net preserves liveness and boundedness in the event of a single resource failure.
Controller Synthesis: The application and adaptation of the TGAL algorithm to the C-LSRR net to generate liveness-enforcing supervisors for both normal and degraded states.
Experimental Verification: Simulation results demonstrating the efficacy of the approach on a standard S4R benchmark model.

Experimental Results
The methodology was validated through simulations on an S4R model containing 23 places, 18 transitions, and 4 unreliable robots ( $R_1$ to $R_4$ ) with 50 initial parts.

Baseline Performance: A non-redundant S4R system achieved an average throughput of 9.3 parts. However, upon the failure of robot $R_1$ , the system stopped completely (0% recovery).
C-LSRR Performance (Normal): The C-LSRR system without failure achieved an average throughput of 7.7 parts, representing a 17% decrease compared to the baseline due to the overhead of the redundancy mechanism.
C-LSRR Performance (Failure): When $R_1$ failed at step 7,500, the C-LSRR system continued to operate with an average throughput of 7.0 parts. This resulted in a 90.5% recovery rate relative to the degraded state of the non-redundant system.
Overhead: The C-LSRR model increased the number of places by 17% (23 to 27) and transitions by 111% (18 to 38). Simulation time increased by 40% (3.2s to 4.5s), which the authors deem reasonable for practical usage.
Comparison: The 90.5% recovery rate outperforms non-redundant solutions (0%) and is competitive with dedicated LSRR solutions (cited as 77.8% in prior literature), without the associated hardware costs.

Significance and Claims
The paper claims that C-LSRR offers a cost-effective and structurally simple solution for fault tolerance in AMS. By arranging resources in a circle, the system achieves high resilience (90.5% recovery) against single-point failures without the need for dedicated backup hardware or complex hierarchical control structures. The authors emphasize that the slight reduction in normal throughput (from 9.3 to 7.7 parts) is a justifiable trade-off for the significant gain in system availability. The approach is presented as a viable alternative to dedicated redundancy, particularly for systems where hardware costs are a constraint.

Limitations and Future Work
The authors explicitly note that the current approach assumes only one resource failure at a time; handling simultaneous multiple failures is deferred to future work. Additionally, the study relies on random transition selection, and the authors suggest that deterministic approaches could further improve throughput. Future research directions include extending the method to multiple failures, optimizing throughput via deterministic transitions, testing on more complex models, and integrating machine learning for failure prediction.

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