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<p>In this paper we propose an approach for a class of dynamic task assignment problems (DTAPs) using Petri nets. A DTAP consists of two parties of agents: the <i>customers</i> who expect to be serviced, and the <i>servers</i> who provide service to customers in multiple rounds of engagements. The aim of solving the DTAP is to synthesize an assignment strategy that maximizes the service rate. The DTAP studied in this paper follows a <i>player-against-nature</i> decision structure, where the decision maker selects assignment actions and the environment reveals stochastic success/failure outcomes. To this end, we propose a novel Petri-net-based approach to model and solve such DTAPs with the fail-and-retry mechanism. In our approach, the behavior of customers and servers are first modeled by path and server subnets, respectively. A novel Petri net model called the <i>Game Petri net</i> (GPN) is then constructed, in which the dynamic multi-stage task assignment is captured. The game Petri net is constructed in a bottom-up manner using a modular synthetic procedure, and its reachability space represents the player-against-nature decision process between the decision maker and the stochastic environment. By constructing the <i>game reachability graph</i> of a GPN as a game tree, the optimal target assignment strategy for the discretization is determined through backward induction. Simulations show that our proposed method achieves better performance in terms of service rate compared with conventional policies.</p>

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A Petri net approach for dynamic task assignment problems and its application in weapon-target assignment

  • 期刊论文

  • 发表日期：

    2026年7月22日

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  • Ziyue Ma,
  • Yi Wang,
  • Yupeng Yang,
  • Yin Tong

摘要

In this paper we propose an approach for a class of dynamic task assignment problems (DTAPs) using Petri nets. A DTAP consists of two parties of agents: the customers who expect to be serviced, and the servers who provide service to customers in multiple rounds of engagements. The aim of solving the DTAP is to synthesize an assignment strategy that maximizes the service rate. The DTAP studied in this paper follows a player-against-nature decision structure, where the decision maker selects assignment actions and the environment reveals stochastic success/failure outcomes. To this end, we propose a novel Petri-net-based approach to model and solve such DTAPs with the fail-and-retry mechanism. In our approach, the behavior of customers and servers are first modeled by path and server subnets, respectively. A novel Petri net model called the Game Petri net (GPN) is then constructed, in which the dynamic multi-stage task assignment is captured. The game Petri net is constructed in a bottom-up manner using a modular synthetic procedure, and its reachability space represents the player-against-nature decision process between the decision maker and the stochastic environment. By constructing the game reachability graph of a GPN as a game tree, the optimal target assignment strategy for the discretization is determined through backward induction. Simulations show that our proposed method achieves better performance in terms of service rate compared with conventional policies.