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Hedonic Coalition Formation for Distributed Task Allocation among Wireless Agents
Walid Saad, Zhu Han, Tamer Basar, Merouane Debbah, Are Hjørungnes
TL;DR
Next-generation wireless networks need autonomous agents that can operate across distributed, heterogeneous, and dynamic environments with limited centralized reliance. This paper models wireless task allocation as hedonic coalition formation and reports higher average player payoff than equal allocation of nearby tasks.
Problem
Distributed wireless networks need autonomous agents to perform data collection and other network functions with limited reliance on centralized authority.
Method
The paper models wireless task allocation as a hedonic coalition formation game, using polling-system coalitions and throughput–delay utility to guide agents and tasks’ join or leave decisions.
Results
The proposed algorithm achieves higher average player payoff than an algorithm that assigns nearby tasks equally among agents.
Takeaways & Limitations
The algorithm converges to a Nash-stable partition and supports coalition structures in which agents serve tasks as collectors or relays.
Abstract
from arXiv · showhide
Autonomous wireless agents such as unmanned aerial vehicles or mobile base stations present a great potential for deployment in next-generation wireless networks. While current literature has been mainly focused on the use of agents within robotics or software applications, we propose a novel usage model for self-organizing agents suited to wireless networks. In the proposed model, a number of agents are required to collect data from several arbitrarily located tasks. Each task represents a queue of packets that require collection and subsequent wireless transmission by the agents to a central receiver. The problem is modeled as a hedonic coalition formation game between the agents and the tasks that interact in order to form disjoint coalitions. Each formed coalition is modeled as a polling system consisting of a number of agents which move between the different tasks present in the coalition, collect and transmit the packets. Within each coalition, some agents can also take the role of a relay for improving the packet success rate of the transmission. The proposed algorithm allows the tasks and the agents to take distributed decisions to join or leave a coalition, based on the achieved benefit in terms of effective throughput, and the cost in terms of delay. As a result of these decisions, the agents and tasks structure themselves into independent disjoint coalitions which constitute a Nash-stable network partition. Moreover, the proposed algorithm allows the agents and tasks to adapt the topology to environmental changes such as the arrival/removal of tasks or the mobility of the tasks. Simulation results show how the proposed algorithm improves the performance, in terms of average player (agent or task) payoff, of at least 30.26% (for a network of 5 agents with up to 25 tasks) relatively to a scheme that allocates nearby tasks equally among agents.
I. INTRODUCTION
The paper addresses distributed task allocation for autonomous wireless agents, proposing a wireless-oriented hedonic coalition framework for collecting and transmitting data from tasks.
- Research on autonomous agents has largely focused on robotics, computer systems, and software engineering, leaving wireless-network applications comparatively underdeveloped.
- Wireless task allocation requires agents to assign tasks autonomously and distributively rather than relying on pre-assigned tasks or centralized entities.
- The proposed model represents each task as a packet queue whose data must be collected and transmitted by wireless agents to a central receiver.
- Hedonic coalition formation is introduced to allocate arbitrarily located tasks among autonomous agents in wireless-network applications.
- The approach is intended for applications including video surveillance, mobile relays, ad hoc data collection, wireless monitoring, and UAV deployment.
II. SYSTEM MODEL
The system models autonomous wireless agents servicing heterogeneous, arbitrarily located packet-generating tasks through mobile collection, transmission, and relay operations.
- The network contains M wireless agents and T tasks, with T > M; tasks generate constant-size packets according to Poisson arrivals with task-specific rates.
- Tasks may be serviced by multiple agents, while each agent or agent group may service multiple tasks as collectors or relays.
- Relay agents are positioned at equal distances along the task-to-receiver path to improve transmission success through multi-hop communication.
- Transmission success is characterized using per-hop packet-success probabilities over a path from the serviced task to the central receiver.
- Agents move cyclically among tasks, collecting and transmitting queued packets before proceeding to the next task.
A. Game Formulation
The task-allocation problem is mapped to coalitions of agents and tasks, with each coalition analyzed as a polling system whose delay and stability influence its formation.
- Game Formulation: The game’s player set contains both wireless agents and tasks, denoted N = M ∪ T.
- Game Formulation: Each coalition operates as a polling system in which collector-agents cyclically service task queues using an exhaustive strategy.
- Game Formulation: The coalition’s switchover time is the constant travel time required for a collector to move between successive tasks.
- Game Formulation: Because exact queue-by-queue polling delays lack general closed forms, the analysis uses a pseudo-conservation law for weighted mean waiting times.
- Game Formulation: The delay expression includes queueing and travel-related switchover effects, while coalition stability requires utilization below one; otherwise delay is infinite.
B. Utility Function
The utility function captures a coalition’s throughput–delay tradeoff while allocating transferable revenue among agents and tasks. Coalition structure is evaluated through routing, polling delay, effective throughput, and fair payoff division.
- B. Utility Function: Task visitation order is selected by minimizing total switchover time, formulated as a traveling-salesman problem.
- B. Utility Function: The nearest-neighbor heuristic provides a sub-optimal route with linear computational complexity in the number of tasks.
- B. Utility Function: Adding collectors increases link capacity and reduces task service time and overall polling delay, while relays improve transmission success by shortening transmission distance.
- B. Utility Function: Coalition utility uses system power to represent the tradeoff between effective throughput and delay.The power criterion is defined as a ratio involving throughput and delay, with β controlling their relative emphasis.
- B. Utility Function: Coalition revenue is transferable and divided using an equal fair allocation rule among coalition members.The rule gives agents and tasks equal treatment when distributing the coalition’s value.
- B. Utility Function: Coalition formation produces independent disjoint coalitions rather than necessarily forming a grand coalition because coalition formation incurs costs.
A. Hedonic Coalition Formation: Concepts and Model
The task-allocation problem is modeled as a hedonic coalition formation game whose players are agents and tasks. Preferences depend on coalition membership and are designed to balance service coverage, payoff, and coalition stability.
- A. Hedonic Coalition Formation: Concepts and Model: A coalition partition divides all agents and tasks into disjoint groups, with each player assigned to exactly one coalition.
- A. Hedonic Coalition Formation: Concepts and Model: Agents prefer coalitions using payoff-based preferences while preserving their current task-only coalition when they are the sole servicing agent.This preference prevents an agent from abandoning tasks that would otherwise become unattended.
- A. Hedonic Coalition Formation: Concepts and Model: Tasks prefer coalitions offering larger payoffs but assign zero preference to coalitions they previously left.
- A. Hedonic Coalition Formation: Concepts and Model: The proposed task-allocation model is a hedonic game in which each player’s payoff depends only on the members of its coalition.
- A. Hedonic Coalition Formation: Concepts and Model: A stable coalition must contain enough collector-agents to satisfy the coalition’s service-load condition, with an upper bound when tasks share one class.
B. Hedonic Coalition Formation: Algorithm
The algorithm forms coalitions through distributed preference-improving switches by agents and tasks, then operates each coalition as a polling system. Finite partition space guarantees convergence to a Nash-stable disjoint partition, with periodic re-formation enabling adaptation.
- B. Hedonic Coalition Formation: Algorithm: Players switch coalitions only when the destination coalition is strictly preferred to the current one, while recording departed coalitions in their histories.
- B. Hedonic Coalition Formation: Algorithm: The algorithm has three phases: task discovery, hedonic coalition formation, and data collection.During data collection, agents visit tasks, transmit packets directly or through relays, and follow a nearest-neighbor visitation order.
- B. Hedonic Coalition Formation: Algorithm: The hedonic coalition-formation phase always converges from any initial partition to a final partition of disjoint coalitions.Each switch produces a previously unvisited partition, and the finite Bell number of partitions makes the sequence terminate.
- B. Hedonic Coalition Formation: Algorithm: The resulting final partition is Nash-stable and therefore individually stable, so no player prefers switching to another coalition or acting alone.
- B. Hedonic Coalition Formation: Algorithm: The first two phases repeat periodically after a fixed data-collection interval to accommodate new, removed, or slowly mobile tasks.
C. Distributed Implementation Possibilities
The implementation separates command and receiver roles while allowing agents and tasks to perform coalition decisions with distributed information exchange. Computational effort is concentrated in switch evaluation, route selection, and collector–relay assignment.
- C. Distributed Implementation Possibilities: The command center controls agents, while the central receiver is the network node that receives their transmitted data; the two may coincide in small networks.
- C. Distributed Implementation Possibilities: Agents require task locations and arrival rates, whereas resource-limited tasks mainly need information about the presence of agents.
- C. Distributed Implementation Possibilities: Coalition formation can be implemented distributively because agents and tasks independently perform switch operations without a centralized decision-maker.
- C. Distributed Implementation Possibilities: The nearest-neighbor route is linear in the number of tasks, while switch evaluation and task-side negotiation scale with the number of coalitions and agents.
- C. Distributed Implementation Possibilities: Agents evaluate collector–relay configurations by inspecting combinations and selecting the assignment that maximizes coalition utility.
V. SIMULATION RESULTS AND ANALYSIS
Simulations evaluate coalition structure, payoff, coalition size, and adaptation under changing task and agent conditions. The proposed hedonic formation algorithm improves or matches equal allocation across several settings while adapting to mobility and task arrivals or departures.
- Coalition structure: For M = 5 and T = 10, the final partition contains three coalitions, including one with two collectors and one relay yielding v(S2) = 52.25.The same coalition yields v(S2) = 10.59 with three collectors and v(S2) = 45.19 with one collector and two relays.
- Payoff performance: At least 30.26% higher average player payoff is achieved than equal allocation for 5 agents and up to 25 tasks.The comparison concerns average payoff per agent or task.
- Coalition structure: Average and maximum coalition sizes increase with task count, and the proposed algorithm produces relatively larger coalitions than equal allocation at all network sizes.The comparison uses M = 5 agents and averages over random task positions and play order.
- Adaptation to mobility: As task velocity increases, switch operations become more frequent while average coalition lifespan decreases for mobile-task networks.The mobility experiments use M = 5 agents over five minutes and compare different numbers of mobile tasks.
- Adaptation to topology changes: The coalition topology varies over time as tasks enter or leave a network starting with T = 15 tasks, under different task arrival/departure rates.A rate of two tasks per minute can represent arrivals, departures, or one of each.
VI. CONCLUSIONS
The paper models wireless task allocation as hedonic coalition formation, enabling agents and tasks to organize into disjoint coalitions. The algorithm supports distributed adaptation to environmental changes while converging to a Nash-stable partition.
- The hedonic coalition formation algorithm enables agents and tasks to self-organize into independent disjoint coalitions.Each coalition represents agents servicing a group of tasks in the wireless network.
- Agents within each coalition collect packets from tasks, while some can act as relays to improve wireless transmission.
- Players join or leave coalitions using preferences that capture the tradeoff between effective throughput and delay.
- The proposed algorithm always converges to a Nash-stable partition.
- Distributed coalition decisions allow the network topology to adapt to new, removed, or mobile tasks.