Macroscopic Mathematical Model of Agent-based Systems Wang Yuanshi (Based on [1,2])

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Presentation transcript:

Macroscopic Mathematical Model of Agent-based Systems Wang Yuanshi (Based on [1,2])

Configuration of System Let q_k be the state, n_k be the number of agents in state k. The configuration of the system is P(n,t) : the probability distribution

Master Equation

Rate Equation

Wide Use of the Two Equations Physics: the growth of semiconductor surfaces Ecology: population dynamics Chemistry: chemical reactions Biology: ant colonies ……

Model for Load Balancing on Grid (1) Assumptions: (1) Agents are homogeneous, in a sense that each agent occupies the same service time and follows the same strategy for leaving and queuing. (2) Initially all the agents queue in the same service site. (3) Each agent is free to choose teams in service sites; teams are not. (4) It is beneficial for agents to join short teams; an agent can not join a team already of maximum size. (5) Agents encounter other agents and service sites randomly. (6) There is no net change in the number of agents in the system.

Model for Load Balancing on Grid (2)

Efficiency Function

Open Problems It is as yet unresolved whether the equilibrium state is stable for high dimensions. How does the efficiency function vary with the general parameters?

References 1.Kristina Lerman and Aram Galstyan (2001) "A General Methodology for Mathematical Analysis of Multi- Agent Systems," USC Information Sciences Technical Report ISI-TR Babaoglu O., Meling H.,Montresor, A., Anthill: Aframework for the development of agent-based peer-to- peer systems. In Proc. of the 22th Int. Conf. on Distributed Computing Systems, Viena, Austria, July 2002.