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Agent-Based Load Balancing on Homogeneous Minigrids: Macroscopic Modeling and Characterization
July 2005 (vol. 16 no. 7)
pp. 586-598

Abstract—In this paper, we present a macroscopic characterization of agent-based load balancing in homogeneous minigrid environments. The agent-based load balancing is regarded as agent distribution from a macroscopic point of view. We study two quantities on minigrids: the number and size of teams where agents (tasks) queue. In macroscopic modeling, the load balancing mechanism is characterized using differential equations. We show that the load balancing we concern always converges to a steady state. Furthermore, we show that load balancing with different initial distributions converges to the same steady state gradually. Also, we prove that the steady state becomes an even distribution if and only if agents have complete knowledge about agent teams on minigrids. Utility gains and efficiency are introduced to measure the quality of load balancing. Through numerical simulations, we discuss the utility gains and efficiency of load balancing in different cases and give a series of analysis. In order to maximize the utility gain and the efficiency, we theoretically study the optimization of agents' strategies. Finally, in order to validate our proposed agent-based load balancing mechanism, we develop a computing platform, called Simulation System for Grid Task Distribution (SSGTD). Through experimentation, we note that our experimental results in general confirm our theoretical proofs and numerical simulation results from the proposed equation system. In addition, we find a very interesting phenomenon, that is, agent-based load balancing mechanism is topology-independent.

[1] I. Foster, “Internet Computing And The Emerging Grid,” Nature Web Matters, Gridgrid.html, 2000.
[2] Grid Computing: Making the Global Infrastructure a Reality, F. Berman, G. Fox, and T. Hey, eds. John Wiley and Sons, 2003.
[3] The Grid: Blueprint for a New Computing Infrastructure, I. Foster and C. Kesselman, eds. Morgan Kaufman, 1999.
[4] I. Foster, J. Geisler, B. Nickless, W. Smith, and S. Tuecke, “Software Infrastructure for the I-WAY High-Performance Distributed Computing Experiment,” Grid Computing: Making the Global Infrastructure a Reality, F. Berman, G. Fox, and T. Hey, eds., chapter 4, pp. 101-116, John Wiley and Sons, 2003.
[5] I. Foster, “The Grid: A New Infrastructure for 21st Century Science,” Grid Computing: Making the Global Infrastructure a Reality, F. Berman, G. Fox, and T. Hey, eds., chapter 2, pp. 51-64, John Wiley and Sons, 2003.
[6] A. Galstyan, K. Czajkowski, and K. Lerman, “Resource Allocation in the Grid Using Reinforcement Learning,” , 2003.
[7] H. Casanova, A. Legrand, D. Zagorodnov, and F. Berman, “Heuristics for Scheduling Parameter Sweep Applications in Grid Environments,” Proc. Ninth Heterogeneous Computing Workshop (HCW 2000), pp. 349-363, May 2000.
[8] H. Casanova, J. Hayes, and Y. Yang, “Algorithms and Software to Schedule and Deploy Independent Tasks in Grid Environments,” Proc. Workshop Distributed Computing, Metacomputing, and Resource Globalization, Dec. 2002.
[9] S. Ho, “Survey of a Grid Meta-Scheduler,” , 2002.
[10] F. Berman, R. Wolski, H. Casanova, W. Cirne, H. Dail, M. Faerman, S. Figueira, J. Hayes, G. Obertelli, J. Schopf, G. Shao, S. Smallen, N. Spring, A. Su, and D. Zagorodnov, “Adaptive Computing on the Grid Using AppLeS,” IEEE Trans. Parallel and Distributed Systems, vol. 14, no. 4, pp. 369-382, Apr. 2003.
[11] F. Berman, R. Wolski, S. Figueira, J. Schopf, and G. Shao, “Application-Level Scheduling on Distributed Heterogeneous Networks,” Proc. 1996 ACM/IEEE Conf. Supercomputing (SC '96), 1996.
[12] D. Abramson, R. Buyya, and J. Giddy, “A Computational Economy for Grid Computing and Its Implementation in the Nimrod-G Resource Broker,” Future Generation Computer System, vol. 18, pp. 1061-1074, 2002.
[13] H. Dail, H. Casanova, and F. Berman, “A Decoupled Scheduling Approach for the GrADS Environment,” Proc. 2002 ACM/IEEE Conf. Supercomputing (SC 2002), Nov. 2002.
[14] S.S. Vadhiyar and J.J. Dongarra, “A Metascheduler for the Grid,” Proc. 11th Symp. High Performance Distributed Computing (HPDC-11), July 2002.
[15] J. Frey, T. Tannenbaum, I. Foster, M. Livny, and S. Tuecke, “Condor-G: A Computation Management Agent for Multi-Institutional Grids,” Proc. 10th IEEE Symp. High Performance Distributed Computing (HPDC-10), Aug. 2001.
[16] Y. Yang and H. Casanova, “Umr: A Multi-Round Algorithm for Scheduling Divisible Workloads,” Proc. Int'l Parallel and Distributed Processing Symp. (IPDPS '03), Apr. 2003.
[17] “Rumr: Robust Scheduling for Divisible Workloads,” Proc. 12th IEEE Symp. High Performance and Distributed Computing (HPDC-12), June 2003.
[18] A. Montresor, H. Meling, and O. Babaoglu, “Messor: Load-Balancing through a Swarm of Autonomous Agents,” Technical Report UBLCS-02-08, Dept. of Computer Science, Univ. of Bologna, Bologna, Italy, May 2002.
[19] O. Babaoglu, H. Meling, and A. Montresor, “Anthill: A Framework for the Development of Agent-Based Peer-to-Peer Systems,” Proc. 22nd Int'l Conf. Distributed Computing Systems (ICDCS 2002), July 2002.
[20] P. Grasse, “La Reconstruction du Nid et Les Coordinations Interindividuelles Chez Bellicositermes Natalensis et Cubitermes Sp,” Insectes Sociaux, vol. 6, pp. 41-80, 1959.
[21] L. Lopez and A.F. Sanjuan, “Defining Strategies to Win in the Internet Market,” Physica A, vol. 301, pp. 512-534, 2001.
[22] K. Lerman and O. Shehory, “Coalition Formation for Large-Scale Electronic Markets,” Proc. Fourth Int'l Conf. Multi-Agent Systems (ICMAS 2000), pp. 167-174, 2000.
[23] K. Lerman, A. Galstyan, A. Martinoli, and A.J. Ijspeert, “A Macroscopic Analytical Model of Collaboration in Distributed Robotic Systems,” Artificial Life, vol. 7, no. 4, pp. 375-393, 2001.
[24] J. Hofbauer and K. Sigmund, Evolutionary Games and Replicator Dynamics. Cambridge Univ. Press, 1998.
[25] F.J. Hoppensteadt and J.S. Pesk, Mathematics in Medicine and the Life Sciences. Springer, 1992.
[26] W.P. Nelson and A.S. Perelson, “Mathematical Analysis of Delay Differential Equation Model of HIV-1 Infection,” Math. Biosciences, vol. 179, pp. 73-94, 2002.
[27] Y. Wang, “The Necessary and Sufficient Conditions for the Existence of Periodic Orbits in a Lotka-Volterra System,” J. Math. Analysis and Applications, 2004.
[28] A.M. Turing, “The Chemical Basis of Morphogenesis,” Philosophical Trans. Royal Soc. B, vol. 327, pp. 37-72, 1952.
[29] Z. Noszticzius, W. Horsthemke, W.D. McCormick, H.L. Swinney, and W.Y. Tam, “Sustained Chemical Waves in an Annular Gel Reactor: A Chemical Pinwheel,” Nature, vol. 329, pp. 619-620, 1987.
[30] T. Hogg and B.A. Huberman, “Dynamics of Large Autonomous Computational Systems,” Proc. Santa Fe Workshop Collective Cognition, 2002.
[31] B. Veeravalli, D. Ghose, V. Mani, and T.G. Robertazzi, Scheduling Divisible Loads in Parallel and Distributed Systems. IEEE CS Press, 1996.
[32] D. Yu and T.G. Robertazzi, “Divisible Load Scheduling for Grid Computing,” Proc. IASTED Int'l Conf. Parallel and Distributed Computing and Systems (PDCS 2003), 2003.
[33] H.E. Bal et al., “The Distributed ASCI Supercomputer Project,” ACM Special Interest Group, Operating Systems Rev., vol. 34, no. 4, pp. 76-96, Oct. 2000.
[34] “The Distributed ASCI Supercomputer (DAS),”, 2005.
[35] W.M. Jones, L.W. Pang, and D. Stanzione, “Computational Mini-Grid Research at Clemson University,” Technical Report PARL-2002-009, Parallel Architecture Research Laboratory, Clemson Univ., Dec. 2002.
[36] W.M. Jones, L.W. Pang, D. Stanzione, and I. Walter, and B. Ligon, “Job Communication Characterization and Its Impact on Meta-Scheduling Co-Allocated Jobs in a Mini-Grid,” Proc. Third Int'l Workshop Performance Modeling, Evaluation, and Optimization of Parallel and Distributed Systems (PMEO-PDS 2004), Apr. 2004.
[37] X. Jin and J. Liu, “Characterizing Autonomic Task Distribution and Handling in Grids,” Eng. Applications of Artificial Intelligence, vol. 17, no. 7, pp. 809-823, 2004.
[38] Y. Wang, J. Liu, and X. Jin, “Modeling Agent-Based Load Balancing with Time Delays,” Proc. 2003 IEEE/WIC Int'l Conf. Intelligent Agent Technology (LAT '03), pp. 189-195, Oct. 2003.
[39] Y. Wang and J. Liu, “Macroscopic Model of Agent Based Load Balancing on Grids,” Proc. Second Int'l Joint Conf. Autonomous Agents and Multi-Agent Systems (AAMAS '03), July 2003.
[40] J. Liu, X. Jin, and Y. Wang, “Agent-Based Load Balancing on Homogeneous Minigrids: Macroscopic Modeling and Characterization,” Technical Report COMP-04-005, Dept. of Computer Science, Hong Kong Baptist Univ., Sept. 2004.
[41] S.-H. Yook, H. Jeong, and A.-L. Barabasi, “Modeling the Internet's Large-Scale Topology,” Proc. Nat'l Academy of Sciences, vol. 99, no. 21, pp. 13382-13386, 2002.
[42] A.-L. Barabasi, R. Albert, and H. Jeong, “Scale-Free Characteristics of Random Networks: The Topology of the World Wide Web,” Physica A, vol. 281, pp. 69-77, 2000.

Index Terms:
Homogeneous minigrids, load balancing, task distribution, agents, macroscopic modeling, steady states, convergence, grid simulation.
Jiming Liu, Xiaolong Jin, Yuanshi Wang, "Agent-Based Load Balancing on Homogeneous Minigrids: Macroscopic Modeling and Characterization," IEEE Transactions on Parallel and Distributed Systems, vol. 16, no. 7, pp. 586-598, July 2005, doi:10.1109/TPDS.2005.76
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