Cooperative load balancing in distributed systems

A serious difficulty in concurrent programming of a distributed system is how to deal with scheduling and load balancing of such a system which may consist of heterogeneous computers. In this paper, we formulate the static load-balancing problem in single class job distributed systems as a cooperative game among computers. The computers comprising the distributed system are modeled as M-M-1 queueing systems. It is shown that the Nash bargaining solution (NBS) provides an optimal solution (operation point) for the distributed system and it is also a fair solution. We propose a cooperative load-balancing game and present the structure of NBS. For this game an algorithm for computing NBS is derived. We show that the fairness index is always equal to 1 using NBS, which means that the solution is fair to all jobs. Finally, the performance of our cooperative load-balancing scheme is compared with that of other existing schemes. Copyright © 2008 John Wiley & Sons, Ltd.

[1]  Christos H. Papadimitriou,et al.  Worst-case equilibria , 1999 .

[2]  Debasish Ghose,et al.  ELISA: An estimated load information scheduling algorithm for distributed computing systems , 1999 .

[3]  Ariel Orda,et al.  Competitive routing in multiuser communication networks , 1993, TNET.

[4]  Noam Nisan,et al.  Algorithmic Mechanism Design , 2001, Games Econ. Behav..

[5]  Anthony T. Chronopoulos,et al.  Noncooperative load balancing in distributed systems , 2005, J. Parallel Distributed Comput..

[6]  Leonard Kleinrock,et al.  Queueing Systems: Volume I-Theory , 1975 .

[7]  Eitan Altman,et al.  Generalized Nash Bargaining Solution for bandwidth allocation , 2006, Comput. Networks.

[8]  Bharadwaj Veeravalli,et al.  Access Time Minimization for Distributed Multimedia Applications , 2000, Multimedia Tools and Applications.

[9]  Debasish Ghose,et al.  Scheduling Divisible Loads in Parallel and Distributed Systems , 1996 .

[10]  Tim Roughgarden,et al.  Stackelberg scheduling strategies , 2001, STOC '01.

[11]  Hisao Kameda,et al.  Optimal static load balancing of multi-class jobs in a distributed computer system , 1990, Proceedings.,10th International Conference on Distributed Computing Systems.

[12]  Éva Tardos,et al.  Truthful mechanisms for one-parameter agents , 2001, Proceedings 2001 IEEE International Conference on Cluster Computing.

[13]  Tim Roughgarden,et al.  How bad is selfish routing? , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[14]  Raj Jain,et al.  A Quantitative Measure Of Fairness And Discrimination For Resource Allocation In Shared Computer Systems , 1998, ArXiv.

[15]  David G. Luenberger,et al.  Linear and nonlinear programming , 1984 .

[16]  Mihalis Yannakakis,et al.  On the approximability of trade-offs and optimal access of Web sources , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[17]  Joan Feigenbaum,et al.  Sharing the cost of muliticast transmissions (preliminary version) , 2000, STOC '00.

[18]  Pradeep Dubey,et al.  Inefficiency of Nash Equilibria , 1986, Math. Oper. Res..

[19]  Kai Hwang,et al.  Correction to “optimal load balancing in a multiple processor system with many job classes” , 1985, IEEE Transactions on Software Engineering.

[20]  Catherine Rosenberg,et al.  A game theoretic framework for bandwidth allocation and pricing in broadband networks , 2000, TNET.

[21]  Anthony T. Chronopoulos,et al.  Load balancing in distributed systems: an approach using cooperative games , 2002, Proceedings 16th International Parallel and Distributed Processing Symposium.

[22]  Anthony T. Chronopoulos,et al.  Price-based user-optimal job allocation scheme for grid systems , 2006, Proceedings 20th IEEE International Parallel & Distributed Processing Symposium.

[23]  Xiaotie Deng,et al.  On the Complexity of Cooperative Solution Concepts , 1994, Math. Oper. Res..

[24]  Jason Lee,et al.  Using High-Speed WANs and Network Data Caches to Enable Remote and Distributed Visualization , 2000, ACM/IEEE SC 2000 Conference (SC'00).

[25]  Debasish Ghose,et al.  Large matrix-vector products on distributed bus networks with communication delays using the divisible load paradigm: performance analysis and simulation , 2001, Math. Comput. Simul..

[26]  Jie Li,et al.  Optimal Static Load Balancing in Star Network Configurations with Two-Way Traffic , 1994, J. Parallel Distributed Comput..

[27]  J. Nash.  THE BARGAINING PROBLEM , 1950, Classics in Game Theory.

[28]  Jie Li,et al.  A Decomposition Algorithm for Optimal Static Load Balancing in Tree Hierarchy Network Configurations , 1994, IEEE Trans. Parallel Distributed Syst..

[29]  Christos Douligeris,et al.  Fairness in network optimal flow control: optimality of product forms , 1991, IEEE Trans. Commun..

[30]  Jie Li,et al.  Optimal Load Balancing in Distributed Computer Systems , 1997 .

[31]  Hisao Kameda,et al.  An algorithm for optimal static load balancing in distributed computer systems , 1992 .

[32]  Eitan Altman,et al.  Routing into Two Parallel Links: Game-Theoretic Distributed Algorithms , 2001, J. Parallel Distributed Comput..

[33]  A. Muthoo.  Bargaining Theory with Applications , 1999 .

[34]  Bharadwaj Veeravalli,et al.  Distributed Image Processing On A Network Of Workstations , 2003 .

[35]  Jie Li,et al.  Load Balancing Problems for Multiclass Jobs in Distributed/Parallel Computer Systems , 1998, IEEE Trans. Computers.

[36]  Walter H. Kohler,et al.  Models for Dynamic Load Balancing in a Heterogeneous Multiple Processor System , 1979, IEEE Transactions on Computers.

[37]  Jacek Blazewicz,et al.  Divisible task scheduling - Concept and verification , 1999, Parallel Comput..

[38]  Joan Feigenbaum,et al.  Sharing the Cost of Multicast Transmissions , 2001, J. Comput. Syst. Sci..

[39]  Paul G. Spirakis,et al.  The price of selfish routing , 2001, STOC '01.

[40]  Asser N. Tantawi,et al.  Optimal static load balancing in distributed computer systems , 1985, JACM.

[41]  Xueyan Tang,et al.  Optimizing static job scheduling in a network of heterogeneous computers , 2000, Proceedings 2000 International Conference on Parallel Processing.

[42]  David D. Yao,et al.  Optimal load balancing and scheduling in a distributed computer system , 1991, JACM.

[43]  Heeseok Lee,et al.  Optimal static distribution of prioritized customers to heterogeneous parallel servers , 1995, Comput. Oper. Res..