Competitive routing in multiuser communication networks
IEEE/ACM Transactions on Networking (TON)
Optimal probabilistic allocation of customer types to servers
Proceedings of the 1995 ACM SIGMETRICS joint international conference on Measurement and modeling of computer systems
Optimal load balancing in distributed computer systems
Optimal load balancing in distributed computer systems
The state of the art in locally distributed Web-server systems
ACM Computing Surveys (CSUR)
Selfish traffic allocation for server farms
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Scheduling and Load Balancing in Parallel and Distributed Systems
Scheduling and Load Balancing in Parallel and Distributed Systems
Optimal state-free, size-aware dispatching for heterogeneous M/G/-type systems
Performance Evaluation - Performance 2005
Analysis of join-the-shortest-queue routing for web server farms
Performance Evaluation
Models for Dynamic Load Balancing in a Heterogeneous Multiple Processor System
IEEE Transactions on Computers
Optimal Load Balancing in a Multiple Processor System with Many Job Classes
IEEE Transactions on Software Engineering
A comparative analysis of server selection in content replication networks
IEEE/ACM Transactions on Networking (TON)
The Impact of Oligopolistic Competition in Networks
Operations Research
STACS'99 Proceedings of the 16th annual conference on Theoretical aspects of computer science
The price of anarchy in an exponential multi-server
Operations Research Letters
The price of forgetting in parallel and non-observable queues
Performance Evaluation
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We investigate the price of anarchy of a load balancing game with K dispatchers. The service rates and holding costs are assumed to depend on the server, and the service discipline is assumed to be processor-sharing at each server. The performance criterion is taken to be the weighted mean number of jobs in the system, or equivalently, the weighted mean sojourn time in the system. For this game, we first show that, for a fixed amount of total incoming traffic, the worst-case Nash equilibrium occurs when each player routes exactly the same amount of traffic, i.e., when the game is symmetric. For this symmetric game, we provide the expression for the loads on the servers at the Nash equilibrium. Using this result we then show that, for a system with two or more servers, the price of anarchy, which is the worst-case ratio of the global cost of the Nash equilibrium to the global cost of the centralized setting, is lower bounded by K/(2√K - 1) and upper bounded by √K, independently of the number of servers.