Balakrishna J. Prabhu

Price of Anarchy in Non-Cooperative Load Balancing

We investigate the price of anarchy of a load balancing game with

On the Design of a Reward-Based Incentive Mechanism for Delay Tolerant Networks

K

Price of anarchy in non-cooperative load balancing games

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

Modeling Rewards and Incentive Mechanisms for Delay Tolerant Networks

K/(2\sqrt{K}-1)

On uncoordinated file distribution with non-altruistic downloaders

and upper bounded by

Worst-case analysis of non-cooperative load balancing

\sqrt{K}

Predicting Response Times of Applications in Virtualized Environments

, independently of the number of servers.

Performance analysis of traffic surges in multi-class communication networks

A central problem in Delay Tolerant Networks (DTNs) is to persuade mobile nodes to participate in relaying messages. Indeed, the delivery of a message incurs a certain number of costs for a relay. We consider a two-hop DTN in which a source node, wanting to get its message across to the destination as fast as possible, promises each relay it meets a reward. This reward is the minimum amount that offsets the expected delivery cost, as estimated by the relay from the information given by the source (number of existing copies of the message, age of these copies). A reward is given only to the relay that is the first one to deliver the message to the destination. We show that under fairly weak assumptions, the expected reward the source pays remains the same irrespective of the information it conveys, provided that the type of information does not vary dynamically over time. On the other hand, the source can gain by adapting the information it conveys to a meeting relay. For the particular cases of two relays or exponentially distributed inter-contact times, we give some structural results on the optimal adaptive policy.

Is the Price of Anarchy the Right Measure for Load-Balancing Games?

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. Independent of the state of the servers, each dispatcher seeks to determine the routing strategy that optimizes the performance for its own traffic. The interaction of the various dispatchers thus gives rise to a non-cooperative game. 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/(2K-1) and upper bounded by K, independent of the number of servers.

Analytic approximations of queues with lightly- and heavily-correlated autoregressive service times

A central problem in Delay Tolerant Networks (DTNs) is to persuade mobile nodes to participate in relaying messages. Indeed, the delivery of a message incurs a certain number of costs for a relay. We consider a two-hop DTN in which a source node, wanting to get its message across to the destination as fast as possible, promises each relay it meets a reward. This reward is the minimum amount that offsets the expected delivery cost, as estimated by the relay from the information given by the source (number of existing copies of the message, age of these copies). A reward is given only to the relay that is the first one to deliver the message to the destination. For two relays and exponentially distributed inter-contact times, we show that the expected reward the source pays remains the same irrespective of the information it conveys, provided that the type of information does not vary dynamically over time. On the other hand, the source can gain by adapting the information that it conveys to a meeting relay.