A simple load balancing problem with decentralized information

The following load balancing problem is investigated in discrete time: A service system consists of two service stations and two controllers, one in front of each station. The service stations provide the same service with identical service time distributions and identical waiting costs. Customers requiring service arrive at a controller's site and are routed to one of the two stations by the controller. The processes describing the two arrival streams are identical. Each controller has perfect knowledge of the workload in its own station and receives information about the other station's workload with one unit of delay. The controllers' routing strategies that minimize the customers' total flowtime are determined for a certain range of the parameters that describe the arrival process and the service distribution. Specifically, we prove that optimal routing strategies are characterized by thresholds that are either precisely specified or take one of two possible values.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/45840/1/186_2005_Article_BF01246331.pd

Prelude to Part II

Due to copyright restrictions, the access to the full text of this article is only available via subscription.In Part II, we focus on decentralized stochastic control problems and their applications. In Chapter 8, we present our results on the finite model approximation of multi-agent stochastic control problems (team decision problems). We show that optimal strategies obtained from finite models approximate the optimal cost with arbitrary precision under mild technical assumptions. In particular, we show that quantized team policies are asymptotically optimal. In Chapter 9, the results are applied to Witsenhausen’s counterexample and the Gaussian relay channel problem

Information constraints in multiple agent problems with i.i.d. states

International audienceIn this chapter we describe several recent results on the problem of coordination among agents when they have partial information about a state which affects their utility, payoff, or reward function. The state is not controlled and rather evolves according to an independent and identically distributed (i.i.d.) random process. This random process might represent various phenomena. In control, it may represent a perturbation or model uncertainty. In the context of smart grids, it may represent a forecasting noise [1]. In wireless communications, it may represent the state of the global communication channel. The approach used is to exploit Shannon theory to characterize the achievable long-term utility region. Two scenarios are described. In the first scenario, the number of agents is arbitrary and the agents have causal knowledge about the state. In the second scenario, there are only two agents and the agents have some knowledge about the future of the state, making its knowledge non-causal

Asymptotic optimality of finite models for witsenhausen’s counterexample and beyond

Due to copyright restrictions, the access to the full text of this article is only available via subscription.In this chapter, we study the approximation of Witsenhausen’s counterexample and the Gaussian relay channel problem by using the results of the previous chapter. In particular, our goal is to establish that finite models obtained through the uniform quantization of the observation and action spaces result in a sequence of policies whose costs converge to the value function. We note that the operation of quantization has typically been the method to show that a non-linear policy can perform better than an optimal linear policy, both for Witsenhausen’s counterexample [10, 86] and the Gaussian relay channel problem [88, 152]. Our findings show that for a large class of problems, quantized policies not only may perform better than linear policies, but that they are actually almost optimal

Limits on the Efficiency of (Ring) LWE Based Non-interactive Key Exchange.

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