We examine a possibly capacitated, periodically reviewed, single-stage inventory system where replenishment can be obtained either through a regular fixed lead time channel, or, for a premium, via a channel with a smaller fixed lead time. We consider the case when the unsatisfied demands are backordered over an infinite horizon, introducing the easily implementable, yet informationally rich dual-index policy. We show very general separability results for the optimal parameter values, providing a simulation-based optimization procedure that exploits these separability properties to calculate the optimal inventory parameters within seconds. We explore the performance of the dual-index policy under stationary demands as well as capacitated production environments, demonstrating when the dual-sourcing option is most valuable. We find that the optimal dual-index policy mimics the behavior of the complex, globally optimal state-dependent policy found via dynamic programming: the dual-index policy is nearly optimal (within 1% or 2%) for the majority of cases, and significantly outperforms single sourcing (up to 50% better). Our results on optimal dual-index parameters are generic, extending to a variety of complex and realistic scenarios such as nonstationary demand, random yields, demand spikes, and supply disruptions.

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Redundancy is an important strategy for reducing response time in multi-server distributed queueing systems. This strategy has been used in a variety of settings, but only recently have researchers begun analytical studies. The idea behind redundancy is that customers can greatly reduce response time by waiting in multiple queues at the same time, thereby experiencing the minimum time across queues. Redundancy has been shown to produce significant response time improvements in applications ranging from organ transplant waitlists to Google's BigTable service. However, despite the growing body of theoretical and empirical work on the benefits of redundancy, there is little work addressing the questions of how many copies one needs to make to achieve a response time benefit, and the magnitude of the potential gains.In this paper we propose a theoretical model and dispatching policy to evaluate these questions. Our system consists of k servers, each with its own queue. We introduce the Redundancy-d policy, under which each incoming job makes copies at a constant number of servers, d, chosen at random. Under the assumption that a job's service times are exponential and independent across servers, we derive the first exact expressions for mean response time in Redundancy-d systems with any finite number of servers, as well as expressions for the distribution of response time which are exact as the number of servers approaches infinity. Using our analysis, we show that mean response time decreases as d increases, and that the biggest marginal response time improvement comes from having each job wait in only d 2 queues. service rate µ, the number of servers k, and the degree of redundancy d, to help us understand the role redundancy can play in reducing response time.

We envision a future economy where e-markets will play an essential role as exchange hubs for commodities and services. Future e-markets should be designed to be robust to manipulation, flexible, and sufficiently efficient in facilitating exchanges. One of the most important aspects of designing an e-market is market mechanism design. A market mechanism defines the organization, information exchange process, trading procedure and clearance rules of a market. If we view an e-market as a multi-agent system, the market mechanism also defines the structure and rules of the environment in which agents (buyers and sellers) play the market game. We design an e-market mechanism that is strategy-proof with respect to reservation price, weakly budget-balanced and individually rational. Our mechanism also makes sellers unlikely to under-report the supply volume to drive up the market price. In addition, by bounding our market's efficiency loss, we provide fairly unrestrictive sufficient conditions for the efficiency of our mechanism to converge in a strong sense when (1) the number of agents who successfully trade is large, or (2) the number of agents, trading and not, is large. We implement our design using the RETSINA infrastructure, a multi-agent system development toolkit. This enables us to validate our analytically derived bounds by numerically testing our e-market. keywords: electronic market, auction, mechanism design, multi-agent system, market clearing.

Recent computer systems research has proposed using redundant requests to reduce latency. The idea is to run a request on multiple servers and wait for the first completion (discarding all remaining copies of the request). However, there is no exact analysis of systems with redundancy. This paper presents the first exact analysis of systems with redundancy. We allow for any number of classes of redundant requests, any number of classes of non-redundant requests, any degree of redundancy, and any number of heterogeneous servers. In all cases we derive the limiting distribution of the state of the system. In small (two or three server) systems, we derive simple forms for the distribution of response time of both the redundant classes and non-redundant classes, and we quantify the "gain" to redundant classes and "pain" to non-redundant classes caused by redundancy. We find some surprising results. First, the response time of a fully redundant class follows a simple exponential distribution and that of the non-redundant class follows a generalized hyperexponential. Second, fully redundant classes are "immune" to any pain caused by other classes becoming redundant. We also compare redundancy with other approaches for reducing latency, such as optimal probabilistic splitting of a class among servers (Opt-Split) and join-the-shortest-queue (JSQ) routing of a class. We find that, in many cases, redundancy outperforms JSQ and Opt-Split with respect to overall response time, making it an attractive solution.