Symmetric Allocations for Distributed Storage

We consider the problem of optimally allocating a given total storage budget in a distributed storage system. A source has a data object which it can code and store over a set of storage nodes; it is allowed to store any amount of coded data in each node, as long as the total amount of storage used does not exceed the given budget. A data collector subsequently attempts to recover the original data object by accessing each of the nodes independently with some constant probability. By using an appropriate code, successful recovery occurs when the total amount of data in the accessed nodes is at least the size of the original data object. The goal is to find an optimal storage allocation that maximizes the probability of successful recovery. This optimization problem is challenging because of its discrete nature and nonconvexity, despite its simple formulation. Symmetric allocations (in which all nonempty nodes store the same amount of data), though intuitive, may be suboptimal; the problem is nontrivial even if we optimize over only symmetric allocations. Our main result shows that the symmetric allocation that spreads the budget maximally over all nodes is asymptotically optimal in a regime of interest. Specifically, we derive an upper bound for the suboptimality of this allocation and show that the performance gap vanishes asymptotically in the specified regime. Further, we explicitly find the optimal symmetric allocation for a variety of cases. Our results can be applied to distributed storage systems and other problems dealing with reliability under uncertainty, including delay tolerant networks (DTNs) and content delivery networks (CDNs).Comment: 7 pages, 3 figures, extended version of an IEEE GLOBECOM 2010 pape

On Distributed Storage Allocations for Memory-Limited Systems

In this paper we consider distributed allocation problems with memory constraint limits. Firstly, we propose a tractable relaxation to the problem of optimal symmetric allocations from [1]. The approximated problem is based on the Q-error function, and its solution approaches the solution of the initial problem, as the number of storage nodes in the network grows. Secondly, exploiting this relaxation, we are able to formulate and to solve the problem for storage allocations for memory-limited DSS storing and arbitrary memory profiles. Finally, we discuss the extension to the case of multiple data objects, stored in the DSS.Comment: Submitted to IEEE GLOBECOM'1

Capacity and Security of Heterogeneous Distributed Storage Systems

We study the capacity of heterogeneous distributed storage systems under repair dynamics. Examples of these systems include peer-to-peer storage clouds, wireless, and Internet caching systems. Nodes in a heterogeneous system can have different storage capacities and different repair bandwidths. We give lower and upper bounds on the system capacity. These bounds depend on either the average resources per node, or on a detailed knowledge of the node characteristics. Moreover, we study the case in which nodes may be compromised by an eavesdropper, and give bounds on the system secrecy capacity. One implication of our results is that symmetric repair maximizes the capacity of a homogeneous system, which justifies the model widely used in the literature.Comment: 7 pages, 2 figure

Distributed Storage Allocations for Optimal Delay

We examine the problem of creating an encoded distributed storage representation of a data object for a network of mobile storage nodes so as to achieve the optimal recovery delay. A source node creates a single data object and disseminates an encoded representation of it to other nodes for storage, subject to a given total storage budget. A data collector node subsequently attempts to recover the original data object by contacting other nodes and accessing the data stored in them. By using an appropriate code, successful recovery is achieved when the total amount of data accessed is at least the size of the original data object. The goal is to find an allocation of the given budget over the nodes that optimizes the recovery delay incurred by the data collector; two objectives are considered: (i) maximization of the probability of successful recovery by a given deadline, and (ii) minimization of the expected recovery delay. We solve the problem completely for the second objective in the case of symmetric allocations (in which all nonempty nodes store the same amount of data), and show that the optimal symmetric allocation for the two objectives can be quite different. A simple data dissemination and storage protocol for a mobile delay-tolerant network is evaluated under various scenarios via simulations. Our results show that the choice of storage allocation can have a significant impact on the recovery delay performance, and that coding may or may not be beneficial depending on the circumstances.Comment: Extended version of an IEEE ISIT 2011 paper. 10 pages, 4 figure

Supply chain collaboration

In the past, research in operations management focused on single-firm analysis. Its goal was to provide managers in practice with suitable tools to improve the performance of their firm by calculating optimal inventory quantities, among others. Nowadays, business decisions are dominated by the globalization of markets and increased competition among firms. Further, more and more products reach the customer through supply chains that are composed of independent firms. Following these trends, research in operations management has shifted its focus from single-firm analysis to multi-firm analysis, in particular to improving the efficiency and performance of supply chains under decentralized control. The main characteristics of such chains are that the firms in the chain are independent actors who try to optimize their individual objectives, and that the decisions taken by a firm do also affect the performance of the other parties in the supply chain. These interactions among firms’ decisions ask for alignment and coordination of actions. Therefore, game theory, the study of situations of cooperation or conflict among heterogenous actors, is very well suited to deal with these interactions. This has been recognized by researchers in the field, since there are an ever increasing number of papers that applies tools, methods and models from game theory to supply chain problems

Distributed Storage Allocation Problems

We investigate the problem of using several storage nodes to store a data object, subject to an aggregate storage budget or redundancy constraint. It is challenging to find the optimal allocation that maximizes the probability of successful recovery by the data collector because of the large space of possible symmetric and nonsymmetric allocations, and the nonconvexity of the problem. For the special case of probability-l recovery, we show that the optimal allocation that minimizes the required budget is symmetric. We further explore several storage allocation and access models, and determine the optimal symmetric allocation in the high-probability regime for a case of interest. Based on our experimental investigation, we make a general conjecture about a phase transition on the optimal allocation

On the Usefulness of the Constrained Planning Problem in a Model of Money

In this paper, we study a decentralized monetary economy with a specified set of markets, rules of trade, an equilibrium concept, and a restricted set of policies and derive a set of equilibrium (monetary) allocations. Next we set up a simpler constrained planning problem in which we restrict the planner to choose from a set that contains the set of equilibrium allocations in the decentralized economy. If there is a government policy that allows the decentralized economy to achieve the constrained planner's allocation, then it is the optimal policy choice. To illustrate the power of such analyses, we solve such planning problems in three monetary environments with limited communication. The upshot is that solving constrained planning problems is an extremely "efficient" (easy and quick) way of deriving optimal policies for the corresponding decentralized economies.planning problems; overlapping generations; random relocation model