When data productions and consumptions are heavily unbalanced and when the origins of data queries are spatially and temporally distributed, the so called in-network data storage paradigm supersedes the conventional data collection paradigm in wireless sensor networks (WSNs). In this paper, we first introduce geometric quorum systems (along with their metrics) to incarnate the idea of in-network data storage. These quorum systems are "geometric" because curves (rather than discrete node sets) are used to form quorums. We then propose GeoQuorum as a new quorum system, for which the quorum forming curves are parameterized. Though our proposal stems from the existing work on using curves to guide data replication and retrieval in dense WSNs, we significantly expand this design methodology, by endowing GeoQuorum with a great flexibility to fine-tune itself towards different application requirements. In particular, the tunability allows GeoQuorum to substantially improve the load balancing performance and to remain competitive in energy efficiency. Both our analysis and simulations confirm the performance enhancement brought by GeoQuorum.
Traditional quorum systems are confined in 2D space, and hence only allow for limited designs, such as the grid shown in Figure (a), or the B-Grid @cite_19 , shown in Figure (b), for improving the robustness. Similar ideas were re-introduced into (MANETs) and WSNs @cite_2 @cite_17 @cite_6 , though sometimes under different names. These designs are often so rigid that they allow very little tunability that adapts a system to various application requirements. To improve the flexibility of the quorum systems, @cite_12 were introduced to relax the intersection rule (making it a random variable) and to leave more freedom in trading load for robustness; they were later applied to MANETs to cope with node mobility @cite_16 . Interested readers are referred to @cite_14 @cite_11 @cite_22 for more recent developments in probabilistic quorum systems. In general, probabilistic quorum systems are designed to cope with system dynamics (e.g., node mobility), hence they are trading system efficiency for higher robustness. As we explained in Sec. , energy efficiency is a crucial issue in WSNs, whereas nodes in WSNs are often static. Consequently, we advocate a deterministic design for quorum systems, while relying on other techniques (rather than pure randomization) to improve its flexibility.
@cite_14 @cite_11 @cite_22 @cite_6 @cite_19 @cite_2 @cite_16 @cite_12 @cite_17
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Reliable storage of data with concurrent read write accesses (or query update) is an ever recurring issue in distributed settings. In mobile ad hoc networks, the problem becomes even more challenging due to highly dynamic and unpredictable topology changes. It is precisely this unpredictability that makes probabilistic protocols very appealing for such environments. Inspired by the principles of probabilistic quorum systems, we present a Probabilistic quorum system for ad hoc networks Pan), a collection of protocols for the reliable storage of data in mobile ad hoc networks. Our system behaves in a predictable way due to the gossip-based diffusion mechanism applied for quorum accesses, and the protocol overhead is reduced by adopting an asymmetric quorum construction. We present an analysis of our Pan system, in terms of both reliability and overhead, which can be used to fine tune protocol parameters to obtain the desired tradeoff between efficiency and fault tolerance. We confirm the predictability and tunability of Pan through simulations with ns-2. It is considered good distributed computing practice to devise object implementations that tolerate contention, periods of asynchrony and a large number of failures, but perform fast if few failures occur, the system is synchronous and there is no contention. This paper initiates the first study of quorum systems that help design such implementations by encompassing, at the same time, optimal resilience (just like traditional quorum systems), as well as optimal best-case complexity (unlike traditional quorum systems). We introduce the notion of a refined quorum system (RQS) of some set S as a set of three classes of subsets (quorums) of S: firstclass quorums are also second class quorums, themselves being also third class quorums. First class quorums have large intersections with all other quorums, second class quorums typically have smaller intersections with those of the third class, the latter simply correspond to traditional quorums. Intuitively, under uncontended and synchronous conditions, a distributed object implementation would expedite an operation if a quorum of the first class is accessed, then degrade gracefully depending on whether a quorum of the second or the third class is accessed. Our notion of refined quorum system is devised assuming a general adversary structure, and this basically allows relying on refined quorum systems to relax the assumption of independent process failures, often questioned in practice. We illustrate the power of refined quorums by introducing two new optimal Byzantine-resilient distributed object implementations: anatomic storage and a consensus algorithm. Both match previously established resilience and best-case complexity lower bounds, closing open gaps, as well as new complexity bounds we establish here. A distributed mobility management scheme using a class of uniform quorum systems (UQS) is proposed for ad hoc networks. In the proposed scheme, location databases are stored in the network nodes themselves, which form a self-organizing virtual backbone within the flat network structure. The databases are dynamically organized into quorums, every two of which intersect at a constant number of databases. Upon location update or call arrival, a mobile's location information is written to or read from all the databases of a quorum, chosen in a nondeterministic manner. Compared with a conventional scheme [such as the use of home location register (HLR)] with fixed associations, this scheme is more suitable for ad hoc networks, where the connectivity of the nodes with the rest of the network can be intermittent and sporadic and the databases are relatively unstable. We introduce UQS, where the size of the quorum intersection is a design parameter that can be tuned to adapt to the traffic and mobility patterns of the network nodes. We propose the construction of UQS through the balanced incomplete block designs. The average cost, due to call loss and location updates using such systems, is analyzed in the presence of database disconnections. Based on the average cost, we investigate the tradeoff between the system reliability and the cost of location updates in the UQS scheme. The problem of optimizing the quorum size under different network traffic and mobility patterns is treated numerically. A dynamic and distributed HLR scheme, as a limiting case of the UQS, is also analyzed and shown to be suboptimal in general. It is also shown that partitioning of the network is sometimes necessary to reduce the cost of mobility management. A quorum system is a collection of sets (quorums) every two of which intersect. Quorum systems have been used for many applications in the area of distributed systems, including mutual exclusion, data replication, and dissemination of information. Given a strategy to pick quorums, the load LS is the minimal access probability of the busiest element, minimizing over the strategies. The capacity is the highest quorum accesses rate that cS can handle, so @math . The availability of a quorum system cS is the probability that at least one quorum survives, assuming that each element fails independently with probability p. A tradeoff between LS and the availability of cS is shown. We present four novel constructions of quorum systems, all featuring optimal or near optimal load, and high availability. The best construction, based on paths in a grid, has a load of @math , and a failure probability of @math when the elements fail with probability @math . Moreover, even in the presence of faults, with exponentially high probability the load of this system is still @math . The analysis of this scheme is based on percolation theory.