Quorum Systems Constructed from Combinatorial Designs

A quorum system is a set system in which any two subsets have nonempty intersection. Quorum systems have been extensively studied as a method of maintaining consistency in distributed systems. Important attributes of a quorum system include the load, balancing ratio, rank (i.e., quorum size) and availability. Many constructions have been presented in the literature for quorum systems in which these attributes take on optimal or otherwise favorable values. In this paper, we point out an elementary connection between quorum systems and the classical covering systems studied in combinatorial design theory. We look more closely at the quorum systems that are obtained from balanced incomplete block designs (BIBDs). We study the properties of these quorum systems, and observe that they have load, balancing ratio and rank that are all within a constant factor of being optimal. We also provide several observations about computing the failure polynomials of a quorum system (failure polynomials are used to measure availability). Asymptotic properties of failure polynomials have previously been analyzed for certain innnite families of quorum systems. We give an explicit formula for the failure polynomials for an easily constructed innnite class of quorum systems. We also develop two algorithms that are useful for computing failure polynomials for quorum systems, and prove that computing failure polynomials is #P-hard. Computational results are presented for several \small" quorum systems obtained from BIBDs.