Expected Quorum Overlap Sizes of Optimal Quorum Systems with the Rotation Closure Property for Asynchronous Power-Saving Algorithms in Mobile Ad Hoc Networks

The FPP, grid, cyclic, torus and e-torus quorum systems satisfy the rotation closure property and have the optimal or near optimal quorum sizes. They can be used to achieve asynchronous power-saving algorithms in mobile ad hoc networks with the lowest or near lowest active ratios. The algorithms guarantee that a node receives one or more beacons from every neighboring node within a round of beacon intervals. Receiving beacons is important for a node to sense the existence and statuses of neighboring nodes. We can use the smallest quorum overlap size (SQOS) or the maximum quorum overlap separation (MQOS) to measure a quorum-based algorithm’s neighbor sensibility. However, it is difficult to judge quorum systems by SQOS or MQOS since most quorum systems have the same SQOS and MQOS values. In this paper, we propose using the expected quorum overlap size (EQOS) of a quorum system as an average-case neighbor sensibility measurement to estimate the expected number of beacons received in a round. Quorum systems have various EQOS values and we can thus choose proper quorum systems accordingly. We analyze EQOS values for the optimal and near optimal quorum systems, and observe that their EQOS values are far more than one. We thus propose a new quorum system, called the fraction torus (f-torus) quorum system, for the construction of flexible mobility-adaptive power saving algorithms. The f-torus quorum systems can further reduce the energy expenditure by shrinking the quorum size, while keeping the EQOS larger than one. We further derive EQOS values for the FPP, grid, cyclic, torus, e-torus and f-torus quorum systems by simulation experiments. As we will show, the EQOS analysis and simulation results coincide very closely.