A class of algorithms for collision resolution with multiplicity estimation

The wireless connectivity in pervasive computing has ephemeral character and can be used for creating ad hoc networks, sensor networks, connection with RFID (Radio Frequency Identification) tags etc. The communication tasks in such wireless networks often involve an inquiry over a shared channel, which can be invoked for: discovery of neighboring devices in ad hoc networks, counting the number of RFID tags that have a certain property, estimating the mean value contained in a group of sensors etc. Such an inquiry solicits replies from possibly large number of terminals n. This necessitates the usage of algorithms for resolving batch collisions (conflicts) with unknown conflict multiplicity n. In this paper we present a novel approach to the problem of collision resolution for batch conflicts. We show how the conventional tree algorithms for collision resolution can be used to obtain progressively accurate estimation of the multiplicity. We use the estimation to propose a more efficient binary tree algorithm, termed Estimating Binary Tree (EBT) algorithm. The EBT algorithm is suited for implementation when the conflicting nodes are passive, such as e.g. RFID tags. We extend the approach to design the Interval Estimation Conflict Resolution (IECR) algorithm. For n -> infinity we prove that the efficiency achieved by IECR for batch arrivals is identical with the efficiency that Gallager's FCFS algorithm achieves for Poisson packet arrivals. For finite n, the simulation results show that IECR is, to the best of our knowledge, the most efficient batch resolution algorithm reported to date.