Optimal Synchronization of ABD Networks

We present in this paper a simple and e cient synchronizer algorithm for Asynchronous Bounded Delay Networks. In these networks each processor has a local clock, and the message delay is bounded by a known constant. The algorithm improves on an earlier synchronizer for this network model, presented by Chou et al.[CCGZ90]. Moreover, using a mathematical model for this type of synchronizer, we show that the round time of the new synchronizer is optimal. 1 A Synchronizer Algorithm Two models of computation have been used for the development of distributed algorithms: the synchronous and the asynchronousmodel. In the synchronous model the execution of an algorithm operates in discrete steps called rounds. The actions of a process in round (i + 1) depend on the state of the process after round i and the messages sent to it in round i. Note that it is therefore necessary that all messages that are sent to some process in round i are received before the process starts its computation of round (i+ 1). We can think of the system as if there were a global clock, giving pulses at regular intervals. Computation takes place at clock pulses, and a message that is sent at one pulse is guaranteed to be received before the next pulse. In the asynchronous model it is assumed that there are no clocks and message delivery time is not bounded a priori. The work of this author was supported by the ESPRIT III Basic Research Actions Program of the EC under contract no. 7141 (project ALCOM II). Author's address: Department of Computer Science, University of Utrecht, P.O. Box 80.089, 3508 TB Utrecht, The Netherlands. Email: [email protected]. Author's address: Department of Industrial Engineering, Ben Gurion University of the Negev, P.O. Box 653, Beer Sheva 84105, Israel. Email: [email protected]. Author's address: Department of Computer Science, The Technion, Technion City, Haifa 32000, Israel. Email: [email protected].