Extremal Codes for Speed-up of Distributed Parallel Arbitration

This paper describes a method that allows the speed up of parallel processes in distributed arbitration schemes as used in Futurebus+. It is based on special arbitration codes that decrease the maximal arbitration time to a specified value. Such codes can be applied with few, if any, minor changes of the hardware. The general structure of these codes is given. Introduction. One important component of every multiprocessor bus is the arbitration system. Many modern multiprocessor buses use arbitration systems principally based on the same distributed parallel arbitration scheme [1]. In this scheme, the time for acquiring bus mastership depends on the maximal arbitration time required. This time is determined by the set of arbitration priorities available [2-4]. Such a set will be called an arbitration code or simply a code below. The maximal arbitration time is reduced, e.g., by using binomial codes as discussed in [4] where these codes were introduced. From the discussion it follows that the achievable speed-up depends on the number of arbitration priorities in the binomial code, i.e., on its capacity. However, it has not been considered whether the binomial codes have the maximal possible capacity, i.e., whether there are other codes with equal or greater capacity that can reduce the maximal arbitration time to the same or a lower limit. In the present paper we derive the general structure of the codes of maximal capacity that we will call extremal codes. It will be shown that there exist different extremal codes with binomial codes as one example only. Arbitration process. We consider a distributed parallel arbitration process for a singlebus multiprocessor system. To each processor a unique arbitration priority is assigned that is a m-bit binary word. It will be called an arbitration word or simply a word below. If one or more processors request bus mastership, an arbitration process is started. At ¶ This work has been supported by the Deutsche Forschungsgemeinschaft (DFG) under grants Ma 1150/8-1 and 436-WER-113-1-0 (438 113/117/0).