Implementation of a Task

In this paper we present a distributed algorithm to implement a task pool. The algorithm can be used to implement a processor farm, i.e., a collection of processes that consume tasks from the task pool and possibly produce tasks into it. There are no restrictions on which process consumes which task nor on the order in which tasks are processed. The algorithm takes care of the distribution of the tasks over the processes and ensures load balancing. We derive the algorithm by transforming a sequential algorithm into a distributed one. The transformation is guided by the distribution of the data over processes. First we discuss the case of two processes, and then the general case of one or more processes. For the sequential part of the algorithms, we use Edsger W. Dijkstra's guarded command language 1]. For statements S0 and S1, statement S0kS1 denotes their concurrent execution. The constituents S0 and S1 are then called processes. The statements may share variables (cf. 5]). We transform our algorithms in such a way, however, that the nal code contains no shared variables and all synchronization and communication is performed by message passing. The semantics of the message passing primitives is as described in 4]. The main diierence with C.A.R. Hoare's proposal in 2] is in the naming of channels rather than processes. In 3], the same author proposes to name channels instead of processes in communication commands, but diiers from our notation by using one name per channel instead of our two: output command R!E in one process is paired with input command L?v in another process by declaring the pair (R; L) to be a channel between the two processes. Each channel is between two processes only. When declaring (R; L) to be a channel, we write the name on which the output actions are performed rst and the name on which the input actions are performed last. For an arbitrary command A, let c A denote the number of completed A actions, i.e., the number of times that command A has been executed since initiation of the program's execution. The synchronization requirement (cf. 4]) fulllled by a channel (R; L) is that c R = c L 0