Optimal bounds on the gain of permitting dynamic allocation of communication channels in distributed computing

Abstract.

Consider a distributed system consisting of n computers connected by a number of identical broadcast channels. All computers may receive messages from all channels. We distinguish between two kinds of systems: systems in which the computers may send on any channel (dynamic allocation) and system where the send port of each computer is statically allocated to a particular channel. A distributed task (application) is executed on the distributed system. A task performs execution as well as communication between its subtasks. We compare the completion time of the communication for such a task using dynamic allocation and $k_d$ channels with the completion time using static allocation and $k_s$ channels. Some distributed tasks will benefit very much from allowing dynamic allocation, whereas others will work fine with static allocation. In this paper we define optimal upper and lower bounds on the gain (or loss) of using dynamic allocation and $k_d$ channels compared to static allocation and $k_s$ channels. Our results show that, for some tasks, the gain of permitting dynamic allocation is substantial, e.g. when $k_s = k_d = 3$, there are tasks which will complete 1.89 times faster using dynamic allocation compared to using the best possible static allocation, but there are no tasks with a higher such ratio.