A Realistic Cost Model for theCommunication Time in Parallel

In this report, we develop a cost model for the communication time on parallel computers consisting of processors and a service network, i.e., a network performing services like broadcast, synchronization, and global variables. Because we do not have a parallel computer at our disposal that is equipped with a service network, we emulate the service network on a reconngurable Transputer network. Our cost model describes the communication time of accesses to global variables and consists of a multi-linear function. The cost model includes the parameters packet size, send hot spot (the number of messages sent out by one processor), and number of processors accessing global variables. We show that these parameters innuence the communication time in a high degree and capture important parameters like network contention. We implement a Bitonic Sort, Sample Sort, Matrix Multiplication, and Connected Components algorithm, and we show that our model is able to predict the communication time within a 10% error if indirect service networks are used. The applications show that it is easy for a programer to determine the parameter values for our model and that our new cost model precisely predicts the communication time of parallel algorithms. We explore the interaction of hot spots and asynchrony and show that the innuence of hot spots to the communication time is not as high as one would expect from theoretical considerations in a synchronous model. Therefore, we do not apprehend the hot spot in our cost model. Furthermore, we minimize the communication time of accesses to global variables by nding a balance between the number of messages in the network and their size. Our model predicts the optimal values for these parameters which we validate by experiments. A modiied implementation of our routing which determines on-line the optimal parameter values for an access to a global variable achieves good speed ups.