Application level modeling of parallel machines

• Authors: K. Kant
• Venue: SIGMETRICS '88 Proceedings of the 1988 ACM SIGMETRICS conference on Measurement and modeling of computer systems
• Year: 1988

In this paper, we consider the application level performance modeling of parallel machines consisting of a large number of processing elements (PE's) connected in some regular structure such as mesh, tree, hypercube, etc. There are K problem types, each arriving according to a Poisson process, and each of which needs a PE substructure of some given size and topology. Thus several problems can run on the machine simultaneously. It is desired to characterize the performance of such a system under various types of allocation schemes.We show that if the queueing is considered external to our model, it is possible to construct a Markovian model with local balance property. The time for which a substructure is held by a problem could be generally distributed. The model can be solved efficiently using standard techniques; however, because of rather complex structure of the state space, its direct enumeration is difficult to avoid. We also show how the size of the state space can be reduced when the set of allowed substructures is highly regular. We then show how queueing delays can be modeled approximately. Finally, we consider the solution of models involving shared resources such as global memory.