Institution: Stanford University, Computer Systems Laboratory

Title: An "almost-exact" solution to the N-processor, M-memory bandwidth problem

Author: Rau, B. Ramakrishna

Date: June 1976

Abstract: A closed-form expression is derived for the memory bandwidth obtained when N processors are permitted to generate requests to M memory modules. Use of generating functions is made, in a rather unusual fashion, to obtain this expressio n. The one approximation involved is shown to result in only a very small error -- and that, too, only for small values of M and N. This expression, which is asymptotically exact, is shown to be more accurate than existing closed form approximations. Lastly, a family of asymptotically exact solutions are presented which are easier to evaluate than is the first one. Although these expressions are less accurate than the previously derived closed-form solution, they are, nevertheless, better than existing solutions.

http://i.stanford.edu/pub/cstr/reports/csl/tr/76/117/CSL-TR-76-117.pdf