BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//CS-TR-74-423
       ENTRY:: August 23, 1995
ORGANIZATION:: Stanford University, Department of Computer Science
       TITLE:: Asymptotic representation of the average number of active
               modules in an n-way interleaved memory.
        TYPE:: Technical Report
      AUTHOR:: Rao, Gururaj S.
        DATE:: April 1974
       PAGES:: 15
    ABSTRACT:: In an n-way interleaved memory the effective bandwidth
               depends on the average number of concurrently active modules.
               Using a model for the memory which does not permit queueing
               on busy modules and which assumes an infinite stream of calls
               on the modules, where the elements in the stream occur with
               equal probability, the average number is a combinatorial
               quantity. Hellerman has previously app oximated this quantity
               by $n^{0.56}$.

               We show in this paper that the average number is
               asymptotically equal to $sqrt{\frac{\pi n}{2}} -
               \frac{1}{3}$. The method is due to Knuth and expresses the
               combinatorial quantity in terms of the incomplete gamma
               function and its deriviatives.
       NOTES:: [Adminitrivia V1/Prg/19950823]
         END:: STAN//CS-TR-74-423