BIB-VERSION:: CS-TR-v2.0
          ID:: STAN//CSL-TR-77-129
       ENTRY:: December 01, 1994
ORGANIZATION:: Stanford University, Computer Systems Laboratory
       TITLE:: ON ACCURACY IMPROVEMENT AND APPLICABILITY CONDITIONS OF
               DIFFUSION APPROXIMATION WITH APPLICATIONS TO MODELLING OF
               COMPUTER SYSTEMS
        TYPE:: Technical Report
      AUTHOR:: Yu, Philip S.
        DATE:: January 1977
       PAGES:: 106
    ABSTRACT:: Starting with single server queueing systems, we find a
               different way to estimate the diffusion parameters. The
               boundary condition is handled using the Feller's elementary
               return process. Extensive comparisons by asymptotic,
               simulation and numerical techniques have been conducted to
               establish the superiority of the proposed method compared
               with conventional methods. The limitation of the diffusion
               approximation is also investigated. When the coefficient of
               variation of interarrival time is larger than one, the mean
               queue length may vary over a wide range even if the mean and
               variance of interarrival time are kept unchanged. The
               diffusion approximation is applicable under the condition
               that the high variation of interarrival time conducted on
               2-stage hyperexponential distributions. A similar anomaly is
               observed in two server closed queueing networks when the
               service time of any server has a large coefficient of
               variation. Again, a similar regularity condition on the
               service time distribution is required in order for the
               diffusion approximation to be applicable. For general
               queueing networks, the problems become more complicated. A
               simple way to estimate the coefficient of variation of
               interarrival time (when the network is decomposable) is
               proposed. Besides the anomalies cited before, networks under
               certain topologies, such as networks with feedback loops,
               especially self loops, can not be decomposed into separate
               single servers when the coefficient of variation of service
               time distributions become large, even if the large variations
               are due to a large number of short service times.
               Nevertheless, the decomposability of a network can be
               improved by replacing each server with a self loop by an
               equivalent server without a self loop. Finally, we consider
               the service center with a queue dependent service rate or
               arrival rate. Generalization to two server closed queueing
               networks where each server may have a self loop is also
               considered.
       NOTES:: [Adminitrivia V1/Prg/19941201]
         END:: STAN//CSL-TR-77-129