Characterizing the Variability of Arrival Processes with
                   Indices of Dispersion

                      Riccardo Gusella

          International Computer Science Institute
               1947 Center Street, Suite 600
                 Berkeley, California 94704

                         TR-90-051
                     September 26, 1990

     We propose to characterize  the  burstiness  of  packet
     arrival processes with indices of dispersion for inter-
     vals and for counts.  These indices,  which  are  func-
     tions  of  the  variance  of  intervals and counts, are
     relatively straightforward to estimate and convey  much
     more  information  than  simpler  indices,  such as the
     coefficient  of  variation,  that  are  often  used  to
     describe burstiness quantitatively.

     We define and evaluate the indices  of  dispersion  for
     some  of  the  simple  analytical  models that are fre-
     quently used to represent  highly  variable  processes.
     We  then  estimate the indices for a number of measured
     point processes that  were  generated  by  workstations
     communicating  to  file  servers over a local-area net-
     work.

     We show that nonstationary components in  the  measured
     packet  arrival  data  distort the shape of the indices
     and  propose  ways  to   handle   nonstationary   data.
     Finally,  to show how to incorporate measures of varia-
     bility into analytical models and to offer  an  example
     of  how to model our measured packet arrival processes,
     we describe a fitting procedure based on the  index  of
     dispersion  for counts for the Markov-modulated Poisson
     process.