A Study on Random Sum Statistics: Application to Wireless Network Performance Analysis

The statistics of random sum is studied and used to evaluate performance metrics
in wireless networks. Pertinent wireless network performance measures such as call
completion/dropping probabilities and the average number of handovers usually require
the probability distributions of the cell dwell time and call holding time; and are therefore
not easy to evaluate. The proposed performance evaluation technique requires the
moments of the cell dwell time and is given in terms of the Laplace transform function of
the call holding time. Multimedia services that have Weibull and generalized gamma
distributed call holding times are investigated. The proposed approximation method uses
the compound geometric random sum distribution and requires that the geometric
parameter be very small. For applications in which this parameter is not sufficiently
small, a result is derived that improves the accuracy (to order of the geometric parameter)
of the performance measures evaluated.