Effects of Erlang call holding times on PCS call completion

Abstract

Previous performance studies of PCS channel allocation assumed that call holding times have an exponential distribution. The exponential call holding time assumption is justified for existing cellular systems, where wireless calls are charged based on the length of the call holding time. Future PCS systems may exercise flat rate billing, and consequently a more general distribution is desirable to model the call holding times. This paper models the call holding times by the Erlang distribution (a generalization of the exponential distribution) to investigate the effect of the variance of the call holding times on the call completion probability. Our analysis indicates that the call completion probability decreases as the variance of the call holding times decreases. This effect becomes more pronounced as the variance of the cell residence times decreases.