Actual holding times for calls in a PCS network

The explicit distribution function of the actual holding time of a new call in a PCS network, with general cell residence time and general requested call holding time, is obtained. The effective call holding time of an incompleted and of completed calls are shown to be the conditional actual holding time of an incompleted call and of a completed call, respectively. If the holding time is of Erlang or if both the residence and requested call holding times belong to the class of new better than used (NBU), we proved that the mean effective call holding time of an incompleted call is less than the mean requested call holding time of a call. For any kind of random variables of the residence time and requested call holding time, we proved that the mean effective call holding time of a completed call is always less than the mean requested call holding time of a call