Joint Probability Density Function of Modulated Synchronous Flow Interval Duration Under Conditions of Fixed Dead Time

Abstract

A modulated synchronous doubly stochastic flow under conditions of a fixed dead time is considered. After each registered event there is a time of fixed duration T (dead time), during which another flow events are inaccessible for observation. When duration of the dead time period finishes, the first happened event creates the dead time period of duration T again and etc. An explicit form of a probability density function of interval duration between two adjacent events of modulated synchronous doubly stochastic flow under conditions of a fixed dead time is derived. Also an explicit form of a joint probability density function for modulated synchronous flow interval duration is obtained. A recurrent conditions for modulated synchronous flow as well as some probabilistic characteristics of the flow are obtained using the formula for a joint probability density function.