Operational Delays Induced by Random Exogeneous Events

Exogeneous events occurring as a Poisson process are assumed to cause stoppages in the normal operation of convoys, road vehicles, or equipments. The operational delay experienced by each stoppage is assumed to have an exponential distribution. By introducing appropriate state variables, a hyperbolic partial differential equation is set up; expressions are obtained for the probability that at a given time the operation has registered at most a given number of cumulative performance units (e.g., distance) and for the probability that the operation has registered a given number of cumulative performance units on or before a specified time.