Non-stationary and stationary coincidence probabilities for intermittent pulse load processes

A train of intermittent rectangular load pulses with arrival times driven by an Erlang renewal process and with durations distributed according to a truncated Erlang distribution is considered. Based on the phase approach of queueing theory the differential equations governing the probabilities of the system being in different Markov states are derived. The differential equations for the coincidence probabilities are also obtained for mutually independent loads arising from different sources. The non-stationary and stationary solution for Markov states probabilities and coincidence probabilities is formulated and these probabilities are evaluated for different models. In particular, the stationary coincidence probabilities are evaluated for the example problem of a steel column under bending and compression caused by three independent intermittent loads.