A random point process or marked point process with marks denoting some aspects of the stream of customers arriving to a queue or some aspects of the queue itself at the times of arrival, with points representing the precise instants of arrivals. For example, in the marked point process (Xv^a, Tv^a), the Xv^a process may represent the sequence of customer priority classes arriving to a queue, while the Tv^a process would be the sequence of actual arrival times.