Excess level processes in queueing

This article analyzes the behaviour of one- and two-dimensional marked point processes (with dependent marks) about some fixed level. The author obtains a joint transformation of the first excess level, first passage time, and the index of the point process (that labels the first passage time). Obtained results are demonstrated on various queueing systems, such as those with quorum, vacations, N-policy, D-policy, and ‘vector’ customers, specifically N-D-policy.