Model-based verification of timing properties has become industrial practice in design processes of safety-critical hard real-time systems. To validate the correctness of the used verification model, systems are additionally monitored during regular operation. With a growing variety of activation patterns considered in verification, some of them with infinite range capturing arbitrary activation patterns, the known approaches to monitoring, which assume periodic streams, have become inapplicable or they suffer from large overhead due to piecewise continuous time monitoring. In this paper we present a light-weight monitoring approach for arbitrary activation patterns. It profits from the discrete time property of a minimum distance event representation which is used instead of the continuous time representation used in earlier approaches. The method has a configurable constant runtime overhead in terms of memory and computation and allows conservative monitoring of a given arbitrary minimum distance function. Furthermore, we provide conditions under which the monitoring function is exact.