In this paper, we consider an event-driven wireless sensor network (WSN) scenario, in which the events arrive with a certain probability in a time of interval. Firstly, we analyze the event delay in a single node in an M/G/1 vacation queueing model. Then, considering the limited buffer space, channel contention and the possibility of a link failure, we derive the total average event delay through a route path. Finally, we build an OMNeT++ simulation and verify our theoretical research results. This research work should provide a guidance for understanding the event delay and future designing more flexible event-driven WSN routing protocols.