Service computing has gained great success because it decouples service providers and consumers. Because of this decoupling, it is possible to reuse software applications without knowing their implementation details. However, business applications consuming complex events (and complex event processing systems in general) are not taking such benefits from service computing, because current service models are not suitable for describing complex events and the reuse mechanisms for complex events are not clear. In this paper, we propose a complex event service description model that captures the exact semantics of complex events, including their patterns and attributes. Then, we propose algorithms to create event service compositions based on event patterns. These algorithms are capable of selecting the composition plans with lowest estimated data traffic demands over the service network. Moreover, we show how to improve the efficiency of event service composition by indexing event patterns