Complex event processing (CEP) is attracting much attention as a method for analyzing streaming data in the IoT environment. Since a CEP system selects and executes a rule from rules that match identified events, i.e., multiple rules are sequentially executed. This, however, causes a problem in the Internet of Things (IoT) environment since rule execution is slow and the remaining rules must wait to be executed. Simply executing rules in parallel may trigger interference between rules, and thus unexpected and undesirable results. This paper extends the traditional CEP system by developing an execution model for parallel rule firing in the IoT environment so as to be able to execute multiple rules in parallel without any interference. We start with an extended parallel firing condition by adding the definition of dependency between sensors and actuators to the condition. Next, we extend synchronization control of parallel firing so as to avoid the interference among rules that can occur when actions take a lot of time to execute. This paper reveals that the extended CEP system (i) realizes triple parallelism (i.e., data parallelism, task parallelism, and pipeline parallelism) in the IoT environment and (ii) avoids the case where rule execution triggers unexpected results.