We propose a scalable service execution control method for a service that is triggered when the context satisfies an execution condition. We call such services context-dependent. A context-dependent service needs to monitor the context that affects the execution condition all the time. The proposed method tremendously reduces the cost of context monitoring operations while it surely executes appropriate services when their execution conditions are satisfied. Our method assumes that there are a lot of terminals monitoring contexts and a server that collects context information from the terminals to manage service executions for a large number of services. Each context is modeled by a probabilistic time series, and thus, the probability that an execution condition is satisfied can be calculated at a given time. The time at which the execution condition is likely to be satisfied is anticipated, and the server instructs relevant terminals to monitor contexts and to send their values to it before the anticipated execution. The time to collect context values is decided by the server, which considers the effect of the statistical variance of each context on the probability of satisfying the execution condition. Moreover, each terminal monitors its context and notifies the server when its value is out of the designated range, even if this occurs before the time set by the server. The range of values is set by the server. We conducted simulation experiments that showed the effectiveness of the proposed method.