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Service-based systems (SBSs) that are built through dynamic composition of component services must be monitored in order to guarantee the response time of the SBSs. However, monitoring consumes resources and very often impacts the quality of the SBSs being monitored. Hence, monitoring incurs resource cost and system cost, which need to be considered in formulating monitoring strategies for SBSs. The critical path of a composite SBS, which is of particular importance in cost-effective monitoring, is probabilistic in volatile operating environments. It is important to estimate the criticalities of different execution paths when deciding which parts of the SBS to monitor. Furthermore, cost-effective monitoring also requires management of the trade-off between the benefit and cost of monitoring. In this paper, we propose CriMon, a novel approach to formulating monitoring strategies for SBSs. CriMon first calculates the criticalities of the execution paths of an SBS and then, based on those criticalities, generates locally or globally optimal monitoring strategy considering both the benefit and cost of monitoring. In-lab experimental results demonstrate that in volatile environments the response time of an SBS can be managed cost-effectively through CriMon-based monitoring. The effectiveness and efficiency of the two monitoring strategy formulation methods are evaluated and compared.