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As availability of web service has become a great concern in SOA, monitoring mechanism is often deployed to detect and recover failures for service composition. While monitoring mechanism could improve the availability to an extent, it may cost more resources and increase the response time perceived by end users. To decrease the overall usage of monitoring resources, this paper proposes to select some services bringing the highest availability improvement to the composition and allocate monitors on them while leaving others unmonitored. This paper first researched two common monitoring mechanisms in service composition and analyzed their different impact on the service composition QoS values. Then continuous-time Markov chain and discrete-time Markov chain were employed to build the availability model related to the monitoring rate or service pool size according to different kind of monitoring mechanisms. Based on these models, two algorithms were proposed, for two monitoring mechanisms respectively, to allocate monitors in the composition aiming at minimizing the overall number of monitors while making sure the composition availability could meet certain requirements. The monitor allocation algorithm could be used to get the overall number of monitors and those services to monitor in different scenarios. Empirical studies results showed that it was feasible to monitor only some services in the composition to meet certain availability requirement. Monitors allocation decreased the overall number of monitors in the service composition and also decreased the mean response time comparing with the scenario that all services were monitored.