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Several recent studies have investigated the virtual machine (VM) provisioning problem for requests with time constraints (deadlines) in cloud systems. These studies typically assumed that a request is associated with a single execution time when running on VMs with a given resource demand. In this paper, we consider modern applications that are normally implemented with generic frameworks that allow them to execute with various numbers of threads on VMs with different resource demands. For such applications, it is possible for the users to specify multiple execution options (MEOs) for a request where each execution option is represented by a certain number of VMs with some resources to run the application and its corresponding execution time. We investigate the problem of virtual machine provisioning for such time-sensitive requests with MEOs in resource-constrained clouds. By incorporating the MEOs of requests, we propose several novel and flexible VM provisioning schemes that carefully balance resource usage efficiency, input workloads and request deadlines with the objective of achieving higher resource utilization and system benefits. We evaluated the proposed MEO-aware schemes on various workloads with both benchmark requests and synthetic requests. The results show that our MEO-aware algorithms outperform the state-of-the-art schemes that consider only a single execution option of requests by serving up to 38% more requests and achieving up to 27% more benefits.