There is a growing demand to execute on-demand jobs with deadlines on a publicly shared High Performance Computing (HPC) system. There are two potential situations, however, in which a node is unavailable for on-demand job execution upon a job request. One is that the node is running another job, and the other is that the node is in a low-power mode or powered off. In the former case, the running job must be suspended, and in the latter case, the node needs to be started up. This work proposes a job scheduling method for selecting whether to suspend running jobs or to start up sleeping nodes when a sufficient amount of resources is unavailable to complete an on-demand job in time. In addition, by estimating the time required to suspend and resume a job, the proposed method considers the optimal combination of jobs to be suspended to minimize the time for suspending the jobs. Our evaluation indicates that the deadline achievement rate is improved by 18% thanks to the proper selection of running jobs to be suspended for on-demand jobs with strict deadlines. In the case of on-demand jobs with loose deadlines, node start successfully improves the execution efficiency of regular jobs by 11%, and suppresses the increase in energy consumption by 0.3% while maintaining a 100% deadline achievement rate.