1. A parallel processing system executing associated processes on a plurality of processing parts, the parallel processing system comprising: a first process processing part configured to execute a predetermined process; a first process scheduler configured to detect and manage a processing status of a process executed by the first process processing part; a second process processing part configured to execute a process associated with a process executed by the first process processing part; and a second process scheduler configured to detect and manage a processing status of a process executed by the second process processing part, wherein: the first process scheduler and the second process scheduler are configured to be able to communicate with each other; the first process scheduler is configured to, in accordance with a processing status of the second process processing part detected by the second process scheduler, control an operation of the first process processing part executing a process associated with a process shown by the processing status; the second process scheduler is configured to, in accordance with a processing status of the first process processing part detected by the first process scheduler, control an operation of the second process processing part executing a process associated with a process shown by the processing status, the first process scheduler is configured to, in switching a process executed by the first process processing part, transmit status notification information showing that the process is switched to the second process scheduler; and the second process scheduler is configured to, on a basis of the status notification information having been received, control an operation of the second process processing part executing a process associated with the process shown by the status notification information.