1. A parallel processing system executing associated processes on a plurality of processing parts, the parallel processing system comprising: a memory; a first process processing part configured to execute a first predetermined process; a first process scheduler configured to detect and manage a first processing status of a first process executed by the first process processing part; a second process processing part configured to execute a second process associated with the first process executed by the first process processing part; and a second process scheduler configured to detect and manage a second processing status of a second process executed by the second process processing part, wherein: the first process scheduler and the second process scheduler are configured to communicate with each other; the first process scheduler is configured to, in accordance with the second 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 the second process shown by the second processing status; the second process scheduler is configured to, in accordance with the first 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 the first process shown by the first 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 first 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 first process shown by the status notification information, wherein: the first process scheduler is configured to, in saving a process context of a process executed by the first process processing part, transmit status notification information showing that the first process has transitioned to a standby state to the second process scheduler; and the second process scheduler is configured to, on a basis of the status notification information having been received, execute control to lower a priority level of causing the second process processing part to process a process associated with the first process having transitioned to the standby state.