In this paper, we describe a new job scheduling class, called \Time Space Sharing Scheduling" (TSSS) for dynamically partitionable parallel machines. As an instance of TSSS, we explain the \Distributed Queue Tree" (DQT) that we have proposed already. We also propose some architectural support to implement TSSS on a parallel machine as adequately as TSS on sequential machines. The most important architectural support is \network preemption." The proposed architectural support will be implemented on our RWC-1, a messagedriven parallel machine, and the DQT will also be implemented in the operating system on the RWC-1, called SCore, under development in our RWC project