We introduce a task scheduling model which is use-ful in the design and analysis of algorithms for small parallel machines. We prove that under our model, the overhead experienced in scheduling an n x n grid graph is O(loglogn) for p processors, p&gt; 2. We also prove a matching lower bound of Q(loglog n) for p processors, p 1 2. We give an extension of the model to cover the case where the processors can have varying speed or are subject to delay. 