Limit allocation: An efficient processor management scheme for hypercubes

Efficient task management in a hypercube multi-processor becomes difficult due to system overflow, where an incoming job cannot be allocated in spite of a sufficient number of free processors. Overflow occurs either due to the inability of recognizing a free subcube or due to external fragmentation. In this paper, we propose an allocation strategy that tries to scale down an incoming job size if it cannot fit into a fragmented hypercube. We call it limit allocation. We discuss three simple schemes, Limit-k, Greedy and Average. We conduct both analysis and simulation to characterize and compare various allocation policies. An M/M/m queueing model is developed to predict the behavior of buddy, free list and limit-k policies. The simulation study shows that the two adaptive schemes, greedy and average, outperform all other schemes reported so far in the literature.