Fault tolerance of allocation schemes in massively parallel computers

The author examines the problem of locating and allocating large fault-free subsystems in multiuser massively parallel computer systems. Since the allocation schemes used in such large systems cannot allocate all possible subsystems a reduction in fault tolerance is experienced. The effects of different allocation methods, including the buddy and Gray-coded buddy schemes for the allocation of subsystems in the hypercube and in the two-dimensional mesh and torus are analyzed. Both worst-case and expected-case performance are studied. Generalizing the buddy and Gray-coded systems, a family of allocation schemes which exhibit a significant improvement in fault tolerance over the existing schemes and which use relatively few additional resources is introduced. For purposes of comparison, the behavior of the various schemes on the allocation of subsystems of 2¹⁸ processors in the hypercube, mesh, and torus consisting of 2²⁰ processors is studied. The methods involve a combination of analytical techniques and simulation