On Load Balancing in Multicomputer/Distributed Systems Equipped with Circuit or Cut-Through Switching Capability

For multicomputer or distributed systems that use circuit switching, wormhole routing, or virtual cut-through, 2 the communication overhead and the message delivery time depend largely upon link contention rather than upon the distance between the source and the destination. That is, a larger communication overhead or a longer delivery delay occurs to a message when it traverses a route with heavier traac than one with a longer distance and lesser traac. This characteristic greatly aaects the selection of routes for interprocessor communication and/or load balancing. We consider the load balancing problem in these types of systems. Our objective is to nd the maximum load imbalance that can be eliminated without violating the (traac) capacity constraint while keeping the maximum link contention as low as possible. We investigate the load balancing problem under various conditions. First, we consider the case in which the excess load on each overloaded node is divisible. We devise a network ow algorithm to solve this type of load balancing problem optimally in polynomial time. Next, we impose the realistic assumption that the system uses a speciic routing scheme so that the excess load transferred from an overloaded node to an underloaded node must use the route found by the routing scheme. For this case, we use a graph transformation technique to transform the system graph to another graph to which the same network ow algorithm can be applied to solve the load balancing problem optimally. Finally, we consider the case in which the excess load on each overloaded node is indivisible, i.e., excess load must be transferred as an entity. We show that the load balancing problem of this type becomes NP-complete, and propose a heuristic algorithm as a solution. Any opinions, ndings, and conclusions or recommendations expressed in this paper are those of the authors and do not necessarily reeect the views of the funding agencies. 2 The last two are collectively called the cut-through switching.