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 (the last two are collectively called the cut-through switching), 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 traffic than the one with a longer distance and lesser traffic. This characteristic greatly affects 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 find the maximum load imbalance that can be eliminated without violating the (traffic) capacity constraint and the route to eliminate the imbalance while keeping the maximum link traffic 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 flow algorithm to solve this type of load balancing problem optimally in polynomial time. Next, we impose the realistic assumption that the system uses a specific 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 flow 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., the 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.