Coincident Cost Improvement vs. Degradation by Adding Connections to Noncooperative Networks and Distributed Systems

In computer and transportation networks, we consider the situation where each user has its own routing or load balancing decision and seeks to minimize noncooperatively the expected passage time of its packet or job, given the routing or load balancing decisions of other users. Intuitively, it is anticipated that adding connections to such a noncooperative system may bring cost improvement at least to some users. The Braess paradox is, however, the first example of paradoxical cases where it is not always the case. A few studies have been published on the degrees of coincident cost degradation for all users by adding connections. In contrast, it has not been certain whether or to what degree adding connections to a network can bring coincident cost improvement for all users. We believe that this paper is the first one that studies the possible degrees of coincident cost improvement for all users by adding connections to noncooperative systems. There has been found no system in Wardrop equilibrium for which the degree of degradation can increase without bound by adding connections with the number of nodes fixed. We show that there exist systems in Wardrop equilibria and ones in Nash equilibria for both of which the degree of coincident cost improvement can increase without bound for all users by adding connections, even if the number of nodes is fixed. We then study, for models reflecting realistic distributed systems, the effects of adding connections to them on the coincident cost improvement or degradation for all users.