Numerical studies on a paradox for non-cooperative static load balancing in distributed computer systems

Numerical examples of a Braess-like paradox in which adding capacity to a distributed computer system may degrade the performance of all users in the system under non-cooperative optimization have been reported. Unlike the original Braess paradox, in the models examined, this behavior occurs only in the case of finitely many users and not in the case of infinite number of users and the degree of performance degradation can increase without bound. This study examines numerically some examples around the Braess-like paradox in a distributed computer system. In the numerical examples, it is observed that the worst-case degree of the paradox (WCDP) is largest in complete symmetry. The dependence of the WCDP on some system parameters is also examined.