Braess Paradox in Non-Cooperative Dynamic Load Balancing For the Cohen-Kelly Computer Network Model

We consider a distributed computer system in Wardrop equilibrium, i.e., situations where no user can reduce its own response time by unilaterally choosing another path, if all the other users retain their present paths. The Braess paradox is a famous example of paradoxical cases where adding capacity to a network degrades the performance of all users. This study examines numerically some examples around the Braess-like paradox in a distributed computer system. We found that Braess’s paradox can occur, namely in equilibrium the mean job response time in the network after adding a communication line for the sharing of jobs between nodes, for some system parameter setting, can be greater than the mean job response time in the network before adding the communication line. Indeed, two different types of paradox called weak and strong paradox have been characterized. In the range of parameter values examined, the worst case ratio of performance degradation obtained in the examined network model is about 75% and 65% for the cases of weak and strong paradox respectively.