In traffic engineering, for effectively distributing traffic flows over multiple network paths, it is vital to take traffic characteristics of individual flows into account in appropriately assigning the flows to the network paths to achieve better delay performance as a whole. We have developed a traffic characteristic-based flow assignment method that reduces queuing delay in a buffer at the beginning of each network path. By taking the traffic characteristics of individual flows into account the method can effectively assigns flows to the paths so as to minimize overall queuing delay. We consider the simple case in which two types of flows with distinct traffic characteristics (burstiness) are assigned to two bandwidth-guaranteed paths. The flow assignment of our method reduces the queuing delay (at the edge router) of the worse path, by attempting to optimize the min-max fairness between the paths in terms of queuing delay. Numerical simulation showed that the method assigned the flows such that the queuing delay was reduced up to 40% compared with that when conventional path utilization based flow assignment was used. This means that taking the traffic characteristics of flows into account significantly improves the queuing delay performance when the flows have distinct characteristics.