We consider a network of parallel, non-observable queues and analyze the Price of Anarchy (PoA) from the new point of view where the router has the memory of previous dispatching choices. In the regime where the demands grow with the network size, we provide an upper bound on the PoA by means of convex programming. To study the impact of non-Bernoulli routers, we introduce the Price of Forgetting (PoF) and prove that it is bounded from above by two. Numerical experiments show that the benefit of having memory in the router is independent of the network size and heterogeneity, and monotonically depends on the network load only.