Load balancing in a system of two queues with resequencing

We consider a system of two independent servers in parallel. The arriving customers can be directed to either of the two waiting lines. We suppose that there are several classes of customers, routed according to Bernoulli process (with rates depending on class only), and that they have to be resequenced before leaving the system. We determine the routing probabilities that optimize the mean sojourn time in the system (resequencing time included).