We consider a system of three queues in which arriving customers are assigned to other queues if rejected from entry to one queue; and thus the work load of each queue is shared. The objective function considered is a combination of holding costs, routing costs, and customer service rewards. We first establish the characteristics of optimal control policies via a Markov decision process formulation. Next, the decomposed problems with partial information for each server are considered and the results compared with the original problem are shown. Appropriate combinations of optimal solutions for the decomposed problems are then used either in approximating the centralized optimal policy or in determining a good starting policy for successive approximation of the multidimensional Markov decision process. Numerical results of specific models are also presented.