Revenue management is the art and science of enhancing firm revenue while sell-ing the same quantity of product. Network revenue management models attempt to maximize revenue when customers buy bundles of multiple resources. Capacity control and overbook-ing are two fundamental pieces of revenue management. Revenue management practices of-ten include overbooking capacity to account for customers who make reservations but later make cancellations or do not show up. Capacity control deals with the question of which requests should be accepted over time. Capacity control and overbooking decisions interact. The joint problem can be formulated as a dynamic program. This dynamic program cannot be solved by using traditional dynamic programming tools for problems of practical size. The paper analyzes linear approximations of the joint problem of capacity control in network revenue management and overbooking.