We consider a rate control algorithm for elastic services to allocate bandwidth in a network subject to throughput and fairness constraints. Our algorithm achieves a max-min fair bandwidth allocation among contending elastic connections, and has desirable properties in that it can operate in a decentralized and asynchronous manner accounting in part for heterogeneity in round trip delays. The algorithm is simple and scalable in that, 1) the network links make local measurements of capacity and calculate local 'explicit rates' which are fed back to sources without requiring knowledge of the number of on-going connections, while 2) sources adjust their transmission rates so as not to exceed the received explicit rate indication. The algorithm is designed to track a "dynamic" network environment. We discuss its stability, convergence, and feasibility issues related to fair allocation and rate-based flow control. We also consider the role of sessions with priorities to differentiate among users with elastic services. Through rigorous analysis and simulations, we have shown that it has indeed desirable characteristics for networks with elastic services as well as other service types, which are expected to be common in future network environment.