In some data centers that have been set up to provide computing and/or storage facilities to remote clients, the set of computational resources at the data center may be dynamically divided into resource pools, with each pool being made available for exclusive use by a given client for designated periods of time. There are a number of alternatives available for how the consumers of these facilities establish network connectivity to the resource pools that have been designated for their use. The customer requests may originate from a wide variety of devices—desktop personal computers, laptops, client-office servers, tablets, smart phones and the like. These devices may use either long-lasting network links (e.g., using a client office network with a T1 connection) to communicate with their proximate private network and/or the public Internet, or they may have transient connectivity (e.g., in the case where the customer uses a mobile smart phone). The proximate networks to which the customer devices are directly connected may in turn route request traffic to the provider network's data centers over a wide variety of paths. Such paths in many cases may have somewhat unpredictable performance, reliability and security characteristics.