1. A method, comprising steps of: providing in a router a database of bindings of client devices to network applications to replicas of a network application, where a client device establishes a session with a replica of a network application, where the session includes a session state, where a binding includes a binding expiration time, and where the router is a first router of a plurality of routers associated with a network in which the network applications run; maintaining a change log of records entered into the database, where a change log entry has a change event generated by the first router and an event number sequential to an event number of a preceding change event in the change log; maintaining a current version vector associated with the database and the change log, the current version vector entry for the first router being a most recent event number from the change log, the current version vector entry for each other router being a most recent event number received at the first router from that other router; receiving an update of change events generated at another router in the plurality; reconciling the current version vector according to the received update, wherein the step of reconciling the current version vector comprises the steps of: comparing a least recent event number of the router that generated the update to the event number in the current version vector entry for that router; if the least recent event number is in series with the event numbers in the database as determined by the current version vector entry for that other router, then entering the most recent event number of the received update into the current version vector entry for the router that generated the update of change events; and if the least recent event number in the update is not in succession to the event number in the current version vector entry for the router that generated the update of change events, then discarding the received update, reconciling the database according to the received update such that the client session is maintained; and providing a consistent DNS binding to a set of related application connection requests from a client device, where the set of related application connection requests request access to a network application having multiple replicas in a distributed network environment, and where the set of requests are associated with a single session established between the client device and a single replica of the network application.