Which protocol transports messages asynchronously over HTTP when implementing long polling?

The Bayeux Protocol is the correct answer because it is specifically designed to enable asynchronous message transport over HTTP, particularly in scenarios that involve long polling and server-sent events. It allows for real-time communication where the server can push messages to the client. This is achieved by establishing a connection that remains open, enabling the server to send data whenever it's available, rather than requiring the client to continuously poll for updates.

In contrast, XMLHttpRequest is primarily used for synchronous or asynchronous data fetching without built-in support for long polling mechanisms. WebSocket, although it does facilitate asynchronous communication, operates differently by establishing a persistent socket connection rather than relying on HTTP request/response patterns, which is characteristic of long polling. The REST API, while it can be used to make requests and receive responses over HTTP, operates on a request/response model rather than a continuous or push-based mechanism suitable for long polling.

In summary, the Bayeux Protocol is tailored for scenarios requiring asynchronous message transport over HTTP and supports long polling effectively, distinguishing it from the other options provided.