Enqueue-related processing is provided based on timing out of an attempted enqueue to a queue, such as to an adjunct processor queue. The processing includes attempting enqueuing a request message to a queue until timing out, where the timing out indicates an unsuccessful enqueuing of the request message. Based on the enqueuing of the request message timing out, the process includes determining a likely cause for the enqueuing being unsuccessful and timing out. Based on determining the likely cause, the process includes performing one or more actions to facilitate enqueue-related processing within the computing environment.