Real-time communications system with intelligent presence indication

In a distributed computing system, clients of a communications application are deployed on user devices. The clients on target user devices collect and report context information for a target user such as location and application-in-use. Reported context information is associated with response time information describing time to respond to initiation of communications in respective contexts, and a predictive model is maintained and used to obtain an estimate for a response time of the target user to respond to a new initiation of communications in a current context. A presence indicator on an initiator user device provides a presence indicator for the target user, and is generated and updated by obtaining current context of the target user and applying it to the predictive model to obtain an estimate of a current response time of the target user, and setting a value of the presence indicator according to the estimate.