If the call is waiting on an agent, customer queue flow logic is used until an agent is available and the call has been successfully routed to that agent.     

If the agent does not accept the call, the agent moves into a Missed Call state and is unable to take calls until the agent, or a call center manager, changes their status to Available again. The caller does not hear ringing while the call is waiting for the agent, and continues to hold until connected with an agent as defined in the customer queue flow logic.  
https://docs.aws.amazon.com/connect/latest/adminguide/ccp-connectivity.html

Agent have 20 seconds to accept or reject a contact. After 20 seconds, the status of the agent will be set to unavailable.
https://docs.aws.amazon.com/connect/latest/adminguide/work-with-calls.html