AbstractIn many practical situations customers applying for service and finding the server busy will not join a queue, but make a new attempt to enter service after some time. In this paper we study single server systems with repeated attempts both for infinite‐source input and finite‐source input where the service times are general and the reattempt times are exponential. Numerically stable recursion schemes are derived by which the time‐average and customer‐average steady‐state probabilities can be effectively