M/G/1 queueing systems with returning customers

Single-channel queues with Poisson arrivals, general service distributions, and no queue capacity are studied. A customer who finds the server busy either leaves the system for ever or may return to try again after an exponentially distributed time. Steady-state probabilities are approximated and bounded in two different ways. The paper characterizes the service distribution by its Laplace transform, and uses this characterization to determine the better method of approximation.