Recurrent retrial queues with service option on arrival

The queueing system to be analyzed is one where customers are not in continuous contact with the server but must call in on the server at intervals to request service. If a customer finds the server busy when he calls in he must wait and try again later. Arriving customers may call in on the server immediately on arrival or join the queue first and then check on the server from time to time. A customer, once served, may leave the system or rejoin the queue and begin requesting service again. A model for the system is derived and used to calculate several characteristic quantities relating to the operation of the system.