Mary (M) and John (J) together run a small insurance agency. Customer calls arrive as a Poisson process of rate 1 call/hour. An arriving customer call is taken for service only if both Mary and John are free, because they need to work together on each call that they take. Processing of a customer consists of John's service time (collecting the information from the customer) and Mary'sservice time (checking customer background). John's service time is exponentially distributed with mean 1 hours. Mary's service time is exponentially distributed with mean 2/3 hours. J and M service times are independent. J and M start serving each call simultaneously, work independently in parallel, and the call service is done when both J and M are done with their services. Any call arriving when another call is being served (i.e., when either J or M are still serving it) is blocked (lost).

Suppose this "system" runs non-stop for a long time. In the long-run, what is the average rate at which calls are actually taken for service?