Customers arrive for service and take their place in a waiting line. There is a single service facility, and a customer undergoing service at the beginning of a period will complete service and depart...

Customers arrive for service and take their place in a waiting line. There is a single service facility, and a customer undergoing service at the beginning of a period will complete service and depart at the end of the period with probability ß and will continue service into the next period with probability α = 1 - ß, and then the process repeats. This description implies that the service time
of an individual is a random variable with the geometric distribution,

and the service times of distinct customers are independent random variables. At most a single customer can arrive during a period. We suppose that the actual number of arrivals during the nth period is a random variable
 taking on the values 0 or 1 according to