For the facility of Prob. 1.10, suppose that the server normally takes a 30-minute lunch b...

For the facility of Prob. 1.10, suppose that the server normally takes a 30-minute lunch break at the first time after 12 noon that the facility is empty. If, however, the server has not gone to lunch by 1 P.M., the server will go after completing the customer in service at 1 P.M. (Assume in this case that all customers in the queue at 1 P.M. will wait until the server returns.) If a customer arrives while the server is at lunch, the customer may leave immediately without being served; this is called balking. Assume that whether such a customer balks depends on the amount of time remaining before the server’s return. (The server posts his time of return from lunch.) In particular, a customer who arrives during lunch will balk with the following probabilities:

(The random-integer-generation method discussed in Sec. 1.5.2 can be used to deter-mine whether a customer balks. For a simpler approach, see Sec. 8.4.1.) Run the simulation and estimate the same measures of performance as before. (Note that the server is not busy when at lunch and that the time-average number in queue is computed including data from the lunch break.) In addition, estimate the expected number of customers who balk.