Steve is the sole server working on a ticket booth every Sunday for entry to an amusement park. Customers are served in the order in which they arrive. Customers arrive randomly to the booth at an average rate of 12.50 every hour, while Steve takes an average of four minutes to serve a customer. Steve is paid $55 per hour by the owner and works at the booth between 8.00am and 5.00pm each Sunday.

(a) (i) Write down the values of the parameters of the problem if a time unit of one hour is used.

lambda =

mu =

rho =

(ii) Calculate the expected amount of time that Steve is idle in his working day. (iii) Calculate the average cost to the owner each Sunday of Steves idle time in terms of his wages.

(iv) What percentage of the time is there more than three customers waiting in the queue? (v) Management now instructs Steve to deal with customers more quickly and to spend an average of only three minutes dealing with each one. In this case find the percentage reduction (to the nearest per cent) in the average customer waiting time in the system.