The William Graham Entertainment Company will be opening a new box office where customers can come to make ticket purchases in advance for the many entertainment events being held in the area. Simulation is being used to analyze whether to have one or two clerks on duty at the box office.
While simulating the beginning of a day at the box office, the first customer arrives 5 minutes after it opens and then the interarrival times for the next four customers (in order) are 3 minutes, 9 minutes, 1 minute, and 4 minutes, after which there is a long delay until the next customer arrives. The service times for these first five customers (in order) are 8 minutes, 6 minutes, 2 minutes, 4 minutes, and 7 minutes.
(a) For the alternative of a single clerk, plot a graph that shows the evolution of the number of customers at the box office over this period.
(b) Use this figure to estimate the usual measures of performance— L, Lq, W, Wq, and the Pn (as defined in Sec. 17.2) — for this queueing system.
(c) Repeat part (a) for the alternative of two clerks.
(d) Repeat part (b) for the alternative of two clerks.