The William Graham Entertainment Company will be open a new box office where customers can come to make ticket purchases in advance for the many entertainment events being held in the area. Computer 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 five minutes after it opens and then the interarrival times for the next four customers (in order) are three minutes, nine minutes, one minute, and four minutes, after which there is a long delay until the next customer arrives. The service times for these first five customers (in order) are eight minutes, six minutes, two minutes, four minutes, and seven minutes.
a. For the alternative of a single clerk, draw a figure like Figure 12.8 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 Sections 11.3 and 12.3)—for this queueing system.
c. Repeat part a for the alternative of two clerks.
d. Repeat part b for the alternative of two clerks.