The ADJO Police Department participates in a work-release program in which prisoners may work at the county dairy show, which has only one entrance where patrons pay for tickets before entering the event. Customers visit the entrance and purchase tickets at a rate of 47 per hour. The entrance typically serves an average rate of 51 people per hour. Further, ADJO estimates that waiting costs of being in the queue are $2.00 per hour. Work release for the prisoners does not occur dur- ing weekends. Further, work release for the prisoners only occurs during the day shift (assuming a 12-hour shift). For the entrance, assuming the Poisson and exponential distributions, answer the fol- lowing questions using the formulae presented within Table 11.1:
a. What is the average rate of serviced consumers per hour?
b. What is the average rate of consumer arrivals?
c. What is the average quantity of consumers within the system?
d. What is the average time a consumer spends in the system?
e. What is the average quantity of consumers within the queue?
f. What is the average time a consumer spends in the queue?
g. What is the utilization factor?
h. What is the probability that no consumers are in the system?
i. What is the probability that more than four consumers are in the system?
j. What is the probability that more than seven consumers are in the system?
k. What is the daily cost of waiting consumers?
l. What is the hourly cost of waiting consumers?
m. What is the weekly cost of waiting consumers?
n. What is the monthly cost of waiting consumers?
o. What is the annual cost of waiting consumers?
Text Book: Economic and Financial Analysis for Criminal Justice Organizations By Daniel Adrian Doss, William H. Sumrall III, David H. McElreath, Don W. Jones.