Dubai airport has three immigration officers that inspect arriving tourists’ travel documents and permit them to enter the country if their visa is genuine. Each officer can check 20 tourists per hour (exponentially distributed). On an average, a tourist arrives every 1.2 minutes (Poisson distributed). The airport quantifies travelers’ satisfaction as a function of waiting time and the worth of waiting time in terms of money.
a. What is the average time a customer spends waiting in the immigration queue?
b. On average, how many customers are waiting in the queue?
c. The airport assigns goodwill cost of AED200 per minute for the time a guest must wait in line.
Each officer receives AED500 per hour. The airport authorities want to find a balance between the cost of service (by providing more officers) and cost of waiting of travelers. Determine the optimum number of officers that will minimize the total cost (cost of service and cost of waiting).