# Property of and for the exclusive use of slu

• 21

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2. The average number of customers in the waiting line is reduced from𝐿𝑞= 2.25customersto𝐿𝑞= 0.1227customer.3. The average time a customer spends in the waiting line is reduced from𝑊𝑞= 3minutes to𝑊𝑞= 0.1636minute.4. The probability that a customer has to wait for service is reduced from𝑃𝑤= 0.75to𝑃0.2045.Clearly the two-channel system will significantly improve the operating characteristics of thewaiting line. The final decision regarding the staffing policy at Burger Dome rests with theBurger Dome management. The waiting line study simply provides the operatingcharacteristics that can be anticipated using the 2 cases presented in Units 4 and 5.Self-TestThe cashier line of a canteen can facilitate up to 60 customers an hour. Frequenters of thecanteen arrive at an average of 50 an hour. Suppose that management wants to evaluatethe desirability of opening a second order-processing station so that two customers can beserved simultaneously. Assume a single waiting line with the first customer in line moving tothe first available server.a. What is the average arrival time in minutes of customers?b. What is the average service time in minutes of the canteen?c. What is the probability that the canteen has a customer?d. What is the probability that the canteen does not have any customer?e. How long would the line be on average (average number of customers in thesystem)?f. How many people are waiting to be served on average?g. How long in minutes would it take the customer from lining up until he leaves thewaiting line?h. How long in minutes would a customer wait to be served on average?i. Find the probability that there are 7 customers in the system.𝑤=

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