Question

Regional Airlines is establishing a new telephone system for handling flight reservations. During the 10:00 AM to 2:00 PM time period, calls to the reservation agent occur randomly at an average rate of one call every 3.75 minutes. Historical service time data show that a reservation agent spends an average of 3 minutes with each customer. The waiting line model assumptions of Poisson arrivals and exponential service times appear reasonable for the telephone reservation system. Regional Airlines management believes that offering an efficient telephone reservation system is important part of establishing an image as a service-oriented airline. If the system is properly implemented, Regional Airlines will establish good customer relations, which in the long run will increase business. However, if the telephone reservation system is frequently overloaded and customers have difficulty contacting an agent, a negative customer reaction may lead to an eventual loss of business. The cost of a ticket reservation agent is $20 per hour. Thus, management wants to provide good service, but it does not want to incur the cost of overstaffing the telephone reservation operation by using more agents than necessary. At a planning meeting, Regional’s management team agreed that an acceptable customer service goal is to answer at least 75% of the incoming calls immediately. During the planning meeting, Regional’s vice president of administration pointed out that the data show that the average service rate for an agent is faster than the average arrival rate of the telephone calls. The vice president’s conclusion was that personnel costs could be minimized by using one agent and that single agent must be able to handle the telephone reservations and still have some idle time. The vice president of marketing restated the importance of customer service and expressed support for at least two reservation agents. Answer to the following questions to help prepare a managerial report to analyze the telephone reservation system with one agent as proposed by the vice president of administration.

11. What is the average number of callers waiting to speak with an agent?

12. What is the average number of callers in the system?

13. How many minutes on average a caller must wait to speak with the agent?

14. How many minutes on average a caller spends in the system (including waiting to speak with the agent and talk duration with the agent)?

Answer 1

Arrival rate, = 60/3.75 = 16 per hour

Service rate, = 60/3 = 20 per hour

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11)

Average number of callers waiting to speak with an agent, Lq = ²/((-))

= 16²/(20*(20-16))

= 3.2

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12)

Average number of callers in the system, L = /(-)

= 16/(20-16)

= 4

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13)

Average waiting time, Wq = Lq/

= 3.2/16

= 0.2 hour

= 12 minutes

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14)

Average time in system, W = L/

= 4/16

= 0.25 hour

= 15 minutes