Regional Airlines is establishing a new telephone system forhandling flight reservations. During the 10:00 AM to 2:00 PM timeperiod, calls to the reservation agent occur randomly at an averagerate of one call every 3.75 minutes. Historical service time datashow that a reservation agent spends an average of 3 minutes witheach customer. The waiting line model assumptions of Poissonarrivals and exponential service times appear reasonable for thetelephone reservation system. Regional Airlines management believesthat offering an efficient telephone reservation system isimportant part of establishing an image as a service-orientedairline. If the system is properly implemented, Regional Airlineswill establish good customer relations, which in the long run willincrease business. However, if the telephone reservation system isfrequently overloaded and customers have difficulty contacting anagent, a negative customer reaction may lead to an eventual loss ofbusiness. The cost of a ticket reservation agent is $20 per hour.Thus, management wants to provide good service, but it does notwant to incur the cost of overstaffing the telephone reservationoperation by using more agents than necessary. At a planningmeeting, Regional’s management team agreed that an acceptablecustomer service goal is to answer at least 75% of the incomingcalls immediately. During the planning meeting, Regional’s vicepresident of administration pointed out that the data show that theaverage service rate for an agent is faster than the averagearrival rate of the telephone calls. The vice president’sconclusion was that personnel costs could be minimized by using oneagent and that single agent must be able to handle the telephonereservations and still have some idle time. The vice president ofmarketing restated the importance of customer service and expressedsupport for at least two reservation agents. Answer to thefollowing questions to help prepare a managerial report to analyzethe telephone reservation system with one agent as proposed by thevice president of administration.

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

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

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

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