Question

Multiple Server Waiting Line Model Regional Airlines Assumptions Poisson Arrivals Exponential Service Times Number of Servers Arrival Rate Service Rate For Each Server Operating Characteristics 4 Probability that no customer are in the system, Po 5 Average number of customer in the waiting line, L 6 Average number of customer in the system, L 7 Average time a customer spends in the waiting line, W 18 Average time a customer spends in the system, W 19 Probability an arriving customer has to wait, P (value can be found on page 519) #DIV/ 0! calls #DIV/0! calls #DIV/0 #DIV/ 0! minutes per hour #DIV/0 #DIV/0! minutes per hour #DIV / 0! 20 Questions 1-4 MULTI SERVER 3 MULTISERVER 2 SINGLE SERVER WaA (11.14) 5. The average time a unit spends in the system: 1 W=Wq + (11.15) arriving unit has to wait for service: 6. The probability that an 1 (11.16) Po kμ-λ) PW -- k! 7. The probability of n units in the system: I (A/u)" Po n! for nk (11.17) Pn= (/μ) P/= kIkn-) (11.18) for n>k Po Problem 1 REGIONAL AIRLINES Regional Airlines is establishing a new telephone system for handling flight reservations. During the 10:00 A.M. to 11:00 A.M. time period, calls to the reservation agent occur ran- domly at an average 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 reserva- tion system is an 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 mor agents than necessary At a planning meeting, Regional's management team agreed that an acceptable cus- tomer service goal is to answer at least 85% 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 mini- mized by using one agent and that the single agent should 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. The current telephone reservation system design does not allow callers to wait. Callers who attempt to reach a reservation agent when all agents are occupied receive a busy signal and are blocked from the system. A representative from the telephone company suggested that Regional Airlines consider an expanded system that accommodates waiting. In the expanded system, when a customer calls and all agents are busy, a recorded message tells the customer that the call is being held in the order received and that an agent will be available shortly. The customer can stay on the line and listen to background niusic while waiting for an agent. Regional's management will need more information before switching to the expanded system.

Answer 1

Sesvers 2Ce No. A Asual rato - 16 Custoras Da L Sence Aato 20 ustones As C) 10*F P- = +0.8 + (0-8)- 201-84 +_0-64 0.4286 r.2- ttep D1524 - 0.1524 0.0095 16 x0-0095 t 16 L: 0 - 9% w-a T -0.009 5 0 D55 20 2 10 0.16 0 228b