This document contains practice questions that supplement review questions for Lessons II-7 and II-8. This document first identifies the learning objectives of solving supplemental questions. The document then lists 35 questions and answers. All questions can be helpful. Questions marked with an asterisk * are similar to review questions. Tip: Supplemental questions are grouped into sets of similar type. Once you have mastered the questions in a set, you can skip the rest of the questions in that set.

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Quantitative Analysis BA 452 Supplemental Questions 9

Objectives

By working through the homework questions and the supplemental questions, you will: 1. Be able to identify where waiting line problems occur and realize why it is important to study these problems. Know the difference between single-channel and multiple-channel waiting lines. Understand how the Poisson distribution is used to describe arrivals and how the exponential distribution is used to describe services times. Learn how to use formulas to identify operating characteristics of the following waiting line models: a. Single-channel model with Poisson arrivals and exponential service times b. Multiple-channel model with Poisson arrivals and exponential service times 5. Know how to incorporate economic considerations to arrive at decisions concerning the operation of a waiting line. Understand the following terms: queuing theory queue single-channel multiple-channel service rate queue discipline steady state utilization factor operating characteristics arrival rate

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Quantitative Analysis BA 452 Supplemental Questions 9

Supplemental Questions 9

1. Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random, with an arrival rate of 24 customers per hour or 0.4 customers per minute. a. What is the mean or expected number of customers that will arrive in a five-minute period? b. Assume that the Poisson probability distribution can be used to describe the arrival process. Use the arrival rate in part (a) and compute the probabilities that exactly 0, 1, 2, and 3 customers will arrive during a five-minute period. c. Delays are expected if more than three customers arrive during any five-minute period. What is the probability that delays will occur? 2. In the Willow Brook National Bank waiting line system (see Problem 1), assume that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 36 customers per hour, or 0.6 customer per minute. Use the exponential probability distribution to answer the following questions: a. What is the probability the service time is one minute or less? b. What is the probability the service time is two minutes or less? c. What is the probability the service time is more than two minutes? 3. Use the single-channel drive-up bank teller operation referred to in Problems 1 and 2 to determine the following operating characteristics for the system: a. The probability that no customers are in the system b. The average number of customers waiting c. The average number of customers in the system d. The average time a customer spends waiting e. The average time a customer spends in the system f. The probability that arriving customers will have to wait for service 4. Use the single-channel drive-up bank teller operation referred to in Problems 1-3 to determine the probabilities of 0, 1, 2, and 3 customers in the system. What is the probability that more than three customers will be in the drive-up teller system at the same time?

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Quantitative Analysis BA 452 Supplemental Questions 9

5. The reference desk of a university library receives requests for assistance. Assume that a Poisson probability distribution with an arrival...