CH_18_10th_Edition - Management of Waiting Lines CHAPTER 18...

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Management of Waiting Lines CHAPTER 18 MANAGEMENT OF WAITING LINES PROBLEMS P1. A bank has a drive-in window, which is open from 10 a.m. to 3 p.m. on business days. Customers drive up at a mean rate of 12 per hour, according to a Poisson distribution. The teller requires a mean of 2.4 minutes to serve each customer. Service times have a negative exponential distribution. a. How many channels are there? b. Do the customers come from a finite source or from an infinite source? c. Which queue model is appropriate here? d. What is the value of λ ? e. What is the interpretation of λ ? f. What is the value of μ ? g. What is the interpretation of μ ? h. What is the system utilization, ρ ? Is this a feasible system? i. What is the proportion of idle time? j. What is the mean number of customers being served? k. What is the expected number of customers waiting for service? l. What is the expected duration of the wait? m. What is the mean number of customers in the system? n. What is the mean time that a customer spends in the system? o. What is the probability that the system will be idle? p. What is the probability that there will be one car in the system? q. What is the probability that there will be three cars in the system? P2. In a factory, the parts to be copper-plated must be immersed in an electrolytic solution so that copper ions will be deposited on the part. The company has one electrolytic bath, in which each part is submerged for 20 minutes. Parts to be copper-plated arrive at a mean rate of 16 per 8-hour shift, according to a Poisson distribution. a. How many channels are there? b. Do the parts come from a finite source or from an infinite source? c. Which queue model is appropriate here? d. What is the value of λ ? e. What is the interpretation of λ ? f. What is the value of μ ? g. What is the interpretation of μ ? h. What is the system utilization, ρ ? Is this a feasible system? 1. What is the proportion of idle time? j. What is the expected number of parts waiting for copper-plating? k. What is the expected duration of the wait? 1. What is the mean number of parts in the system? 243
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Chapter 18 m. What is the mean time that a part spends in the system? P3. A bank has an array of five drive-in windows, some or all of which may be open from 10 a.m. to 3 p.m. on normal business days. At each window, the teller requires a mean of 2.4 minutes to serve each customer; service times have a negative exponential distribution. Customers arrive at a mean rate of 65 per hour, according to a Poisson distribution. (Use Table 19-4) a. Do the customers come from a finite source or from an infinite source? b. What is the value of λ ? c. What is the interpretation of λ ? d. What is the value of μ ? e. What is the interpretation of μ ? f. What is the minimum number of drive-in windows which should be open to have an underloaded system?
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