eBookProblem 15-27 (Algorithmic)Gubser Welding, Inc., operates a welding service for construction and automotive repair jobs. Assume that the arrival of jobs at the company's office can be described by a Poisson probability distribution with an arrival rate of four jobs per 8-hour day. The time required tocomplete the jobs follows a normal probability distribution, with a mean time of 1.4 hours and a standard deviation of 1 hour. Answer the following questions, assuming that Gubser uses one welder to complete all jobs:a. Wd. What is the average time a job waits before the welder can begin working on it? If required, round your answer to one decimal place.hoursplaces.e. What is the average number of hours between when a job is received and when it is completed? If required, round your answer to one decimal place.hoursf. What percentage of the time is Gubser's welder busy?of the time the welder is busy.

Queuing theory-Is about the mathematical study of of waiting lines, or queues. Queuing models are…

Answered: Gubser Welding, Inc., operates a…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section12.5: Analytic Steady-state Queueing Models

Problem 11P

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eBook Problem 15-27 (Algorithmic) Gubser Welding, Inc., operates a welding service for construction and automotive repair jobs. Assume that the arrival of jobs at the company's office can be described by a Poisson probability distribution with an arrival rate of four jobs per 8-hour day. The time required to complete the jobs follows a normal probability distribution, with a mean time of 1.4 hours and a standard deviation of 1 hour. Answer the following questions, assuming that Gubser uses one welder to complete all jobs: a. What is the mean arrival rate in jobs per hour? If required, round your answer to two decimal places. per hour b. What is the mean service rate in jobs per hour? If required, round your answer to four decimal places. per hour c. What is the average number of jobs waiting for service? If required, round your answer to three decimal places.
Chapter 5. (M/M/s/K Model). Leia is responsible for 12 computers in the IT offices in a small business called DataWish. Each computer runs on an average for 4 weeks and requires an average of ½ or 0.5 weeks to get reset by Leia before it can start up again. If we assign the Poisson distribution to the “arrival” of each computer for service and an exponential distribution to the actual service provided, answer the following questions: a. The arrival rate would be units per week and the service rate would be units per week. b. Calculate the following operating characteristics for the M/M/s/K system: Utilization Factor (ρ) % Performance Measures P0 (probability that sytem is empty) % L (average units in system) units Lq (average units waiting in queue) units W (average time in the system) weeks Wq (average time in the queue) weeks c. If we assign a cost of waiting as $750 per week per computer and $800 per week of…
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. What is the mean or expected number of customers that will arrive in a five-minute period?λ = fill in the blank 1 per five minute period 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. If required, round your answers to four decimal places. x P(x) 0 fill in the blank 2 1 fill in the blank 3 2 fill in the blank 4 3 fill in the blank 5 Delays are expected if more than three customers arrive during any five-minute period. What is the probability that delays will occur? If required, round your…
11. Automobiles arrive at a tollbooth on a highway completely at random according to a Poisson process with rate À = 4 cars per hour. Determine the following: a. The probability that the time between any two successive arrivals exceeds 20 minutes. b. The probability that exactly four cars arrive in any given hour. c. The probability that more than five cars arrive in any given hour. d. The probability that more than 10 cars arrive in any given two-hour period. e. A person working for the transportation department begins counting arrivals at the tollbooth at 8 A.M. What is the probability that he counts 20 arrivals before 12 noon? (Use a normal approximation for your calculations.)
The average time between the arrivals of the taxis arriving at the airport to pick up passengers has an exponential distribution, with an average of 10 minutes. a) What is the probability that a passenger will wait for the taxi less than 15 minutes? b) What is the probability that a passenger will wait for the taxi between 20 and 30 minutes? Solve using the cumulative distribution function H1
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. Assume that Poisson probability distribution with an arrival rate of 24 customers per hour or 0.4 customer per minute can be used to describe the arrival pattern. Assume further 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. a. Use the single-channel drive-up bank teller operation to determine the average time a customer spends waiting b. Use the single-channel drive-up bank teller operation to determine the average time a customer spends in the system c. Use the single-channel drive-up bank teller operation to determine the probability that arriving customers will have to wait for service d.Use the single-channel drive-up bank teller operation…
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. Assume that Poisson probability distribution with an arrival rate of 24 customers per hour or 0.4 customer per minute can be used to describe the arrival pattern. Assume further 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. 1.) Use the single-channel drive-up bank teller operation to determine the probability of 4 customers in the system 2.) Use the single-channel drive-up bank teller operation to determine the average arrival time in minutes of customers 3.) Use the single-channel drive-up bank teller operation to determine the average service time in minutes of the drive-up teller
Chapter 5. (M/M/s/K Model). Leia is responsible for 8 computers in the IT offices in a small business called DataWish. Each computer runs on an average for 3 weeks and requires an average of ½ or 0.5 weeks to get reset by Leia before it can start up again. If we assign the Poisson distribution to the "arrival" of each computer for service and an exponential distribution to the actual service provided, answer the following questions: a. The arrival rate would be units per week and the service rate would be units per week. b. Calculate the following operating characteristics for the M/M/s/K system: Utilization Factor (p) % Performance Measures PO (probability that sytem is empty) L (average units in units system) La (average units waiting in queue) units W (average time in the weeks system) Wq (average time in the queue) weeks c. If we assign a cost of waiting as $500 per week per computer and $800 per week of hiring Leia, what is the Total Time Cost per week cost of servicing the…
Chapter 5. (M/M/s/K Model). Leia is responsible for 8 computers in the IT offices in a small business called DataWish. Each computer runs on an average for 3 weeks and requires an average of ½ or 0.5 weeks to get reset by Leia before it can start up again. If we assign the Poisson distribution to the "arrival" of each computer for service and an exponential distribution to the actual service provided, answer the following questions: a. The arrival rate would bel units per week and the service rate would be units per week. b. Calculate the following operating characteristics for the M/M/s/K system: Utilization Factor (p) Performance Measures c. If we assign a cost of waiting as $500 per week per computer and $800 per week of hiring Leia, what is the Total Time Cost per week cost of servicing the machines? PO (probability that sytem is empty) % dollars L (average units in system) units d. If DataWish decides to hire another individual to help Leia, what would the new Total Time Cost per…
Customers arrive at a one window drive according to a poison distribution with mean of 10 minutes and service time per customer is exponential with mean of 6 minutes. The space in front of the window can accommodate only three vehicles including the serviced ones. Other vehicles are have to wait outside this space. Calculate:a. A. probability that an arriving customer can drive directly to the space in front of the windowb. Probability that an arriving customer will have to wait outside the directed space c. How long an arriving customer is expected to wait before getting the service?
Consider the M/M/1 queueing system with arrival rate λ > 0 and service rate μ > 0. (a) Compute the expected number of arrivals during a service time (also called service period). (b) Compute the probability that no customers arrive during a service period. You may use the trick of computing expectation/probability by conditioning, i.e., “unconditional expectation (or probability) is equal to the expectation of conditional expectation (or probability)”.
Chapter 5. (M/M/s/K Model). Leia is responsible for 12 dataunits in the IT offices in a small business called DataWish. Each dataunit runs on an average for 3 weeks and requires an average of ½ or 0.5 weeks to get reset by Leia before it can start up again. If we assign the Poisson distribution to the "arrival" of each dataunit for service and an exponential distribution to the actual service provided, answer the following questions: a. The arrival rate would be units per week and the service rate would be units per week. b. Calculate the following operating characteristics for the M/M/S/K system: Utilization Factor (p) % Performance Measures PO (probability that sytem is empty) % L (average units in system) units Lq (average units waiting in queue) units W (average time in the weeks system) Wq (average time in the queue) weeks c. If we assign a cost of waiting as $400 per week per dataunit and $800 per week of hiring Leia, what is the Total Time Cost per week cost of servicing the…

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