3 proPlot the percentage of machines not running as a function of the service factor for a popula-tion of 20 machines with exponential arrivals and services (a) if a single channel is employedand (b) if two channels are employed.uknemn number of rervice channelk The

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Answered: Plot the percentage of machines not…

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 16P

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Give typed full explanation In an M/D/2 system, a. the service time is exponentially distributed, b. the service time is a constant, c. the interarrival time is exponentially distributed, d. the interarrival time is a constant
A study-aid desk staffed by a graduate student has been established to answer students’questions and help in working problems in your OSCM course. The desk is staffed eighthours per day. The dean wants to know how the facility is working. Statistics show thatstudents arrive at a rate of four per hour and the distribution is approximately Poisson.Assistance time averages 10 minutes, distributed exponentially. Assume population andline length can be ini nite and queue discipline is FCFS.Before a test, the arrival of students increases to six per hour on the average. What willthe new average line length be?
Practice example. Please shoow solution.
What effect would decreasing arrival and service variability have on the effective capacity of asystem?
A study-aid desk staffed by a graduate student has been established to answer students' questions and help in working problems in your OSCM course. The desk is staffed eight hours per day. The dean wants to know how the facility is working. Statistics show that students arrive at a rate of four per hour and the distribution is approximately Poisson. Assistance time averages 10 minutes, distributed exponentially. Assume population and line length can be infinite and queue discipline is FCFS. Calculate the percentage utilization of the graduate student. Note: Round your answer to 1 decimal place. Calculate the average number of students in the system, including the graduate student service desk. Note: Round your answer to the nearest whole number. Calculate the average time in the system. Note: Round your answer to the nearest whole number. Calculate the probability of four or more students being in line or being served. Note: Round your intermediate calculations to 3…
A study-aid desk staffed by a graduate student has been established to answer students' questions and help in working problems in your OSCM course. The desk is staffed eight hours per day. The dean wants to know how the facility is working. Statistics show that students arrive at a rate of four per hour and the distribution is approximately Poisson. Assistance time averages 10 minutes, distributed exponentially. Assume population and line length can be infinite and queue discipline is FCFS.a. Calculate the percentage utilization of the graduate student.b. Calculate the average number of students in the system, excluding the graduate student service.c. Calculate the average time in the system.d. Calculate the probability of four or more students being in line or being served.e. Before a test, the arrival of students increases to six per hour, on average. What will the new average line length be?
Marty's Barber Shop has one barber. Customers have an arrival rate of 2.2 customers per hour, and haircuts are given with a service rate of 4 per hour. Use the Poisson arrivals and exponential service times model to answer the following questions: What is the probability that one customer is receiving a haircut and two customers are waiting? If required, round your answer to four decimal places.P3 = fill in the blank 4 What is the probability that more than two customers are waiting? If required, round your answer to four decimal places.P(More than 2 waiting) = fill in the blank 5 What is the average time a customer waits for service? If required, round your answer to four decimal places.Wq = fill in the blank 6 hours
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Food Goblin Supermarkets use both cashiers and baggers toserve customers at check out. During the first 6 hours of eachworkday (Monday–Friday), 4 cashiers and 2 baggers serveapproximately 20 customers per hour. A cashier and a baggerwho require approximately 5 minutes at checkout and 5 min-utes at bagging serve each customer.a. Calculate the utilization of both cashiers and baggers.b. Assume that both baggers and cashiers are cross-trainedto perform both activities so that they can serve customersindependently. Customers are now both checked andtheir groceries bagged by one individual. Further, assumethat it takes 12 minutes for one individual to both cash outand bag each customer’s groceries. Calculate the utiliza-tion of this new group of 6 cross-trained employees.
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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…
1. A multiple channel queuing system with a Poisson arrival rate, and an exponential service time distribution has an average arrival rate of 2.5 customers per hour and an average service time of eighty minutes per customer. A queuing system is described as unstable or overloaded if its utilization rate is greater than, or equal to one. For the system just described, what is the minimum number of servers required to retain stability i.e., to avoid overloading? A. 2 B. 3 C. 1 D. 4

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Plot the percentage of machines not running as a function of the service factor for a popula- tion of 20 machines with exponential arrivals and services (a) if a single channel is employed and (b) if two channels are employed.