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 ini nite and queue discipline is FCFS. Before a test, the arrival of students increases to six per hour on the average. What will the new average line length be?

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 ini nite and queue discipline is FCFS. Before a test, the arrival of students increases to six per hour on the average. What will the new average line length be?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter12: Queueing Models

Section: Chapter Questions

Problem 52P

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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?
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…
The Minute Stop Market has one pump for gasoline, which can service 10 customers per hour (Poisson distrib-uted). Cars arrive at the pump at a rate of 5 per hour (Poisson distributed). a. Determine the average queue length, the average time acar is in the system, and the average time a car must wait.b. If, during the period from 4:00 P.M. to 5:00 P.M., thearrival rate increases to 12 cars per hour, what will bethe effect on the average queue length?
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An office employs several clerks who create documents and has one operator who enters the document information in a computer system. The group creates documents at a rate of 25 per hour. The operator can enter the information with an average exponentially distributed time of two minutes. Assume the population is infinite, arrivals are Poisson, and queue length is infinite with FCFS discipline.a. Calculate the percentage utilization of the operator.b. Calculate the average number of documents in the system.c. Calculate the average time in the system.d. Calculate the probability of four or more documents being in the system.e. If another clerk were added, the document origination rate would increase to 30 per hour.What would the expected average number of documents in the system become? Show why.
An ofi ce employs several clerks who create documents and one operator who entersthe document information in a computer system. The group creates documents at a rateof 25 per hour. The operator can enter the information with an average exponentiallydistributed time of two minutes. Assume the population is ini nite, arrivals are Poisson,and queue length is ini nite with FCFS discipline.a. Calculate the percentage utilization of the operator.b. Calculate the average number of documents in the system.c. Calculate the average time in the system.d. Calculate the probability of four or more documents being in the system.e. If another clerk were added, the document origination rate would increase to 30 perhour. What would the expected average number of documents in the system become?Show why.
Give an example of when a first-in, first-out (FIFO) rule for queue discipline would not be appropriate?
To support National Heart Week, the Heart Association plans to install a free blood pressure testing booth in El Con Mall for the week. Previous experience indicates that, on average, 10 persons per hour request a test. Assume arrivals are Poisson distributed from an infinite population. Blood pressure measurements can be made at a constant time of five minutes each. Assume the queue length can be infinite with the FCFS discipline.a. What average number in line can be expected?b. What the average number of persons can be expected to be in the system?c. What is the average amount of time a person can expect to spend in line?d. On average, how much time will it take to measure a person’s blood pressure, includingwaiting time?e. On weekends, the arrival rate can be expected to increase to over 12 per hour. Whateffect will this have on the number in the waiting line?
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