Assume that orders arrive at a mean rate of λ orders per minute, and that interarrival times are exponentially distributed. For what range of λ is the average cycle time of an order 5 minutes or less? Flo's Quick-Lube performs fast oil changes (A) and checks for tire pressure and wear (B) andbrakes and alignment (C) according to the process flow indicated by the diagram below. Eachincoming car is put on a jack while one technician performs task A and another simultaneouslyperforms task B and a third performs task C (which must follow task B due to the limited spaceunder the vehicle on the jack). The server for task A takes on average 3 minutes to process a job,the server for task B takes on average 2 minutes to process a job, and the server for task C takeson average 2 minutes to process a job. Server A can be operated in parallel with Servers B and C.All processing times are random and exponentially distributed, and jobs are allowed to queue infront of each server. (You can assume that the number of jacks is sufficient to allow any length ofqueue.)ANDB89A

The arrival rate of orders per minuteThe interarrival times have an exponential distribution.The…

Answered: Assume that orders arrive at a mean…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Assume that orders arrive at a mean rate of λ orders per minute, and that interarrival times are exponentially distributed. For what range of λ is the average cycle time of an order 5 minutes or less?

Flo's Quick-Lube performs fast oil changes (A) and checks for tire pressure and wear (B) and
brakes and alignment (C) according to the process flow indicated by the diagram below. Each
incoming car is put on a jack while one technician performs task A and another simultaneously
performs task B and a third performs task C (which must follow task B due to the limited space
under the vehicle on the jack). The server for task A takes on average 3 minutes to process a job,
the server for task B takes on average 2 minutes to process a job, and the server for task C takes
on average 2 minutes to process a job. Server A can be operated in parallel with Servers B and C.
All processing times are random and exponentially distributed, and jobs are allowed to queue in
front of each server. (You can assume that the number of jacks is sufficient to allow any length of
queue.)
AND
B
89
A

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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