Suppose we have a small call center staffed by two operators A and B handling three telephone lines.A only handles line 1, and B only handles only line 2 and 3. Calls arrive according to a Poisson processwith rate A = 100 calls per hour. All arrivals prefer line 1. Arrivals find all lines are busy will go away.Service times are exponentially distributed with a mean of 4 minutes. Customers are willing to waitan exponentially distributed length of time with a mean of 8 minutes before reneging if service has notbegun.Describe a continuous time Markov chain to model the system and give the rate transition diagramand the generator G.

There are operators in the call center A and B. telephone lines are handled.Line is handled by…

Answered: Suppose we have a small call center…

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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Matthew the Barber owns a one-chair shop. At barber college, they told Matthew that his customers would exhibit a Poisson arrival distribution and that he would provide an exponential service distribution. His market survey data indicate that customers arrive at a rate of two per hour. It will take Matthew an average of 20 minutes to give a haircut. Based on these figures, find the following: Part (a): The average number of customers waiting. Part (b): The average time a customer waits. Part (c): The average time a customer is in the shop. Part (d): The average utilization of Matthew's time.
Two geysers that are near to each other are labelled as Geyser A and Geyser B. The time between eruptions for a given geyser follows an exponential distribution. The eruption times of the two geysers are independent of one another. The mean amount of time between eruptions of Geyser A is 39 minutes, and the mean amount of time between eruptions of Geyser B is 66 minutes. Given that exactly one of the geysers erupts within the next 49 minutes, determine the probability that it will be Geyser A. O 0.6654 0.7850 O 0.7252 O 0.6953 O 0.7551
One tree in the study had a weight that exceeded its expected weight (according to the best fit curve) by more than that of any other tree. By how many tons did the trees actual weight exceed the expected weight for its height?
A researcher is studying the intensity of hurricanes that entered the Gulf of Mexico between 1975-2015 and the average water temperature of the Gulf of Mexico at the hurricane's peak strength. What is the independent and dependent variable in this study?
Suppose a local university researcher wants to build a linear model that predicts the freshman year GPA of incoming students based on high school SAT scores. The researcher randomly selects a sample of 40 sophomore students at the university and gathers their freshman year GPA data and the high school SAT score reported on each of their college applications. He produces a scatterplot with SAT scores on the horizontal axis and GPA on the vertical axis. The data has a linear correlation coefficient of 0.481202. Additional sample statistics are summarized in the table below. Variable Sample Sample standard Variable description mean deviation high school SAT score x = 1495.716802 Sx = 109.915203 y freshman year GPA y = 3.260911 Sy 0.492802 r = 0.481202 slope = 0.002157 Determine the y-intercept, a, of the least-squares regression line for this data. Give your answer precise to at least four decimal places. a =
Consider a two-dimensional scatterplot representing the relationship between two continuous variables. If the correlation coefficient is -1, then: a. All points lie in a straight line with a slope of -1. b. All points lie in a straight line with an unknown negative slope. c. All points do not lie in a straight line but the best fitting regression line has a slope of -1 d. There is a strong positive relationship between the two variables.
4. As fallen trees lie on the forest floor they slowly decay. Will the amount of light present have an impact on the rate of decay? In the following table x is a random variable representing the remaining percentage of total mass of a log after it was exposed to the elements for three weeks while y represents the numbers of hours of direct sunlight the log received each day. X 0.60 .70 .65 .82 .87 y 1.0 2.3 3.0 4.0 4.5 (a) Plot a scatter diagram of the data. Remember to label your axes appropriately and choose a consistent scale. (b) Based on a scatter diagram, would you estimate the correlation coefficient to be positive, close to zero, or negative? Please circle one of the following choices: A. Positive B. Close to zero C. Negative (c) Interpret your results from parts (a) and (b). 16 tv
Question 4 Multi-Server QueueA supermarket manager is trying to decide how many cashers to employ for the peak time. The service times for check outs are exponentially distributed with a mean service time of 3 minutes. Customer arrivals to cashiers follow a Poisson arrival process with an average 110 customers per hour.a. What is the minimum number of cashers that would be needed to have the utilization less than one?b. If the waiting time is too long, customers might leave the store or even do not enter the store. It is estimated that for every minute of waiting time, the supermarket loses a potential profit of 50 HKD every hour from lost sales. The hourly wage for a casher is 80 HKD / hour. How many cashers should the supermarket employ to maximize its profit? (Keep four decimal places.

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