9. Consider a bank office where customers arriveaccording to a Poisson process withan average arrival rate of customers per minute. Thebank has only one teller servicing the arriving customers.The service time is exponentially distributed and themean service rate is μ customers per minute. It turns outthat the customers are impatient and are only willing towait in line for an exponential distributed time with amean of 1/μ minutes. Assume that there is no limitationon the number of customersthat can be in the bank at the same time.a. Construct a rate diagram for the process and determinewhat type of queuingsystem this correspond to on the form A1/A2/A3.b. Determine the expected number of customers in thesystem when λ = 1 and μ = 2.c. Determine the average number of customers per timeunit that leave the bankwithout being served by the teller when λ = 1 and µ = 2.

In this problem, we consider a bank office where customers arrive following a Poisson process with…

Answered: 9. Consider a bank office where…

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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Accounting Today identified the top accounting firms in 10 geographic regions across the United States. All 10 regions reported growth in 2014. The Southeast and Gulf Coast regions reported growth of 12.36% and 5.8%, respectively. A characteristic description of the accounting firms in the Southeast and Gulf Coast regions included the number of partners in the firm. The file AccountingPartners3 contains the number of partners. (Data extracted from bit.ly/1BoMzsv) Assuming that the population variances from both offices are equal, at the 0.10 level of significance, is there evidence of a difference between Southeast region accounting firms and Gulf Coast accounting firms with respect to the mean number of partners? Referring to Table 10-1, the proper conclusion for this test is Question 5 options: 1) at the α = 0.10 level, there is sufficient evidence to indicate a difference in the mean time to clear problems in the two offices.…
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A manufacturer who produces cereal wants to check the quality of their production line. If the cereal boxes are under filled, then customers may complain and the company’s image will suffer. If the cereal boxes are over filled, then the cost of production will go up which will negatively impact the profit made from sales. The company has set up production so that the boxes, on average, have 17 ounces of cereal. Assume that the weight of cereal in a box is normally distributed. Suppose we select a random sample of 15 cereal boxes and find that the average number of ounces per box is 16.2 ounces with standard deviation 2.1 ounces. Conduct a hypothesis test using α = 0.1. Make sure to state the null and alternative hypotheses, state the appropriate test statistic, set up the rejection region, and state your conclusion in the context of the problem.
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Moore’s portable X-ray equipment repair service shop receives an average of 6 portable X-ray sets per 8-hour day to be repaired. Moore would like to be able to tell his customers that they can expect one day service. What average repair time per set will the repair shop have to achieve to provide 1-day service on average? Assume that the arrival rate is Poisson distributed and repair times are exponentially distributed.
Q1) A document printing machine receives documents according to a Poisson process with an expected interarrival time of 5 minutes from the legal department. When the machine has just one document to print, the expected processing time is 5 minutes. When machine has more than one document, then it does not require initial set-up time and expected processing time for each document to 4 minutes. In both cases, the processing times have an exponential distribution. (a) Construct the rate diagram for this queueing system. (b) Check that this is a birth-and-death process and find the steady-state distribution of the number of documents in the system but not yet finished printing. (Hint: Use the sum of Geometric series) (c) Derive L and Lq for this system. (Hint: Use the sum of Arithmetic-Geometric series) (d) Use the information of L and Lq to determine W and Wq. Q2) Jacob runs a shoe repair store by himself. Customers arrive to bring a pair of shoes to be repaired according to a Poisson…
In a continuous-time surplus model, the claim severity is distributed as BN(2, 0.4). Determine the Lundberg upper bound for the probability of ultimate ruin if the initial surplus is 2 and the prIn a continuous-time surplus model, the claim severity is distributed as BN(2, 0.4). Determine the Lundberg upper bound for the probability of ultimate ruin if the initial surplus is 2 and the premium loading factor is 0.25.emium loading factor is 0.25.

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