Using R (show your code) Suppose the distributions of arrival and service times were normal instead of exponential. Let the arrival times have a standard deviation of 1 minutes, and the teller service times have a standard deviation of 2 minutes. Make arrival and service rates to be 1 every 6 minutes(arriving) and 1 every 4 minutes(serving). Using simulation, estimate the long-run average number of people that would be in the bank.

Using R (show your code) Suppose the distributions of arrival and service times were normal instead of exponential. Let the arrival times have a standard deviation of 1 minutes, and the teller service times have a standard deviation of 2 minutes. Make arrival and service rates to be 1 every 6 minutes(arriving) and 1 every 4 minutes(serving). Using simulation, estimate the long-run average number of people that would be in the bank.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter20: Queuing Theory

Section20.2: Modeling Arrival And Service Processes

Problem 4P

See similar textbooks

Similar questions

A particular telephone number is used to receive both voice calls and fax messages. Suppose that 20% of the incoming calls involve fax messages, and consider a sample of 20 incoming calls. (Round your answers to three decimal places.) (a) What is the probability that at most 6 of the calls involve a fax message?(b) What is the probability that exactly 6 of the calls involve a fax message?(c) What is the probability that at least 6 of the calls involve a fax message?(d) What is the probability that more than 6 of the calls involve a fax message?
With given mean and standard deviation we can simulate values for that normal distribution using the excel formula NORMINV(Rand(),mean,sd). This is applicable for X, Y & Z and thus the W value can also be simulated ( W = (X+Y)/Z) The simulation of 50 values are prepared and the histogram with width 3 class interval is shown in the excel sheet. Random Values around the mean and Standard deviation Y Y W Mean 1.. Y.. 0. Deviation Variance Frequency of Simulated Values Bins Frequency
We want to predict maintenance expense ( y) for a truck during the current year, from the independent variables x1 miles driven (in thousands) during the current year and x2age of the truck (in years) at the beginning of the current year. We are given the information in
At the stadium, there are five lines for arriving customers, each staffed by a single worker, If the arrival rate for customers is 108 per hour and each customer takes (on average) 1.9 minutes for a worker to process. (Round your anwer to three decimal places.) What is the worker utilization?
The length of a particular species of fish can be assumed to be normally distributed with mean 25cm and standard deviation 3cm. An angler catches one of these fish from a river. What is the chance that the fish is between 19cm and 31cm in length? 95 100 68 50
Solve in R programming language: Suppose that the number of years that a used car will run before a major breakdown is exponentially distributed with an average of 0.25 major breakdowns per year. (a) If you buy a used car today, what is the probability that it will not have experienced a major breakdown after 4 years. (b) How long must a used car run before a major breakdown if it is in the top 25% of used cars with respect to breakdown time.
An assignment was given to four students attending a sample survey course. The problem was to estimate the average time per week devoted to study in Punjab Agricultural University (PAU) library by the students of this university. The university is running undergraduate, master's degree and doctoral programs. Number of students registered for the three programs is 1300, 450, and 250 respectively. Since the value of the study variable is likely to differ considerably with the program, the investigator divided the population of students into 3 strata: undergraduate program (stratum I), master's program (stratum II), ånd doctoral program (stratum III). First of the four students selected WOR simple random samples of sizes 20, 10, and 12 students from strata I, II, and III respectively, so that, the total sample is of size 42. The information about weekly time devoted in library is given in table 5.1. Table 5.1 Time (in hours) devoted to study in the university library during a week Stratum…
Use the pigeonhole principle to determine how many people are needed in a group to say that at least three were born on the same day of the year (each year is assumed to have 365 days).
Consider the following. Year 1790 1800 1810 1820 1830 1840 1850 1860 1870 1880 1890 1900 1910 1920 1930 1940 1950 P(t) = (a) Census data for the United States between 1790 and 1950 are given in the table above. Construct a logistic population model using the data from 1790, 1860, and 1920. (Assume that t is years since 1790 and P is population in millions. Round all coefficients to four decimal places.) 143.56 1+ 35.53e Year Population (in millions) 3.929 5.308 7.240 9.638 12.866 17.069 23.192 31.433 38.558 50.156 62.948 75.996 91.972 1820 (b) Construct a table comparing actual census population with the population predicted by the model in part (a). Compute the error and the percentage error for each entry pair. 1910 -0.0353-t) 105.711 122.775 131.669 150.697 Census Population (in Millions) 9.638 91.972 Predicted Population (in Millions, rounded to three decimal places) 9.989 9.174 X Error (rounded to three decimal places) -0.351 0 % Error (rounded to two decimal places) -3.64 0 % %
Suppose the U.S. Census Bureau projects the population of the state to be 2.6 million in 2003 and 4.1 million in 2023. Assuming the population growth is linear, Use t years since 1993 and p the population of the state in millions. According to your linear model, what is the population of the state in 2032? (Round your final answer to two decimal places}.
Using the Gaussian Probability Density function write a function that will calculate the probability that variable x will be in the range µ − ασ < x < µ + ασ, where α is some multiple of the variance.
Information on morphine: Morphine can be administered via injection / IV. The quantity of morphine in a given dose may vary, but one guideline is to use 0.1 mg of morphine for each kg of the patient's body mass. The time taken for half the quantity of morphine to be removed from the body is 2 hours. An exponential function can be used to model the amount of morphine in the body over time: ?=?0???A=A0ekt (note that ?k will be negative). Calculate the value of ?k for morphine. Write a Python function called MorphineModel, which takes two arguments: dose amount ?0A0 and time since last dose ?t, and returns the amount of morphine in the body at this time ?t. Add to your computer code so that you have a program which is an implementation of the following flowchart. Ensure that your code is well-communicated to a user of the program (via the print statements) and well-communicated to someone reading the code (via comments).