2. Consider a queuing system with a Poisson input and exponential service times. Suppose there is one server and the expected service time is exactly one minute. Compare Ls for the cases where the mean arrival rate is 0.5, 0.9 and 0.99 customers per minute, respectively. Do the same for Lq, Ws, Wq and P(W>5) or the probability of waiting time in the system. Öperations ResearchASSIGNMENT NO.9 (Queueing Theory)1. The jobs to be performed on a particular machine arriveaccording to a Poisson input process with a mean rate oftwo per hour. Suppose that the machine breaks down andwill require 1 hour to be repaired. What is the probabilitythat the number of new jobs that will arrive during this timeis: (2a) Zerob) twoc) five or more?2. Consider a queuing system with a Poisson input andexponential service times. Suppose there is one server andthe expected service time is exactly one minute. CompareLs for the cases where the mean arrival rate is 0.5, 0.9 and0.99 customers per minute, respectively. Do the same forLq, Ws, Wq and P(W>5) or the probability of waiting timein the system.

Since you have asked multiple question, we will solve the first question for you. If you want any…

Consider a queuing system with a Poisson input and exponential service times. Suppose there is one server and the expected service time is exactly one minute. Compare Ls for the cases where the mean arrival rate is 0.5, 0.9 and 0.99 customers per minute, respectively. Do the same for Lq, Ws, Wq and P(W>5) or the probability of waiting time in the system.

Consider a queuing system with a Poisson input and exponential service times. Suppose there is one server and the expected service time is exactly one minute. Compare Ls for the cases where the mean arrival rate is 0.5, 0.9 and 0.99 customers per minute, respectively. Do the same for Lq, Ws, Wq and P(W>5) or the probability of waiting time in the system.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

See similar textbooks

Similar questions

A company manufactures products in its factory in Turkey for sale in Asia. Products sold in different countries differ in terms of the power outlet as well as the language of the manuals. Currently, the company assembles and packs products for sale in individual countries. The distribution of weekly demand in different countries is normally distributed with means and standard deviations as shown in the table Assume that demand in countries to be independent. Given that the lead time from the Turkey factory is (X/4) weeks, how much safety inventory does the company require in Asia if it targets a CSL level of 95 percent?X= 96 b. The company builds a distribution center in Asia. It will ship base products to this center. When an order is received, the center will assemble power supplies, add manuals, and ship the products to the appropriate country. The base products are still to be manufactured in Turkey with the same lead time. How much saving of safety inventory can the company expect…
A weight-loss program wants to test how well their program is working. The company selects a simple random sample of 51 individual that have been using their program for 15 months. For each individual person, the company records the individual's weight when they started the program 15 months ago as an x-value. The subject's current weight is recorded as a y-value. Therefore, a data point such as (205, 190) would be for a specific person and it would indicate that the individual started the program weighing 205 pounds and currently weighs 190 pounds. In other words, they lost 15 pounds. When the company performed a regression analysis, they found a correlation coefficient of r = 0.707. This clearly shows there is strong correlation, which got the company excited. However, when they showed their data to a statistics professor, the professor pointed out that correlation was not the right tool to show that their program was effective. Correlation will NOT show whether or not there is…
Suppose we want to test the hypothesis that mothers with low socioeconomic status (SES) deliver babies whose birth weights are different from normal. To test this hypothesis, a random sample of 100 birth weights is selected from a list of full-term babies of SES mothers. The mean birth weight is found to be 115 oz. Suppose the average birth weight of all babies (based on nationwide surveys of millions of deliveries) is known to be 120 oz with = 24 oz. Set = .05 Assume all conditions are met, what is the p-value of their test? Give your answer to 4 decimal places.
Answer #2
If the duration of a disease is long and the incidence of the disease is low, the prevalence rate of that disease will be similar to the incidence rate of that disease. True False
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?
The Abendigo Division of Block C Enterprises has a product designed to operate for 1000 hours with a failure rate of 2.2%. Calculate the Mean Time to Failure.
6. True or False? Assume the below life table was constructed from following individuals who were diagnosed with slow-progressing form of prostate cancer and decided not to receive treatment of any form. The calculated survival probability for year 3, if the Kaplan-Meir approach is used to calculate the survival probability, is approximately 0.7438. Time in years Number at risk Nt Number of deaths, Dt Number of censored Ct Survival Probability 0 20 1 1 20 3 2 17 1 3 16 2 1
Problem : The following system has a radar, a computer and an auxiliary unit connected in series as shown with mean time between failures (MTBF’s) of 91,202 and 500 hours respectively. MTBF=91 HRS MTBF=202 HRS MTBF=500 HRS INPUT RADAR COMPUTER AUXILIARY OUTPUT SYSTEM Determine the following. The unit reliability of each component. System reliability * System MTBF for an operating period of 10 hours
3. Show your complete solution.
Q2. Assume we have two populations represent the mercury contamination (g/Km3) in two different European cities. The mean of mercury contamination in the first city is 50 g/Km3 with standard deviation of 1O, and mean of mercury contamination in the second city is 40 g/Km3 with standard deviation of 8 g/Km3. If a sample of n=9 is taken form first city and a sample of n=16 is taken form second city, what is the probability that the difference between these two sample means is less than 9 g/Km3? 0.0614 0.0359 0.3985 0.0992 0.6015
A random sample of n = 19 winter days in Denver gave a sample mean pollution index x1 = 43. Previous studies show that o1 = 10. For Englewood (a suburb of Denver), a random sample of n2 = 18 winter days gave a sample mean pollution index of x2 = 34. Previous studies show that o2 = 13. Assume the pollution index is normally distributed in both Englewood and Denver. Do these data indicate that the mean population pollution index of Englewood is different (either way) from that of Denver in the winter? Use a 1% level of significance. (a) What is the level of significance? State the null and alternate hypotheses. O Ho: H1 H2 O Ho: H1 = l2; H1: H1 < µ2 (b) What sampling distribution will you use? What assumptions are you making? O The standard normal. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's t. We assume that both population distributions are approximately normal with unknown standard deviations. O The Student's…