Customers arrive at a railway ticket counter at the rate of 30 per hour. Assuming Poisson arrivals, exponential service time distribution and a single-server queue (M/M/1) model, find the average waiting time (before being served) if the average service time is 100 seconds.
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- Does Table 1 represent a linear function? If so, finda linear equation that models the data.In this problem, assume Poisson arrivals and exponential service times.Customers of Plaka Record rental outlet arrive at the store to rent CDs with an arrivalrate of 1.25 customers per minute. The store has only 1 counter with a service rate of 2 customers per minute. Suppose that Plaka Record rental outlet adds another counter to serve thecustomers simultaneously.1. The average number of customers in the waiting line2. The average number of customers in the system3. The average time a customer spends in the waiting line. The average time a customer spends in the systemVehicles arrive at a car detailing service at a rate of 10 per minute according to a Poissondistribution. For simplicity, assume that there is only one lane and one worker who can serve atan average rate of 12 vehicles per minute. Service times are exponentially distributed. Part A: What is the average length of the queue? Part B: What is the average time a vehicle must spend to get through the system? Part C: What is the utilization rate of the worker? Part D: What is the probability that when you arrive at the shop, there will be three ormore vehicles ahead of you?
- A mechanic who works in the maintenance center of a large company and requires an average time of 4 hours to repair a machine, distributed exponentially. Damaged machines arrive in a queue based on a Poisson check-in process at an average rate of 0.25 per hour. If the mechanic used a more modern tool, the average repair time would be reduced to 2.5 hours (also exponentially distributed). If an hour of standby for a machine costs USD25, calculate the expected hourly savings that would result from using the latest tool.Confirm that the total population in this model remains constant.Assume a single server queueing system with exponential inter-arrival times, and service times. Assume that the expected inter-arrival time is 10 minutes, and the expected service time is 7.5 minutes. We are interested in the expected time the customers spend waiting in queue (in minutes). Develop a Monte Carlo simulation model to estimate Wg Calculate W (expected wait time in queue), and compare it with the previous result
- what would the maximum return be?find the critical point.A police station had to deploy police officers for emergencies multiple times the lastfour evenings. The numbers of emergencies for Monday, Tuesday, Wednesday, andThursday were 7, 4, 8, and 11, respectively. What would be the station’s forecast forFriday using an exponential smoothing forecasting approach? Use α = 0.3 and aforecast for Monday of 9.
- An online clothing company is keeping track of their customers purchases. Company also offers a credit card where customers get additional offers if they use that card when they make purchases from their online store. For those customers who has their credit card, the company has additional information such as age, yearly income, etc. The company management is interested in looking at the relationship between the income (in 1000s of dollars) and the total yearly purchases from their store for these credit card holders . They have gathered this information from a random sample of 42 credit card holders. Below provided is a partial MINITAB output for predicting the yearly purchases from the income. Identify the response and the predictor variable in this study. Write the equation of the least squares regression line for predicting the total yearly purchase from the income of the customer. What percentage of variation in total yearly purchase is explained by income of the customer?…Movies Tonight is a typical video and DVD movie rental outlet for home-viewing customers. During the weeknight evenings, customers arrive at Movies Tonight with an arrival rate of 1.25 customers per minute. The checkout clerk has a service rate of 2 customers per minute. Assume Poisson arrivals and exponential service times. What is the average number of customers waiting for service?Over the past 40 years, the percentage of homes in the United States with smoke detectors has risen steadily and has plateaued at about 96% as of 2015.† With this increase in the use of home smoke detectors, what has happened to the death rate from home fires? Suppose the following contains 17 years of data on the estimated percentage of homes with smoke detectors and the estimated home fire deaths per million of population. Percentage ofHomes withSmoke Detectors Home Fire Deathsper Millionof Population 0.52 22.8 0.69 20.7 0.76 17.2 0.78 20.4 0.79 19.3 0.84 18.8 0.83 17.5 0.87 16.1 0.88 13.5 0.90 14.3 0.92 14.2 0.94 12.9 0.95 10.8 0.96 10.8 0.97 10.1 0.96 8.3 0.96 8.0 (a) Do you expect a positive or negative relationship between smoke detector use and deaths from home fires? Why or why not? We would expect there would be a ---Select--- negative positive relationship between smoke detector use and deaths from home fires. As more households have…
