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
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- The Baytown Post Office has four stations for service. Customers line up in single file for service on an FIFO basis. Themean arrival rate is 40 per hour, Poisson distributed, and themean service time per server is five minutes, exponentiallydistributed. Compute the operating characteristics for this operation. Does the operation appear to be satisfactory in termsof: (a) postal workers’ (servers’) idle time; (b) customer waiting time and/or the number waiting for service; and (c) thepercentage of the time a customer can walk in and get servedwithout waiting at all?Suppose that 2% of the employed lose their job each month. Further suppose that 25% of the unemployed find a job each month. a. What is the average duration of employment in this labor market? b. Do you think this is a reasonable figure given estimates of the natural rate? Why or why not? c. If you wanted to reduce the steady-state level of unemployment, what type of policies might you pursue and why?Dentists are increasingly concerned about the growing trend of local school districts to grant soft drink companies exclusive rights to install soda pop machines in schools in return for money-usually millions-that goes directly into school coffers. According to a recent study by the National Soft Drink Association, 62% of schools nationally already have such contracts. This comes at a time when dentists are seeing an alarming increase in horribly decayed teeth and eroded enamel in the mouths of teenagers and young adults. With ready access to soft drinks, children tend to drink them all day. That, combined with no opportunity to brush, leads to disaster, dentists say. Suppose that 20 schools around the country are randomly selected and asked if they have a soft drink contract. Find the probability that the number of 'Yes" answers is A. exactly 8 B. at most 8 C. at least 4 D. between 4 and 12, inclusive
- A Packages arrive at a warehouse that has a single reception point with a Poissondistribution mean of once every 12 minutes. It takes on the exponentially distributedaverage of 9-minutes to process each package.(a) What is the average wait time of a package in the queue?(b) On the average, how many packages are in the queue at any given time?(c) On the average, how many packages are in the system at any given time?(d) On the average, what is the wait time of packages in the system?(e) What percent of the time is the server idle?(f) What is the probability that there are exactly 7 packages in the system at any givenpoint in time>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.A bank with a branch located in a commercial district of a city has the business objective of developing an improved process for serving customers during the noon-to-1pm lunch period. Management decides to first study the waiting time in the current process. The waiting time is defined as the number of minutes that elapse from when the customer enters the queue until he/she reaches the teller’s window. In addition, suppose that another branch, located in a residential area, is also concerned with improving the process of serving customers in the noon-to-1 pm lunch period and data were collected at random at these branches and recorded below; No of Customers Commercial dist branch (time) Residential area branch (time) 1 – 5 3 3 6 - 10 5 6 11 - 15 8 5 16 – 20 8 3 21 - 25 4 2 Required Which of the branches has a relatively better mean waiting time? Which shop can be surer of meeting the mean waiting time at the two branches? Assuming…
- Suppose the customers arrive at a Poisson rate of on eper every 12 minutes, and that the service time is exponential at a rate of one service per 8 minutes. What are the average number of customers in the system(L) and the average time a customer spends in the system(W)?Explain Estimation and Inference in the Logit and Probit Models2?Given that a zone has 350 households with access to cars and 295 households without access to cars and the average trip generation rates for each group are 4.0 and 2.0 trips per day, respectively. Assuming that in the future, households will have similar distribution with access and without access to a car, as per the existing situation. There will be an addition of 650 households with a similar distribution of car ownership. Find the growth factor and future trips from that zone.
- Financial analysts have developed models based on financial ratios that predict whether or not a company will go bankrupt within the next year. In a test of one such model, the model correctly predicted the bankruptcy of 88% of firms that in fact did fail. The model also correctly predicted the non-bankruptcy for 82% of firms that did not fail. Suppose that the model maintains the same reliability when applied to a new group of 82 firms, of which 7 fail in the year following the time at which the model makes its predictions. Define the event F as firm failure and event B as the outcome of a test for bankruptcy. Given this information, what is the probability that a firm will fail P(F)?write the log likelihood for the null model and the number of parameters associated with the maximal modelSuppose the customers arrive at a Poisson rate of on eper every 12 minutes, and that the service time is exponential at a rate of one service per 8 minutes. What are the average number of customers in the system(L) and the average time a customer spends in the system(W)? Now suppose that the arrival rate increases 20 percent.What is the corresponding change in L and W?