You have determined that waiting times at a toll booth are uniformly distributed over the interval 50 to 110 seconds. Your simulation generates the following random numbers. Complete the table with the waiting time associated with each random number. (Round your answers to the nearest whole number.) Random Number Waiting Time 0.64 0.87 0.57
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Q: You have determined that waiting times at a toll booth are uniformly distributed over the interval…
A: Below is the solution:-
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Q: You have determined that waiting times at a toll booth are uniformly distributed over the interval…
A: Given data: Interval 50 to 110 seconds Lower limit = 50 range = 60
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- The following information pertains to telephone calls to a motel switchboard on a typical Tuesday.PeriodIncoming Rate(calls perminute)Service Rate(calls per minuteper operator)Number ofOperatorsMorning 1.8 1.5 2Afternoon 2.2 1.0 3Evening 1.4 0.7 3a. Determine the average time callers wait to have their calls answered for each period and theprobability that a caller will have to wait for each period.b. For each case in the previous problem, determine the maximum line length for a probability of96 percent.The manager of a bank wants to use an MyMys queueingmodel to weigh the costs of extra tellers against the costof having customers wait in line. The arrival rate is 60customers per hour, and the average service time is fourminutes. The cost of each teller is easy to gauge at the$11.50 per hour wage rate. However, because estimatingthe cost per minute of waiting time is difficult, the bankmanager decides to hire the minimum number of tellersso that a typical customer has probability 0.05 of waitingmore than five minutes in line.a. How many tellers will the manager use, given thiscriterion?b. By deciding on this many tellers as “optimal,” themanager is implicitly using some value (or some range of values) for the cost per minute of wait-ing time. That is, a certain cost (or cost range) would lead to the same number of tellers as sug-gested in part a. What is this implied cost (or cost range)?. For the MyMy1 queueing model, why do the following results hold? (Hint: Remember that 1ym is the meanservice time. Then think how long a typical arrival must wait in the system or in the queue.) a. W 5 (L 1 1)ym b. WQ 5 Lym
- Based on Jacobs (1954). The Carter Caterer Company must have the following number of clean napkins available at the beginning of each of the next four days: day 1, 1500; day 2, 1200; day 3, 1800; day 4, 600. After being used, a napkin can be cleaned by one of two methods: fast service or slow service. Fast service costs 50 cents per napkin, and a napkin cleaned via fast service is available for use the day after it is last used. Slow service costs 30 cents per napkin, and these napkins can be reused two days after they are last used. New napkins can be purchased for a cost of 95 cents per napkin. Determine how to minimize the cost of meeting the demand for napkins during the next four days. (Note: There are at least two possible modeling approaches, one network and one nonnetwork. See if you can model it each way.)CPU-on-Demand (CPUD) offers real-time high-performance computing services. CPUD owns 1 supercomputer that can be accessed through the Internet. Their customers send jobs that arrive, on average, every 5 hours. The standard deviation of the interarrival times is 5 hours. Executing each job takes on average 3 hours on the supercomputer and the standard deviation of the processing time is 4.5 hours. How long does a customer have to wait to have a job completed?MacBurger’s is attempting to determine how manyservers (or lines) should be available during the breakfastshift. During each hour, an average of 100 customers arriveat the restaurant. Each line or server can handle an averageof 50 customers per hour. A server costs $5 per hour, andthe cost of a customer waiting in line for 1 hour is $20.Assuming that an M/M/s/GD/∞/∞ model is applicable,determine the number of lines that minimizes the sum ofdelay and service costs.
- Suppose a supermarket uses a system in which allcustomers wait in a single line for the first available cashier.Assume that the service time for a customer who purchasesk items is exponentially distributed, with mean k seconds.Also, a customer who purchases k items feels that the costof waiting in line for 1 minute is $k1. If customers can beassigned priorities, what priority assignment will minimizethe expected waiting cost incurred by the supermarket’scustomers? Why would a customer’s waiting cost per minutebe a decreasing function of k?The Decision Sciences Department is tyring to determine whether to rent a slow or fast copier. The department believes that an employee's time is worth $15/hour. The slow copier rents for $4/hr, and it takes an employee an average of 10 minutes to complete copying. The fast copier rents for $15/hr, and it takes an employee an average of 6 minutes to complete copying. On average, four employees per hour need to use the copying machine. (Assume the copying times and interarrival times to the copying machine are exponentially distributed.) Which machine should the department rent to minimize expected total cost per hour? Please note this class revolves around Microsoft Excel so the answer I need needs to show the formulas in Excel, along with any corresponding graphs, etc. Thank you in advance!CPU-on-Demand (CPUD) offers real-time high-performance computing services. CPUD owns 1 supercomputer that can be accessed through the Internet. Their customers send jobs that arrive, on average, every 4 hours. The standard deviation of the interarrival times is 4 hours. Executing each job takes, on average, 3 hours on the supercomputer and the standard deviation of the processing time is 3.6 hours. On average, how long will it take to complete a job (from the time it is submitted by the customer until the time it is completed)?
- On average, 40 jobs arrive per day at a factory. The time between arrivals of jobs is exponentially distrib-uted. The factory can process an average of 42 jobs per day, and the time to process a job is exponentiallydistributed.a. On average, how long does it take before a job iscompleted (measured from the time the job arrivesat the factory)?b. What fraction of the time is the factory idle?c. What is the probability that work on a job willbegin within two days of its arrival at the factory?A supermarket has just added a new cash register to reduce the waiting times of the customers during weekends. Since a new cash register is added, the customers expect that their waiting time will be less than the waiting time before the cash register was added. Suppose the sample variance of the waiting times for 25 customers before adding the new cash register is sĩ = 4.8 minutes, while the sample variance of the waiting times for 25 customers after adding the cash register is sź = 2.2 minutes. The manager of the supermarket believes that the waiting times are normally distributed and that the two samples are drawn independently. What is the conclusion? Given that all other criteria are satisfied, should the supermarket continue with the new cash register?Each airline passenger and his or her luggage must bechecked to determine whether he or she is carrying weaponsonto the airplane. Suppose that at Gotham City Airport, anaverage of 10 passengers per minute arrive (interarrivaltimes are exponential). To check passengers for weapons,the airport must have a checkpoint consisting of a metal detector and baggage X-ray machine. Whenever a check-point is in operation, two employees are required. A checkpoint can check an average of 12 passengers perminute (the time to check a passenger is exponential). Underthe assumption that the airport has only one checkpoint,answer the following questions:a What is the probability that a passenger will have towait before being checked for weapons?b On the average, how many passengers are waiting in line to enter the checkpoint? 1082 CHAPTER 2 0 Queuing Theoryc On the average, how long will a passenger spend atthe checkpoint?