A single server drive-thru facility has room for a maximum of 4 cars (the one being serviced and 3 in queue). Whenever the facility is full, newly arriving potential customers do not stay. Customers arrive in a Poisson manner at an average of 24 per hour. Service times are exponential with a mean of 3 minutes.
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- 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)?The average demand on a factory store for a certain electric motor is 8 per week. When the storeman places an order for these motors, delivery takes one week. If the demand for motors has a Poisson distribution, how low can the storeman allow his stock to fall before ordering a new supply if he wants to be at least 95% sure of meeting all requirements while waiting for his new supply to arrive?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)? Now suppose that the arrival rate increases 20 percent.What is the corresponding change in L and W?
- The number of visits to a website is known to have a Poisson distribution with a mean of 10 visits per minute Within what limits does Tchebysheff's Theorem suggest you would expect the number of visits to this website to lie at least 75% of the time?The Mega Multiplex Cinema runs three cinema box offices to sell tickets to film- goers. The service time for a film-goer varies due to number of sold tickets, special requests for the seats, etc. but can be assumed to be exponentially distributed with a mean value of 2 min. Film-goers queue up in a single queue for all three box offices and are served on a FCFS (First Come First Served) rule. On average 71 film-goers are expected per hour (Poisson distributed). Opening credits last 10 minutes; therefore the time for queuing and buying a ticket should not on average be longer than 10 min. How long do you expect the average time for queuing and buying for the given data?Ali Baba's Car Wash Service Centre is open 6 days a week, but its busiest day is always on Sunday. From the previous data, Ali Baba estimates that dirty cars arrive at the rate of one every two minutes, One car at a time is cleaned in this example of a single-channel waiting line. Assuming Poisson arrivals and exponential service times, find the following: iii) Compute the average time that a car spends in the system.
- Suppose an electric-vehicle manufacturing company estimates that a driver who commutes 50 miles per day in a particular vehicle has a recharging time that has a uniformly distributed between 70 and 110 minutes. What is the expected recharging time in minutes?(Enter your answer with no decimal places).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>The manager of a fast-food store realizes that her staffing problems are a result of the variation in the number of customers that arrive at the store. If the same number of customers came each hour, she would know exactly how many servers to have working. It turns out that the Poisson distribution works well to describe the arrivals of customers in any given hour. Explain why the manager has more trouble staffing the store during those hours when the average arrival rate is higher.
- The number of passengers willing to travel with a certain train is as- sumed to be a Poisson variabel with parameter µ = 300. How many seats should the train have if the probability for an over-booked train should be at most 1%?The time to failure of a certain type fo electrical component is assumed to follow an exponential distribution with a mean of 4 years. The manufacturer replaces free all components that fail while under guarantee. If the manufacturer wants to replace a maximum of 3% of the ocmponents, for how long should the manufacturer's stated guarantee on the component be?Consider the previous question above, A further study determined that cars arrive to this shopping center according to a non-stationary Poisson process. The mean arrival rate increases linearly from 0.17 to 0.49 cars per minute between 10 am and 2 pm. Then the rate remains constant at 0.49 cars per minute between 2 pm and 4 pm. Finally, the rate changes to a constant 0.33 cars per minute between 4 pm and 5 pm. What is the probability that 60 cars will arrive between 1:45 pm and 4:15 pm?