a. if you arrived at a random time and waited for 5 minutes what is the probability the next train will come within 5 minutes? %% b. if you arrive at a random time, waited for 5 mins, how much more time do you have to wait for the next train, on average? number of mins
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- Customers arrive to a local bakery with an average time between arrivals of5 minutes. However, there is quite a lot of variability in the customers’ arrivals, asone would expect in an unscheduled system. The single bakery server requires anamount of time having the exponential distribution with mean 4.5 minutes to servecustomers (in the order in which they arrive). No customers leave without service.d. Calculate the probability a customer will spend more than an hour at the bakery(time in queue plus service time).c. The probability that more than five cars arrive in any given hourCustomer arrive at one-window drive in bank according to Poisson distribution with mean 10 per hour. Service time per customer is exponential with mean 5 minutes. There are three spaces in front of the window, including the car being served. Other arriving cars can wait outside these three spaces. A. What is the probability that an arriving customer can enter one of these three spaces? B. What is the probability that an arriving customer is expected to wait outside the three spaces. C.How long is an arriving customer expected to wait before starting service.
- Bank with 2 tellers. Customers arrive at a rate 80 per hour and wait in a single line. Average time to serve is 1.2 minutes per customer What is the expected number of customers present in the bank? = What is the expected length of time a customer spends in the bank? = What is the fraction of time any specific teller is idle? = probability that the system is empty + 0.5(probability that the system has 1 customer9. A gas station with only one gas pump employs the following policy: If a customer has to wait, the price is $3.50 per gallon; if she does not have to wait, the price is $4.00 per gallon. Customers arrive according to a Poisson process with a mean rate of 15 per hour. Service times at the pump have an exponential distribution with a mean of 3 minutes. Arriving customers always wait until they can eventually buy gasoline. Determine the expected price of gasoline per gallon.Consider a bank with two tellers. An average of 2 customers per hour arrive at the bank and wait in a single línea for an idle teller. The average time it takes to serve a customer is triangular (x1=1, y1=0), (x2=4, y2=2/3) Assume that inter-arrival times and services time is exponential. Develop the service (ST) equation? a. Y=2x-22/6B. Y=2x-22/3C. Y=22/3x-2/3D. Y=2x-3/22