Dr. Tarun Gupta, a Michigan vet, is running a rabies vaccination clinic for dogs at the local grade school. Tarun can "shoot" a dog every 3 minutes. It is estimated that the dogs will arrive independently and randomly throughout the day at a rate of one dog every 6 minutes according to a Poisson distribution. Also assume that Tarun's shooting times are negative exponentially distributed. a) The probability that Tarun is idle =

Dr. Tarun Gupta, a Michigan vet, is running a rabies vaccination clinic for dogs at the local grade school. Tarun can "shoot" a dog every 3 minutes. It is estimated that the dogs will arrive independently and randomly throughout the day at a rate of one dog every 6 minutes according to a Poisson distribution. Also assume that Tarun's shooting times are negative exponentially distributed. a) The probability that Tarun is idle =

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter5: Network Models

Section: Chapter Questions

Problem 71P

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Dr. Tarun Gupta, a Michigan vet, is running a rabies vaccination clinic for dogs at the local grade school. Tarun can "shoot" a dog every 3 minutes. It is estimated that the dogs will arrive independently and randomly throughout the day at a rate of one dog every 6 minutes according to a Poisson distribution. Also assume that Tarun's shooting times are negative exponentially distributed. a) The probability that Tarun is idle = enter your response here (round your response to two decimal places). b) The proportion of the time that Tarun is busy = enter your response here (round your response to two decimal places). c) The average number of dogs being vaccinated and waiting to be vaccinated = enter your response here dogs (round your response to two decimal places).
The average time between the arrivals of the taxis arriving at the airport to pick up passengers has an exponential distribution, with an average of 10 minutes. a) What is the probability that a passenger will wait for the taxi less than 15 minutes? b) What is the probability that a passenger will wait for the taxi between 20 and 30 minutes? Solve using the cumulative distribution function H1
Car arrivals at a gas station follow a Poisson distribution with a mean of λ=6 and the length of service is exponential with a mean of 1/3. How many gasoline pumps must be placed so that the probability that the number of customers at the station equals or exceeds the number of pumps is at most 0.2?
Consider a bank with two tellers. Service times by each teller are exponentially distributed withmean of 1 hour per customer. Customers also arrive with an exponential interarrival times withmean of 1 hour. Suppose a customer has just arrived at 2pm:a. What is the probability that the next customer will arrive between 3:00 pm and 4:00 pm?b. If no customer arrives before 4:00 pm, what is the probability that the next customer willarrive between 4:00 pm and 5:00 pm?c. What is the probability that the number of arrivals between 2:00 pm and 4:00 pm will be morethan one?
Customers arrive at a one window drive according to a poison distribution with mean of 10 minutes and service time per customer is exponential with mean of 6 minutes. The space in front of the window can accommodate only three vehicles including the serviced ones. Other vehicles are have to wait outside this space. Calculate:a. A. probability that an arriving customer can drive directly to the space in front of the windowb. Probability that an arriving customer will have to wait outside the directed space c. How long an arriving customer is expected to wait before getting the service?
Users are connected to a database server through a network. Users request files from the Database server. The database server takes a period of time that is exponentially distributed with mean 5 seconds to process a request. Find the probability that 10 requests are processed by the server during the first 1 minutes. Determine the probability that no request is processed by the server during the first 2 minutes Determine the average number of requests processed in 2 minutes
Larry Ellison starts a company that manufactures high-end custom leather bags. Hehires two employees. Each employee only begins working on a bag when a customerorder has been received and then she makes the bag from beginning to end. The average production time of a bag is 1.8 days, with a standard deviation of 2.7 days. Larryexpects to receive one customer order per day on average. The interarrival times oforders have a coefficient of variation of one. What is the expected duration, in days,between when an order is received and when production begins on the bag?
11. Automobiles arrive at a tollbooth on a highway completely at random according to a Poisson process with rate À = 4 cars per hour. Determine the following: a. The probability that the time between any two successive arrivals exceeds 20 minutes. b. The probability that exactly four cars arrive in any given hour. c. The probability that more than five cars arrive in any given hour. d. The probability that more than 10 cars arrive in any given two-hour period. e. A person working for the transportation department begins counting arrivals at the tollbooth at 8 A.M. What is the probability that he counts 20 arrivals before 12 noon? (Use a normal approximation for your calculations.)
Consider a Poisson queue with the following steady-state probabilities: po = 1/3, p1 = 1/2, p2 = 1/6, and pn = for n = 3,4,5, ... . What is the minimum number of stools that would accommodate all customers in the system at least 75% of the time in steady state? 3 stools O 2 stools none of the other choices O 1 stool
Willow Brook National Bank operates a drive-up teller window that allows customers to complete bank transactions without getting out of their cars. On weekday mornings, arrivals to the drive-up teller window occur at random, with an arrival rate of 24 customers per hour or 0.4 customers per minute. What is the mean or expected number of customers that will arrive in a five-minute period?λ = fill in the blank 1 per five minute period Assume that the Poisson probability distribution can be used to describe the arrival process. Use the arrival rate in part (a) and compute the probabilities that exactly 0, 1, 2, and 3 customers will arrive during a five-minute period. If required, round your answers to four decimal places. x P(x) 0 fill in the blank 2 1 fill in the blank 3 2 fill in the blank 4 3 fill in the blank 5 Delays are expected if more than three customers arrive during any five-minute period. What is the probability that delays will occur? If required, round your…
Larry Ellison starts a company that manufactures high-end custom leather bags. He hires two employees. Each employee only begins working on a bag when a customer order has been received and then she makes the bag from beginning to end. The average production time of a bag is 1.7 days, with a standard deviation of 3 days. Larry expects to receive one customer order per day on average. The interarrival times of orders have a coefficient of variation of one. X Answer Is complete but not entirely correct. (Carry at least 4 decimal places in all intermediate calculations. Round your final answer to 2 decimal places.) What is the expected duration, in days, between when an order is received and when production begins on the bag? 30.39 8 days
A cafeteria can seat a maximum of 20 persons. Each customer arrives in a Poisson stream with mean value 4 minutes. They are serviced at the rate of 10 per hour. For simplicity, assume that customers are serviced one at a time by one waiter. c) Suppose that two customers (with random arrival times) would like to be seated together. What is the probability that their wish can be fulfilled? Assume that arrangements can be made to seat them together as long as there are three empty seats anywhere in the cafeteria. d) Determine the expected number of customers waiting but currently not being served