What is the probability that no cars are in the system? What is the average number of cars waiting for service? What is the average number of cars in the system? What is the average time a car waits for service?
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A fast-food franchise is considering operating a drive-up window food-service operation. Assume that customer arrivals follow a Poisson probability distribution, with an arrival rate of 24 cars per hour, and that service times follow an exponential probability distribution. Arriving customers place orders at an intercom station at the back of the parking lot and then drive to the service window to pay for and receive their orders. Consider a two-channel operation with two service windows and two employees. The employee stationed at each window fills the order and takes the money from customers arriving at the window. The average service time for this alternative is 3 minutes for each channel.
- What is the probability that no cars are in the system?
- What is the average number of cars waiting for service?
- What is the average number of cars in the system?
- What is the average time a car waits for service?
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- A fast-food franchise is considering operating a drive-up window food- service operation. Assume that customer arrivals follow a Poisson probability distribution, with an arrival rate of 24 cars per hour, and that service times follow an exponential probability distribution. Arriving customers place orders at an intercomstation at the back of the parking lot and then drive to the service window to pay for and receive their orders. Consider a two-channel operation with two service windows and two employees. The employee stationed at each window fills the order and takesthe money from customers arriving at the window. The average service time for this alternative is 3 minutes for each channel.1. What is the probability that no cars are in the system?2. What is the average number of cars waiting for service?3. What is the average number of cars in the system? What is the average time a car waits for service (in hours)?A fast-food franchise is considering operating a drive-up window food-service operation. Assume that customer arrivals follow a Poisson probability distribution, with an arrival rate of24 cars per hour, and that service times follow an exponential probability distribution. Arriving customers place orders at an intercom station at the back of the parking lot and then drive to the service window to pay for and receive their orders. Consider a two-channel operation with two service windows and two employees. The employee stationed at each window fills the order and takes the money from customers arriving at the window.The average service time for this alternative is 2 minutes for each channel. What is the average time a car waits for service?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. Assume that Poisson probability distribution with an arrival rate of 24 customers per hour or 0.4 customer per minute can be used to describe the arrival pattern. Assume further that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 36 customers per hour, or 0.6 customer per minute. a. Use the single-channel drive-up bank teller operation to determine the probability that no customers are in the system b. Use the single-channel drive-up bank teller operation to determine the average number of customers waiting c. Use the single-channel drive-up bank teller operation to determine the average number of customers in the system
- 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. Assume that Poisson probability distribution with an arrival rate of 24 customers per hour or 0.4 customer per minute can be used to describe the arrival pattern. Assume further that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 36 customers per hour, or 0.6 customer per minute. a. Use the single-channel drive-up bank teller operation to determine the average time a customer spends waiting b. Use the single-channel drive-up bank teller operation to determine the average time a customer spends in the system c. Use the single-channel drive-up bank teller operation to determine the probability that arriving customers will have to wait for service d.Use the single-channel drive-up bank teller operation…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. Assume that Poisson probability distribution with an arrival rate of 24 customers per hour or 0.4 customer per minute can be used to describe the arrival pattern. Assume further that the service times for the drive-up teller follow an exponential probability distribution with a service rate of 36 customers per hour, or 0.6 customer per minute. 1.) Use the single-channel drive-up bank teller operation to determine the probability of 4 customers in the system 2.) Use the single-channel drive-up bank teller operation to determine the average arrival time in minutes of customers 3.) Use the single-channel drive-up bank teller operation to determine the average service time in minutes of the drive-up tellerShauna’s Fast-food Service is considering operating a drive-up window food-service operation. Assume that customer arrivals follow a Poison probability distribution, with an arrival rate of 24 cars per hour and the service times follow an exponential probability distribution. Arriving customers place orders at an intercom station at the back of the parking lot and then drive to the service window to pay for and receive their orders. The following three service alternatives are being considered: A single-server operation in which one employee fills the order and takes the money from the customer. The average service time for this alternative is 2 minutes. A single-server operation in which one employee fills the order while a second employee takes the money from the customer. The average service time for this alternative is 1.25 minutes A two-server operation with two service windows and two employees. The employee stationed at each window fills the order and takes the money from…
- Shauna’s Fast-food Service is considering operating a drive-up window food-service operation. Assume that customer arrivals follow a Poison probability distribution, with an arrival rate of 24 cars per hour and the service times follow an exponential probability distribution. Arriving customers place orders at an intercom station at the back of the parking lot and then drive to the service window to pay for and receive their orders. The following three service alternatives are being considered: A single-server operation in which one employee fills the order and takes the money from the customer. The average service time for this alternative is 2 minutes. A single-server operation in which one employee fills the order while a second employee takes the money from the customer. The average service time for this alternative is 1.25 minutes A two-server operation with two service windows and two employees. The employee stationed at each window fills the order and takes the money from…BBA Bank (a fictitious one) has a drive-through teller window and observed that 15 customers arrive for service per hour, on an average, and the average service time per customer is 3 minutes. Assume inter-arrival time and service time follow a negative Exponential distribution. The bank hires you as a consultant. You guess that this is an M|M|1 system and you are required to determine the following: Probability (teller is busy) Probability (teller is idle) Probability of 3 customers in the system. Average number of customers waiting for service, that is, number of autos in the line excluding the one at the teller window. Average number of customers in the system, that is, number of autos in the line including the one at the teller window. Average time a customer spends in the system, that is, waiting time plus service time. Average time a customer spends in the waiting line before reaching the teller window.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…
- The time between arrivals of buses follows anexponential distribution, with a mean of 60 minutes.a What is the probability that exactly four buses willarrive during the next 2 hours?b That at least two buses will arrive during the next 2hours?c That no buses will arrive during the next 2 hours? d A bus has just arrived. What is the probability thatit will be between 30 and 90 minutes before the next busarrives?A restaurant manager is considering to hire waiters. Arrival rates have been found to follow the Poisson distribution, and the service times follow the negative exponential distribution. The average arrival rate is 12 customers per hour, and the average service time is 15 minutes. The manager hopes that there is on average 1 customer waiting in line, so at least how many waiters does he need to hire?