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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 customers arriving at the window. The average service time for this alternative is 2 minutes for each server. Answer the following questions and recommend one of the design options
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- 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?
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- 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…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?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?
- 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)?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 systemWillow 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 tellerA 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?Jobs arrive at Loaf Machine Shop. Assume the arrival rate is five jobs per hour. Service times (in minutes per job) do not follow the exponential probability distribution. Two proposed designs for Loaf Machine Shop operation are shown. Design Mean Standard Deviation A 6.0 3.0 B 6.25 0.6 What is the service rate in jobs per hour for each design? For the service rate in part (a), what design appears to provide the best or fastest service rate?
- A petrol station in the capital Kingstown has a single pump manned by one attendant.Vehicles arrive at the rate of 20 customers per hour and petrol filling takes 2 minutes on anaverage. Assume the arrival rate is Poisson probability distribution and service rate isexponentially distributed. Arrivals tend to follow a Poisson distribution, and service timestend to be exponential. The attendant is paid $10 per hour, but because of lost goodwill andsales, station loses about $15 per hour of customer time spent waiting for the attendant toservice and order. Part BThe Petrol station is considering adding a second pump with an attendant to servicecustomers. The station would pay that person the same $10 per hour.Using appropriate formula for the multiple channel model, answer the following questions:a. What is the probability that no customers are in the system (Po)?b. What is the average number of customers waiting for service (Lq)? c. What is the average number of customers in the system…A petrol station in the capital Kingstown has a single pump manned by one attendant.Vehicles arrive at the rate of 20 customers per hour and petrol filling takes 2 minutes on anaverage. Assume the arrival rate is Poisson probability distribution and service rate isexponentially distributed. Arrivals tend to follow a Poisson distribution, and service timestend to be exponential. The attendant is paid $10 per hour, but because of lost goodwill andsales, station loses about $15 per hour of customer time spent waiting for the attendant toservice and order. a. What is the probability that no customers are in the system (Po)?b. What is the average number of customers waiting for service ( Lq)? c. What is the average number of customers in the system (L)?d. What is the average time a customer waits for service(Wq)? e. What is the average time in the system (W)?f. What is the probability that a customer will have to wait for service (Pw)?g What is the probability that there is exactly 2…The Rockwell Electronics Corporation retains a service crew to repair machine breakdown that occur on an average of λ = 3 per day (approximately Poisson in nature). The crew service an average of μ = 8 machines per day, with a repair time distribution that resemble the exponential distribution. a. What is the probability that more than one machine is in the system? Probability that more than two are broken and waiting to be repaired or being serviced? More than three? More than four?