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3. A fast food restaurant has a drive-thru window. On average 40 customers arrive at the...
7.4 During lunch hour, customers arrive at a fast-food restaurant at the rate of T20 customers...
7.4 During lunch hour, customers arrive at a fast-food restaurant at the rate of T20 customers per hour. The restaurant has one line, with three workers taking food orders at independent service stations. Each worker takes an exponentially dis- tributed amount of time-on average 1 minute-to service a customer. Let X, denote the number of customers in the restaurant (in line and being serviced) at time t. The process (Xt)PO Is a continuous-time Markov chain. Exhibit the generator matrix
7. The Canara Bank drive-thru teller window can serve a customer at an average of 4...
7. The Canara Bank drive-thru teller window can serve a customer at an average of 4 minutes per customer. Service time has a negative exponential distribution. Customers arrive in their cars at a rate (Poisson distributed) of 12 per hour and form a single waiting line: a. Determine the average waiting time, the average queue length, and the probability that there is no customer in the system. b. If Canara Bank decides to open a second drive-thru teller window with...
A Fast Food drive-through Restaurant with a single check-out counter opens six days a week, but...
A Fast Food drive-through Restaurant with a single check-out counter opens six days a week, but its heaviest day of business is on Saturdays. Customers arrive at an average rate of 20 per hour on Saturdays. Customers can be provided service at the rate of one every two minutes. Assuming Poisson arrivals and exponential service times, find: The average number of customers in line The average time a car waits before being served The average time a customer spends in...
A quick-service restaurant has a single drive-through lane with one worker at the window. It is...
A quick-service restaurant has a single drive-through lane with one worker at the window. It is assumed that the worker can process an order every 3 minutes on average and that the processing (service) times are exponentially distributed. Customers arrive at the drive-through at the rate of 15 per hour. a. The worker at the drive-thru is busy ????? of time. (Enter your response rounded to two decimal places.) b. The average number of cars waiting at the drive-thru is...
3. Customers arrive at the drive-through lane of a fast food restaurant at a rate of...
3. Customers arrive at the drive-through lane of a fast food restaurant at a rate of one every 3 minutes. Use the Poisson probability distribution to answer the following (12 Marks) a. What is the expected number of customers in one hour? b. What is the probability that exactly two customers arriving at the drive-through lane in a nine-minutes interval? c. What is the probability that less than two customers arrive at the drive through lane a nine-minutes interval? d....
Problem 1. Consider a fast food restaurant where customers arrive and get in line according to...
Problem 1. Consider a fast food restaurant where customers arrive and get in line according to a Poisson process with an average rate of 120 customers per hour. The restaurant has one line and the amount of time it takes the cashier to serve a customer is exponentially distributed with a mean of 2 minutes. Let X_t denote the number of customers in line at time t. 1. Give the state space of the chain (X_t)t≥0. 2. For each state...
Question 2 A fast-food franchise is considering operating a drive-up window food-service operatio...
Question 2 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. The following three service alternatives are being considered: A single-channel operation...
During lunchtime at a certain fast food restaurant, customers arrive at an average rate of 7...
During lunchtime at a certain fast food restaurant, customers arrive at an average rate of 7 customers every 5 minutes. assume a poisson distribution to find the probability that: A) exactly 12 customers arrive in a given 10 minute interval (perform this calculation using an appropriate formula, showing the setup.) b) between 5 and 10 customers (inclusive) arrive in a given 5 minute interval (show how you can answer this from the table) c) after a customer arrives, find the...
27) A fast food restaurant wants to know about how long, on average, a customer spends...
27) A fast food restaurant wants to know about how long, on average, a customer spends waiting in a drive-thru from the time their order ends to the time that they get their food. To investigate this, the restaurant takes a random sample of 36 cars and finds that it takes an average of 2.4 minutes. Suppose the restaurant knows that drive-thru times have a population standard deviation of 7 minutes. Calculate a 95% Confidence Interval for drive-thru times: (5...
A fast food franchise is considering a drive-up window food-service operation. Assume that customer arrivals follow...
A fast food franchise is considering a drive-up window food-service operation. Assume that customer arrivals follow a Poisson probability distribution with a mean 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 up to the service window to pay for and receive their order. The following three service alternatives are being considered: a) A single-channel...
7.4 During lunch hour, customers arrive at a fast-food restaurant at the rate of T20 customers per hour. The restaurant has one line, with three workers taking food orders at independent service stations. Each worker takes an exponentially dis- tributed amount of time-on average 1 minute-to service a customer. Let X, denote the number of customers in the restaurant (in line and being serviced) at time t. The process (Xt)PO Is a continuous-time Markov chain. Exhibit the generator matrix
7. The Canara Bank drive-thru teller window can serve a customer at an average of 4 minutes per customer. Service time has a negative exponential distribution. Customers arrive in their cars at a rate (Poisson distributed) of 12 per hour and form a single waiting line: a. Determine the average waiting time, the average queue length, and the probability that there is no customer in the system. b. If Canara Bank decides to open a second drive-thru teller window with...
3. Customers arrive at the drive-through lane of a fast food restaurant at a rate of one every 3 minutes. Use the Poisson probability distribution to answer the following (12 Marks) a. What is the expected number of customers in one hour? b. What is the probability that exactly two customers arriving at the drive-through lane in a nine-minutes interval? c. What is the probability that less than two customers arrive at the drive through lane a nine-minutes interval? d....
27) A fast food restaurant wants to know about how long, on average, a customer spends waiting in a drive-thru from the time their order ends to the time that they get their food. To investigate this, the restaurant takes a random sample of 36 cars and finds that it takes an average of 2.4 minutes. Suppose the restaurant knows that drive-thru times have a population standard deviation of 7 minutes. Calculate a 95% Confidence Interval for drive-thru times: (5...
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