Homework Answers
| Service time | 4.000 | |
| Interarrival time | 4.138 | |
| Arrival per hr | 14.500 | |
| Service per hr | 15.000 | |
| Р | 0.966666667 | |
| Number in queue | .967/(1-.967) | |
| Avg. time waiting in queue | 14.5/(15*(15-14.5)) | |
| Avg. time waiting in queue | 1.933 | hrs |
| 116.00 | mins | |
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Customers arrive at a bank that has 1 teller and they wait in line on a...
Please answer using stochastic operations principles Cars arrive at a rate of 10 per hour in a single-server drive-in restaurant. Assume that the teller serves vehicles with a rate exponentially distr...
Please answer using stochastic
operations principles
Cars arrive at a rate of 10 per hour in a single-server drive-in restaurant. Assume that the teller serves vehicles with a rate exponentially distributed with a mean of 4 minutes per car (ie, a rate of 1 car every 4 minutes). Answer the following questions: (a) What is the probability that the teller is idle? (b) What is the average number of cars waiting in line for the teller? (A car that is...
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...
At a hair salon served by only one hairdresser, customers arrive at the rate of about...
At a hair salon served by only one hairdresser, customers arrive at the rate of about 8 per hour according to a Poisson distribution. It takes about 5 minutes for the hair dresser to complete each customer, following an exponential distribution. What is the average time (in hours)the customer has to wait in the salon?
QUESTION 1 Customers arrive at a hair salon according to a Poisson process with an average of 1...
QUESTION 1 Customers arrive at a hair salon according to a Poisson process with an average of 16 customers per hour. Which of the following is most likely true, based on this information: a. The hair salon serves customers on a walk-in basis (rather than by appointment times) b. If 10 customers arrive in the first hour, it is likely that 22 customers will arrive in the next hour. c. If the salon can serve an average of 20 customers...
Customers arrive at bank according to a Poisson process with rate 20 customers per hour. The bank...
Customers arrive at bank according to a Poisson process with rate 20 customers per hour. The bank lobby has enough space for 10 customers. When the lobby is full, an arriving customers goes to another branch and is lost. The bank manager assigns one teller to customer service as long as the number of customers in the lobby is 3 or less. She assigns two tellers if the number is more than 3 but less than 8. Otherwise she assigns...
Many of a bank’s customers use its automatic teller machine to transact business after normal banking...
Many of a bank’s customers use its automatic teller machine to transact business after normal banking hours. During the early evening hours in the summer months, customers arrive at a certain location at the rate of one every other minute. This can be modeled using a Poisson distribution. Each customer spends an average of 83 seconds completing his or her transactions. Transaction time is exponentially distributed. a. Determine the average time customers spend at the machine, including waiting in line...
Queueing models with variance 3. National Bank currently employs a single teller to assist customers over...
Queueing models with variance
3. National Bank currently employs a single teller to assist customers over their lunch breaks. The typical inter-arrival time for customers is 10 minutes with a standard deviation of 8 minutes. The teller can service people, on average, every 8 minutes with a standard deviation of 7 minutes. Find the following: a. The utilization of the teller b. The average number of customers in line c. The average time a customer waits before it seeing the...
Problem 4. The Security & Trust Bank employs 4 tellers to serve its customers. Customers arrive a...
Problem 4. The Security & Trust Bank employs 4 tellers to serve its customers. Customers arrive ac cording to a Poisson process at a mean rate of 4 per minute. However, business is growing and management projects that the mean arrival rate will be 6 per minute a year from now. The transaction time between the teller and customer has an exponential distribution with a mean of 0.5 minute. Management has established the following guidelines for a satis- factory level...
The Quick Snap photo machine at the Lemon County bus station takes snapshots in exactly 80...
The Quick Snap photo machine at the Lemon County bus station takes snapshots in exactly 80 seconds. Customers arrive at the machine according to a Poisson distribution at the mean rate of 15 per hour. On the basis of this information, determine the following: (Provide formulas) a. the average number of customers waiting to use the photo machine b. the average time a customer spends in the system c. the probability an arriving customer must wait for service.
A hair salon is run by two stylists, Darrel and Jill, each capable of serving four...
A hair salon is run by two stylists, Darrel and Jill, each capable of serving four customers per hour, on average. Six customers, on average, arrive at the salon each hour. (Assume Poisson arrivals and exponential service times) a) If all arriving customers wait in a common line for the next available stylist, how long would a customer wait in line, on average, before being served? b) Suppose that 50 percent of the customers want to be served only by...
Please answer using stochastic
operations principles
Cars arrive at a rate of 10 per hour in a single-server drive-in restaurant. Assume that the teller serves vehicles with a rate exponentially distributed with a mean of 4 minutes per car (ie, a rate of 1 car every 4 minutes). Answer the following questions: (a) What is the probability that the teller is idle? (b) What is the average number of cars waiting in line for the teller? (A car that is...
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...
Queueing models with variance
3. National Bank currently employs a single teller to assist customers over their lunch breaks. The typical inter-arrival time for customers is 10 minutes with a standard deviation of 8 minutes. The teller can service people, on average, every 8 minutes with a standard deviation of 7 minutes. Find the following: a. The utilization of the teller b. The average number of customers in line c. The average time a customer waits before it seeing the...
Problem 4. The Security & Trust Bank employs 4 tellers to serve its customers. Customers arrive ac cording to a Poisson process at a mean rate of 4 per minute. However, business is growing and management projects that the mean arrival rate will be 6 per minute a year from now. The transaction time between the teller and customer has an exponential distribution with a mean of 0.5 minute. Management has established the following guidelines for a satis- factory level...
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