Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -The objective in queuing problems is to find the service level that achieves an acceptable balance between the cost of providing service and customer satisfaction.

The objective in queuing problems is indeed to balance the cost of providing service with the level of customer satisfaction, ensuring that service is efficient while keeping customers happy.

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -A situation where cars arrive at an intersection can be modeled as an M/D/s queue with finite capacity.

The information provided does not mention anything about cars arriving at an intersection, so it cannot be modeled as an M/D/s queue with finite capacity.

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -The amount of time a customer spends with the server is referred to as A) system time. B) queue time. C) service time. D) served time.

The amount of time a customer spends with the server is referred to as service time. It is the time taken for the server to serve the customer and can vary based on factors such as order size, complexity, and server efficiency.

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -One way to improve performance of a queuing system from the customer perspective is to reduce the number of servers.

The statement is not directly related to the information given in Exhibit 12.5 about simulating the growth of Sal's Italian Restaurant. While reducing the number of servers may have some impact on the queuing system, it is not stated in the exhibit and cannot be inferred without further information.

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -What is the service policy in the queuing systems presented in this chapter that is considered "fair" by the customers? A) FIFO B) LIFO C) FILO D) Priority

FIFO (First-In-First-Out) is considered "fair" by customers in queuing systems presented in this chapter. This means that customers who arrive first should be served first, reducing wait time and perceived unfairness.

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -If the number of arrivals in a given period of time follows a Poisson distribution with mean , the interarrival times follow an exponential probability distribution with mean 1/λ

This statement is true as per the properties of a Poisson process.

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -Which of the following best describes queuing theory? A) The study of arrival rates. B) The study of service times. C) The study of waiting lines. D) The evaluation of service time costs.

Queuing theory is the study of waiting lines which involves analyzing the behavior of customers waiting in line, the service process, and resource utilization.

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -If the arrival process is modeled as a Poisson random variable with arrival rate λ, then the average time between arrivals is A) 1/μ B) 1/λ C) 1/λ 2 D) σ

For a Poisson process, the interarrival times are exponentially distributed with mean 1/λ. Therefore, the average time between arrivals is also 1/λ.

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -The term queuing theory refers to the body of knowledge dealing with waiting lines.

Queuing theory is the study of waiting lines and the mathematical models used to analyze them. Therefore, the statement is true.

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -The M in M/G/1 stands for A) Markovian inter-arrival times. B) Mendelian inter-arrival times. C) Mean inter-arrival times. D) Mathematical inter-arrival times.

The M in M/G/1 stands for Markovian inter-arrival times, indicating that the time between arrivals follows an exponential distribution.

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -In a queuing problem, Wq > W.

Wq represents the average time a customer spends waiting in line, while W represents the total average time a customer spends in the system (which includes both waiting time in line, Wq, and service time). Therefore, W is always greater than or equal to Wq.

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -If the service rate decreases as the arrival rate remains constant, then, in general A) customer waiting time increases. B) customer waiting time decreases. C) service costs increase. D) customer dissatisfaction decreases.

If the service rate decreases while the arrival rate remains constant, the system will become more congested with more waiting customers, and therefore, the customer waiting time will increase.

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -Joe's Copy Center has 10 copiers. They break down and require service quite often. Time between breakdowns follows an exponential distribution for each copier. The repair person services machines as quickly as possible, but the service time follows an exponential distribution. What type of system is it? A) M/M/1 with Finite Population B) M/M/1 with Finite Queue C) M/M/1 D) M/M/10

This is an M/M/1 with Finite Population system because there is a finite number of copiers (10) that can break down and require service, and both the time between breakdowns and the service time follow exponential distributions.

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -What is the formula for P(t ≤ T) under the exponential distribution with rate μ? A) 1 − eμ T B) eμ T C) 1 − e−μ T D) 1 − e T

The formula for P(t ≤ T) under the exponential distribution with rate μ is 1 − e−μT. In the spreadsheet, the rate parameter μ is represented by the value of cell D2, which is 0.02. So, the formula for P(t ≤ T) is 1 − e−0.02T. This corresponds to choice C, 1 − e−μ T , with S1 = 1, U1 = 0.02, P1 = T, P0 = 0.

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -An arrival process is memoryless if the time until the next arrival occurs is inversely proportional to the time elapsed since the last arrival.

The statement describes the property of a Poisson process, not necessarily all memoryless arrival processes. A memoryless arrival process only requires that the probability distribution of the time until the next arrival does not depend on how much time has elapsed since the last arrival.

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -The number of arrivals that occurs in a given time period represents a random variable in a queuing system.

The number of customers arriving at Sal's Italian Restaurant is a random variable, which is a common feature of queuing systems.

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -A barber shop has one barber, a Poisson arrival rate and exponentially distributed service times. What is the Kendall notation for this system? A) M/M/E B) M/M/1 C) M/E/1 D) P/M/1

The Kendall notation for this system is M/M/1. "M" represents Poisson arrivals, "M" represents exponentially distributed service times, and "1" represents a single server or barber.

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -The memoryless property is also referred to as the ____ property. A) Markov B) Erlang C) Poisson D) Normal

The memoryless property is a characteristic of Markov processes, where the future state of the process only depends on the current state and not on any past events. It is not related to the other options listed (Erlang, Poisson, Normal).

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -A balk refers to A) a customer who refuses to join the queue. B) a customer who refuses service by a specific server. C) a customer who joins the queue but leaves before service is complete. D) a customer who requires extra service time.

A balk refers to a customer who decides not to join the queue at all, typically due to perceived long wait times or other deterrents.

Exhibit 12.5 The following questions use the information below. The owner of Sal's Italian Restaurant wants to study the growth of his business using simulation. He is interested in simulating the number of customers and the amount ordered by customers each month. He currently serves 1000 customers per month and feels this can vary uniformly between a decrease of as much as 5% and an increase of up to 9%. The bill for each customer is a normally distributed random variable with a mean of $20 and a standard deviation of $5. The average order has been increasing steadily over the years and the owner expects the mean order will increase by 2% per month. You have created the following spreadsheet to simulate the problem. -In the Kendall notation M/D/4, D stands for A) memoryless arrival distribution B) deterministic departure distribution C) memoryless arrival and departure distributions D) none of the above

In the Kendall notation M/D/4, "D" stands for "deterministic service time distribution," meaning that the time it takes to serve each customer is a constant. This notation does not directly refer to departure distribution, but the deterministic service time implies a predictable pattern of departures given a steady arrival rate.

Quiz 13: Queuing Theory

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