Exam 12: Queueing Models

Exhibit 12-3 A Credit Union has a small branch in which a single customer service representative serves the needs of customers who arrive at an average rate of 24 per hour. The service representative can typically handle 30 customers per hour. Based on an analysis of historical data, it is reasonable to assume that customer interarrival times and service times are exponentially distributed. Assume that all arriving customers enter the branch, regardless of the number already waiting in line. -Refer to Exhibit 12-3.What is the average length of time (in hours)spent waiting in line

Exhibit 12-2 An oil-change facility serves customers that enter at a rate of 8 per hour. There are five servers available to perform oil changes for entering customers. Customers wait in a single line and enter the facility, in first-come-first-serve fashion, to the first of the five servers who is available. Each server can change the oil of one customer's car every 30 minutes on average. -Refer to Exhibit 12-2.How many of the servers are busy on average

The mean and standard deviation of an exponential distribution are both equal to the parameter λ.

Exhibit 12-3 A Credit Union has a small branch in which a single customer service representative serves the needs of customers who arrive at an average rate of 24 per hour. The service representative can typically handle 30 customers per hour. Based on an analysis of historical data, it is reasonable to assume that customer interarrival times and service times are exponentially distributed. Assume that all arriving customers enter the branch, regardless of the number already waiting in line. -Refer to Exhibit 12-3.What is the average length of the waiting line

Exhibit 12-4 Consider a fast-food restaurant where customers arrive at a Poisson rate of 100 per hour. Four equally capable servers work at the restaurant during a typical hour of operation. Each employee takes, on average, 2 minutes to serve a customer, and service times are exponentially distributed. Customers who arrive and find all 4 servers busy join a single queue and are then served in first-come-first-served fashion. -Refer to Exhibit 12-4.What percentage of customers do not wait in the queue

Congestion in a queuing system will be unaffected by changes in the variability of the interarrival time and service time distributions,as long as the distributions retain the same means.

Exhibit 12-1 A grocery store manager would like to use an analytical queueing model to study the lines of customers that form in front of the checkout stations in the store. During a period of time when business is steady, several store employees have gathered data on customer interarrival times, which are shown below. -[Part 1] Refer to Exhibit 12-1.Is it reasonable to assume exponentially distributed interarrival times for the grocery store customers If so,what is λ

Almost all queuing systems are alike in that customers enter a system,possibly wait in one or more queues,get served,and then depart.

In queuing systems with a finite number of customers allowed,there is no need to require that the traffic intensity be less than 1 to ensure stability.

In a process where interarrival times are exponentially distributed,the time since the last arrival is irrelevant.

As the traffic intensity approaches 1:

Exponentially distributed service times are often more realistic than exponentially distributed interarrival times.

Exhibit 12-1 A grocery store manager would like to use an analytical queueing model to study the lines of customers that form in front of the checkout stations in the store. During a period of time when business is steady, several store employees have gathered data on customer interarrival times, which are shown below. -[Part 2] Refer to Exhibit 12-1.Assuming an exponential distribution with the parameter λ you obtained in Part 1,what is the probability that a customer interarrival time will be less than 2 minutes

Which of the following is not one of the important issues defining types of arrivals in a queuing system

The exponential distribution is:

Exhibit 12-4 Consider a fast-food restaurant where customers arrive at a Poisson rate of 100 per hour. Four equally capable servers work at the restaurant during a typical hour of operation. Each employee takes, on average, 2 minutes to serve a customer, and service times are exponentially distributed. Customers who arrive and find all 4 servers busy join a single queue and are then served in first-come-first-served fashion. -Refer to Exhibit 12-4.Use the M/M/s template to find the expected number of busy servers,and the expected fraction of time each server is busy

A requirement for steady state analysis of a queuing system is that:

The parameter λ in an exponential distribution can be interpreted as a:

Exhibit 12-3 A Credit Union has a small branch in which a single customer service representative serves the needs of customers who arrive at an average rate of 24 per hour. The service representative can typically handle 30 customers per hour. Based on an analysis of historical data, it is reasonable to assume that customer interarrival times and service times are exponentially distributed. Assume that all arriving customers enter the branch, regardless of the number already waiting in line. -Refer to Exhibit 12-3.What percentage of all customers have to spend at least some small amount of time waiting in line

Traffic intensity is a very useful measure of: