Exam 13: Queuing Theory

Exhibit 13.7 The following questions refer to the information and output below. A tax accountant has found that the time to serve a customer has a mean of 30 minutes (or 0.5 hours) and a standard deviation of 6 minutes (or 0.1 hours). Customer arrivals follow a Poisson distribution with an average of 60 minutes between arrivals. The following queuing analysis spreadsheet was developed from this information. -Refer to Exhibit 13.7. What is the Kendall notation for this system?

Exhibit 13.5 The following questions refer to the information and output below. A computer printer in a large administrative office has a printer buffer (memory to store printing jobs) capacity of 3 jobs. If the buffer is full when a user wants to print a file the user is told that the job cannot be printed and to try again later. There are so many users in this office that we can assume that there is an infinite calling population. Jobs arrive at the printer at a Poisson rate of 55 jobs per hour and take an average of 1 minute to print. Printing times are exponentially distributed. The following queuing analysis spreadsheet was developed from this information. -Refer to Exhibit 13.5. Based on this report what is the probability that a computer user will be told to resubmit a print job at a later time?

What is the formula for P(t  T) under the exponential distribution with rate ?

Exhibit 13.5 The following questions refer to the information and output below. A computer printer in a large administrative office has a printer buffer (memory to store printing jobs) capacity of 3 jobs. If the buffer is full when a user wants to print a file the user is told that the job cannot be printed and to try again later. There are so many users in this office that we can assume that there is an infinite calling population. Jobs arrive at the printer at a Poisson rate of 55 jobs per hour and take an average of 1 minute to print. Printing times are exponentially distributed. The following queuing analysis spreadsheet was developed from this information. -Refer to Exhibit 13.5. Based on this report how long does a computer user have to wait for his/her job to be completed?

Exhibit 13.1 The following questions are based on the output below. A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system. -Refer to Exhibit 13.1. What is the probability that a customer can go directly into service without waiting in line?

Joe's Copy Center has 10 copiers. They break down at a rate of 0.02 copiers per hour and are sent to the service facility. What is the average arrival rate of broken copiers to the service facility?

Project 13.1  Internet Sales, Inc. Internet Sales, Inc. is establishing a new ordering system to handle its on-line sales. Customers arrive randomly at an average of one every minute. On average it takes 45 seconds to process a customer's order. The current system employs one network server to process orders. This server processes orders requests one at a time in the order received. The Internet Sales, Inc., Analysis Team has determined that customer orders arrive according to a Poisson process and the average time spent processing an order is exponentially distributed. Internet Sales' management knows that offering prompt, reliable on-line service is critical to their continued success. Upgrading the current on-line ordering capacity will establish their image as a "cutting edge" on-line sales company. On the other hand, too much unused capacity is inefficient and will ultimately cause company profits to decline. Recently, the management group established a goal of serving an on-line customer immediately, 90% of the time. This means that 90% of the time a customer does not have to wait to place an order on-line after using the Internet Sales, Inc. web page. A heated discussion ensued over the current system's capability of meeting this goal. Under the current system, a customer waits if the system is busy processing another order. Network server upgrades are available in increments of $5000. Each upgrade adds the capability to process an additional order in parallel. For example if two upgrades were purchased at a cost of $10,000, orders will be processed by three independent network servers each serving at an exponential rate of one order per 45 seconds. The Analysis Team was asked to consider the alternatives and recommend a course of action to the management group. What upgrade (if any) will meet the service goal set by the management group? What are the cost and performance trade-offs?

The number of arrivals to a store follows a Poisson distribution with mean  = 10/hour. What is the mean inter-arrival time?

A balk refers to

Exhibit 13.2 The following questions refer to the information and output below. A barber shop has one barber who can give 12 haircuts per hour. Customers arrive at a rate of 8 customers per hour. Customer inter-arrival times and service times are exponentially distributed. The following queuing analysis spreadsheet was developed from this information. -Refer to Exhibit 13.2. Based on this report what is the average number of customers waiting for a haircut?

A grocery clerk can serve 20 customers per hour on average and the service time follows an exponential distribution. What is the probability that a customer's service time is more than 4 minutes?

Which of the following is the typical operating characteristic for average time a unit spends waiting for service?

A doctor's office only has 8 chairs. The doctor's service times and customer inter-arrival times are exponentially distributed. What type of system is it?

Exhibit 13.1 The following questions are based on the output below. A store currently operates its service system with 1 operator. Arrivals follow a Poisson distribution and service times are exponentially distributed. The following spreadsheet has been developed for the system. -Refer to Exhibit 13.1. What is the probability that a customer must wait in queue before being served?

Exhibit 13.7 The following questions refer to the information and output below. A tax accountant has found that the time to serve a customer has a mean of 30 minutes (or 0.5 hours) and a standard deviation of 6 minutes (or 0.1 hours). Customer arrivals follow a Poisson distribution with an average of 60 minutes between arrivals. The following queuing analysis spreadsheet was developed from this information. -Refer to Exhibit 13.7. Based on this report how long does a customer spend at the tax accountant's office?

If a company adds an additional identical server to its M/M/1 system, making an M/M/2 system, what happens to a customer's average service time?

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?

The M in M/G/1 stands for

A grocery clerk can serve 20 customers per hour on average and the service time follows an exponential distribution. What is the expected service time per customer?