Exam 13: Queuing Theory

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?

A grocery store can serve an average of 360 customers per hour. The service times are exponentially distributed. The store has 4 checkout lines each of which serves 90 customers per hour. Customers arrive at the store at a Poisson rate of 240 customers per hour. The following queuing analysis spreadsheet was developed from this information. -Refer to Exhibit 13.4. Based on this report how long does a customer wait before the checker begins serving them?

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?

The memoryless property is also referred to as the ____ property.

What is the probability that it will take less than or equal to 0.25 hours to service any call based on the following exponential probability distribution with rate $\mu$ = 5?

The M/D/1 model results can be derived from which of the following systems?

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?

A company has recorded the following customer inter-arrival times and service times for 10 customers at one of its single teller service lines. Assume the data are exponentially distributed and the 10 data points represent a reasonable sample. -Refer to Exhibit 13.3. What is the mean arrival rate per hour?

A grocery store can serve an average of 360 customers per hour. The service times are exponentially distributed. The store has 4 checkout lines each of which serves 90 customers per hour. Customers arrive at the store at a Poisson rate of 240 customers per hour. The following queuing analysis spreadsheet was developed from this information. -Refer to Exhibit 13.4. What is the Kendall notation for this system?

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 service times for a grocery store with one checkout line have a mean of 3 minutes and a standard deviation of 20 seconds. Customer arrivals at the checkout stand follow a Poisson distribution. What type of system is it?

For a Poisson random variable, $\lambda$ represents the ____ number of arrivals per time period

A renege refers to

Customers arrive at a store randomly, following a Poisson distribution at an average rate of 90 per hour. How many customers arrive per minute, on average?

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?

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?

If the number of arrivals in a time period follow a Poisson distribution with mean $\lambda$ then the inter-arrival times follow a(n) ____ distribution with mean ____.

A company has recorded the following customer inter-arrival times and service times for 10 customers at one of its single teller service lines. Assume the data are exponentially distributed and the 10 data points represent a reasonable sample. -Refer to Exhibit 13.3. What is the average time a customer spends in the service line?

Which of the following is the typical operating characteristic for the probability an arriving unit has to wait for service?

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. What is the Kendall notation for this system?