Exam 13: Queuing Theory

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?

If the number of arrivals in a time period follow a Poisson distribution with mean λ then the inter-arrival times follow an)distribution with mean .

Exhibit 13. The following questions refer to the information and output below. 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 what is the average total time spent in line and being checked out?

To find steady-state values for the M/M/S queuing system,which of the following statements must be true about the arrival rate?

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.How many customers will be in the store on average at any one time?

A company has recorded the following list of service rates customers/hour)for one of its servers.What is the mean service time for this server? Customers / hour 2 3 3 4 2 3 3 3 4 2 4 3 2 4

One reason to use queuing models in business is

Customers arrive at a store randomly,following a Poisson distribution at an average rate of 20 per hour.What is the probability of exactly 0,1 2,and 3 arrivals in a 15 minute period?

If cell B2 contains the value for ? and cell A5 contains the value for T,what formula should go in cell B5 to compute the PService time)? T for this exponential distribution?

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 average amount of time spent waiting in line?

The customer service desk at Joe's Discount Electronics store receives 5 customers per hour on average.On average,each customer requires 10 minutes for service.The customer service desk is staffed by a single person.What is the average number of customers in the customer service area,if modeled as an M/M/1 queuing system?

The M/D/1 model with infinite capacity queue can be used to model

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?

In the Kendall notation M/D/4,D stands for

What is the formula for Pt ≤ T)under the exponential distribution with rate μ?

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?

The M/M/s model with finite capacity queue can be used to model

Exhibit 13. 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. The following questions refer to the information and output below. 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 what is the average number of customers waiting for a checker?

A jockey refers to