Queuing Questions
EBBD EMAIL – for Internal Use Only
To: You
From: Danny Wilco <dwilco@ebbd.com>
Subject: Re: Deliveries clogging the loading dock area
OK, here’s what I want to know: how often do we have more than 5 trucks, more than 6 trucks, and more than 7 trucks. What is the highest number of trucks we may have in the system with a 95% probability? And then, assuming the arrival rate of the deliveries does not change, what does the unload rate need to be so that we can service up to five trucks 95% of the time? In other words if we want a 95% probability of 5 or fewer trucks in the system at any one time, what does the unloading (service) rate need to be? Then, consider that we have two unloading teams, each able to unload trucks at the same rate. What does the unloading rate need to be for each team in order to ensure (100%) 5 or fewer trucks in the system at any time? I know we don’t have room for two unloading teams at this time, but there is a possibility we might make room in the future.
Analyze this situation and determine what we need to know and give me report. At this point in time, I am looking only for the problem to be quantified and the unload rate determined for the current situation (single server) and possible two servers.
Let me know if you have any questions.
~DW, VP LogOps.
If you have mastered the examples and exercises provided in the Background from the Queuing PowerPoint, you are ready to tackle the EBBD problem.
The current situation is a Single Server situation. Enter the arrival rate and service rate to calculate the pertinent queuing system state data. Find out the probabilities of 5 or more trucks in the system, then 6, then 7. Then use trial and error to find the greatest number of trucks or less that can be in the system with 95% (or as close to 95%).
For the Multi-server problem you will need to use a similar process.
Record the results of your calculations and save the Excel file.
Then write your report.
Queuing systems are “stochastic”, which means based on random variables. The arrival rate of the customers is random but is theorized to follow a specific probability function. The key to analyzing queues is using the theory and equations that allow you to determine the probabilities
This website provides a good general overview of Queuing and waiting lines in business.
Queuing Theory. (n.d.). Encyclopedia of Business, 2nd Ed.; Reference for Business, retrieved from: http://www.referenceforbusiness.com/encyclopedia/Pro-Res/Queuing-Theory.html
Download this PowerPoint file [Waiting Lines Queues] which provides lecture notes on queuing and queuing equations. It also has Exercises for you work on.
****WATCH THESE TWO VIDEOS THAT EXPLAINS THE POWERPOINT – IN YOUTUBE:
PART 1: http://youtu.be/xxlixF0deqE
PART 2: http://youtu.be/NQdt2ldymaM
Download the Excel file [Excel QueueCalc]. There are two Tabs – the first is for Single Server models, and the second is for Multi-Server models. You enter the relevant information of a queuing problem and it will calculate the pertinent results. The values shown in this worksheet when you open it are the Phlebotomy Examples in the PowerPoint.
You can use the QueueCalc spreadsheet to try all of the examples and exercises in the PowerPoint.
Once you have mastered the examples and exercises you should be ready to tackle the EBBD problem. You can use the QueueCalc for the EBBD problem in the Case.
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