# Queuing Analysis: Deliveries clogging the loading dock area

See attached Excel file.

Deliveries clogging the loading dock area

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 unload (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 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 a report. At this point in time, looking only for the problem to be quantified and the unload rate determined for the current situation (single server) and possible two servers.

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 the report.

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#### Solution Preview

Please see the attached files for the complete tutorial.

Queuing Analysis

Deliveries clogging the loading dock area

To be able to compute for the expected number of trucks in the system, we need the following variables:

1. Arrival rate of trucks - in several of the queuing analyses, this rate is estimated to be at

2. Service rate - in one of the questions, this is the variable we need to solve for.

3. Number of servers - in some of the questions, we were instructed to assign 1 server while in others, two.

The variables below are assumed, hence if you wish to use ...

#### Solution Summary

The deliveries clogging the loading dock area are examined for queuing analysis are examined.