Mink Hollow Media

Democratizing Information Technology

7: Example: Single Server Queuing System

Chapter 7

Here’s were we will put color versions of the images, updates, and other extras.

This example is a classic first example in digital systems: namely that of a single server queueing system. Banks typically have a single queue where people line up and several tellers to serve them. This example demonstrates the organization and approach that will be used for the more complex examples later in the book.

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  1. Introduction
  2. System Analysis
    1. Needs Analysis
    2. Original System
    3. Observable Elements
    4. Obtainable Data
    5. Simulation Events
    6. Simulation Input Data
    7. Collectable Data
    8. Conceptual Model
  3. The Arrival Process
    1. Distributions
    2. Simulating Arrivals
  4. The Queue
  5. The Server
  6. The Simulation
    1. The Main Loop
    2. The Sequencing Set
    3. Arrivals
    4. The Queue
    5. Departures
  7. System Output
  8. Summary
    1. Concepts
    2. Terminology
  9. References, Notes & Further Resources

Images

*Please note: all images are copyrighted, permission to use an image must be obtained from Wiley (and possibly also the original sources).

Figure 7-1: A hot dog cart, an example of a single server queuing system.
Figure 7-2: A hot dog cart abstracted into a model before the simulation is created.
Figure 7-3: Histograms of interarrival times of customers at a hot dog vendor. (a) 1200 times measured and plotted shows the shape of what is called the distribution function.
Figure 7-3: Histograms of interarrival times of customers at a hot dog vendor. (b) Plotting 10000 interarrival times shows that the curve becomes smoother.
Figure 7-3: Histograms of interarrival times of customers at a hot dog vendor. (c) Plotting a million samples has the histogram approaching the shape of a smooth continuous function.
Figure 7-4: Calculating the area under the probability density function between two points. (a) The area between t0 and t1 is the probability of the interarrival time falling into that range.
Figure 7-4: Calculating the area under the probability density function between two points. (b) Using the average of the function value of D at the points t0 and t1 to make a rectangle, for which the area is easy to calculate.

 

Figure 7-5: Other probability distributions. (a) The well-known bell shaped curve of the nNormal distribution.
Figure 7-5: Other probability distributions. (b) The uUniform distribution, which is what the values from a basic random number generator produce.
Figure 7-6: Converting a uniformly distributed random number into an exponentially distributed one. A random number generator yields a uniformly distributed number (left). The area under the curve between 0 and X equals X in this case, and is the probability of a value less than X being generated. On the right, the exponential distribution has a different shape, but the exponentially distributed variable Y that corresponds to X should have the same area under the curve between 0 and Y. In this case X=0.35 and Y=0.12.
Figure 7-7: How a queue works in a simulation. Top to bottom: A new arrival means the creation of a new record; the record is placed at the end of the queue, and contains a link to the record in front of it; when a departure occurs it leaves from the front of the queue; the remaining records all move ahead in the queue.

 

Figure 7-8: Flowchart for Main Loop
Figure 7-9: Flowchart for Scheduling an Event
Figure 7-10: Flowchart for an Arrival
Figure 7-11: Flowchart for Starting the Server
Figure 7-12: Flowchart for a Departure