Operations Research Models and Methods / Computation

Queueing Add-in


Queue Simulation

 

This program simulates a queueing station with arbitrary distributions for interarrival and service times. Note that both the Random Variables and Queueing add-ins must be installed to run the simulation. Selecting this item from the OR_MM menu brings the following dialog box.

The arrival and service distribution entries provide the names of random variables that have previously defined using the Add_RV item of the Random Variables add-in. For the example, the interarrival times have a generalized Beta distribution ranging from 0 to 0.4. The service process is Poisson with lambda= 2 (or mean time to service of 0.5). Other simulation parameters are: the cell location of the upper left corner where the data and averages of the simulation will be placed, the number of channels, the maximum number in system if the queue is finite, the cell location of the upper left hand corner of the simulated observations, random number seeds for the arrival and service processes, the number of arrivals to be simulated and the initial number in the system. Pressing the OK button causes the simulation to be performed and results formulas to be placed on the worksheet. The data and results for the example are given below.
 

The actual simulation is accomplished using functions made available by the add-in and is shown below. The advantages of this display over those of a dedicated simulation language is the presentation of the important times for each simulated individual. This helps the student to understand the processes related to the next-event simulation of the queue.
 

There are two ways to run the simulation, dynamic or not dynamic. The choice is determined by the button on the simulation dialog. A dynamic simulation places the formulas for the simulation directly on the worksheet. Changing the parameters of the simulation such as number of servers, arrival rate, or random number seeds causes the simulation to be automatically recalculated. This provides the students with immediate feedback on the effect of queueing system design changes. Although the number of iterations of the simulation is not limited by the program, the dynamic simulation requires a large amount of memory. This may crash the system if too large a simulation is attempted. Fifty iterations is the default value.

When the dynamic option is not selected, the formulas are replaced by the values they produce at each iteration. Although the results are not dynamic, the number of iterations possible is much greater.

 

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Operations Research Models and Methods
by Paul A. Jensen and Jon Bard, University of Texas, Copyright by the Authors