To simulate a Queuing system, select Simulate Queue from the OR_MM menu. The following dialog box is presented.

The arrival and service distribution entries provide the names of random variables that have been 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, random number seeds for the arrival and service processes, the number of arrivals to be simulated, the start time for data collection and and the stop time for data collection.

There are two types of simulation, Entity and Next Event. We illustrate the entity simulation first. A checkbox allows the student to use Exponential distributions instead of named distributions. When this box is checked the Arrival and Service distribution cells accept the arrival and service rates.

Entity Simulation

There are two ways to run the simulation, dynamic or not dynamic. The choice is determined by Dynamic button on the 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 students with immediate feedback on the effect of queuing 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.

Pressing the OK button causes the simulation to be performed and the results to be placed on the worksheet. The data and results for the example are given below.

The entity simulation is accomplished using functions made available by the add-in. The average results of the simulation are in column E for the example. The simulated values of TBA and TFS are in columns I and J. We only show 25 of the 50 simulated entities. Columns M through P show the important times determined by the simulation, with one row for each arrival. The results give when the entity arrived, entered the queue, entered service and left service. For the finite queue, an entity may arrive, but not enter the queue. The Entity simulation provides one row for each simulated individual. Many Excel columns are hidden for this display. The columns are all colored yellow to indicate that they contain formulas. The items not colored yellow in column D, may be changed and the simulation will automatically recompute. For a non-dynamic simulation, numbers replace the formulas and the cells are not colored yellow.

The Start and Stop Data times are initially set to 0 and the time of the last arrival respectively. These may be changed to allow warm up and cool down periods for the simulation.

Next Event Simulation