gpss_manual

∙GROUP SIZE. The number of Transactions which are members of the group at the end of the simulation.

∙RETRY. The number of Transactions waiting for a specific condition depending on the state of this

Transaction Group entity.

Numeric Groups

NUMERIC GROUP GROUP SIZE RETRY

NUMGRP 2 0

∙NUMERIC GROUP. Name or number of the

Numeric Group entity.

∙GROUP SIZE. The number of numeric values which are members of the group at the end of the simulation.

∙RETRY. The number of Transactions waiting for a specific condition depending on the state of this Numeric Group entity.

Logicswitches

LOGICSWITCH VALUE RETRY

SWITCH_1 1 0

· LOGICSWITCH. Name or number of the

Logicswitch entity.

∙VALUE. The value of the Logicswitch entity at the end of the simulation. 1 denotes "set" or

"true", 0 denotes "reset" or "false".

∙RETRY. The number of Transactions waiting for a specific condition depending on the state of this Logicswitch entity.

Savevalues

SAVEVALUE RETRY VALUE

ADDUP 0 60.000

COLLECT 0 -50.000

∙SAVEVALUE. Name or number of the

Savevalue entity.

∙VALUE. The value of the Savevalue entity at the end of the simulation.

∙ RETRY. The number of Transactions waiting for a specific condition depending on the state of this Savevalue entity.

Matrix Entities

MATRIX RETRY INDICES NUMERIC VALUE MATRIX1 0

Intermediate Values are Zero. (2,2) 6.413

Intermediate Values are Zero.

∙MATRIX. Name or number of the Matrix entity.

∙RETRY. The number of Transactions waiting for a specific condition depending on the state of this Matrix entity.

∙INDICES. Up to 6 integers that specify the element of the Matrix.

∙NUMERIC VALUE. The value of this Matrix entity element at the end of the simulation. Elements with 0 values are reported in groups.

The Current Events Chain

CEC XN PRI M1 ASSEM CURRENT NEXT PARAMETER VALUE 61 0 5187.692 61 1 2

∙XN. Transaction number of each Transaction on the Current Events Chain

∙PRI. Scheduling priority of the Transaction.

∙M1. Mark time. The time the Transaction, or its earliest ancestor, was GENERATEd, or the time the Transaction entered a MARK Block with no operands.

∙ASSEM. The Assembly Set number of the Transaction.

∙CURRENT. The number of the Block where the

Transaction existed at the end of the simulation or at the time of this report.

∙NEXT. The number of the next Block scheduled to be entered by the Transaction.

∙PARAMETER. The names or numbers of parameters of the Transaction.

∙ VALUE. The value of the parameter.

The Future Events Chain

FEC XN PRI BDT ASSEM CURRENT NEXT PARAMETER VALUE 51 0 5389.554 51 15 16

PARAM_1 232.000

62 0 5523.253 62 0 1

∙XN. Transaction number of each Transaction on the Future Events Chain.

∙PRI. Scheduling priority of the Transaction.

∙BDT. Block departure time. The time of the absolute system clock when the Transaction is scheduled to leave the Future Events Chain.

∙ASSEM. The Assembly Set number of the

Transaction.

∙CURRENT. The number of the Block where the Transaction existed at the end of the simulation or at the time of this report.

∙NEXT. The number of the next Block scheduled to be entered by the Transaction.

∙PARAMETER. The names or numbers of parameters of the Transaction.

∙VALUE. The value of the parameter.

Chapter 12 - GPSS

World Statistics

12.1. Collecting Statistics

GPSS World has a versatile statistics collection capability. For uncomplicated simulations, the statistics in the Standard Report and the ANOVA Library Procedure will meet the needs of most users. GPSS World will collect and report the simulation statistics automatically. This is discussed in Chapter 11.

If you need more detailed statistics, the use of variable entities and PLUS Procedures provides excellent control in the collection of statistics. In these definitions, the power of the mathematical library functions is at your disposal. You then define statistics tables in one or more TABLE or QTABLE Statements. The actual recording of data is triggered by one or more TABULATE Blocks in the simulation. Each time a TABULATE is entered, a datum is registered in the table. Alternately, you could record values in Savevalue or Matrix

Entities just prior to the completion of the simulation. Tables, Qtables, Savevalues, and Matrices are all reported automatically in the Standard Report, if you have checked them in the Report Page of the Model Settings Notebook.

QTABLE Commands provide an easier way to collect statistics based on Queue Entities. In this case, the tabulations are triggered by entry into DEPART Blocks instead of TABULATE

Blocks.

You can accumulate simulation results in a Result File by using the Data Stream Blocks, as discussed in Chapter 4. This will accumulate simulation results in an historical data base which can be used with the ANOVA Window to calculate confidence intervals and to perform an automatic Analysis of Variance.

ANOVA

If you are new to simulation, you will notice that when you repeat a simulation in the same session you may get different results due to randomness. Such effects must be carefully distinguished from the real effects caused by new designs in your simulated systems. The ANOVA Library Procedure provides you with a simple and yet powerful technique for establishing that your results do or do not emerge above the noise level caused by randomness.

In order to measure the amount of random noise, you must repeat your simulations changing nothing except the random number seeds. These repeat runs are called replications and

are important for measuring the statistical noise, i.e. the Standard Error, in your experiment. In the simplest scheme, each different design you choose to simulate would be replicated several times. Then the ANOVA Library Procedure will use the data to detect if the effects of changing the factors of your experiment were significantly greater than the statistical noise level. The results of this analysis will appear automatically in the Simulation Object's Journal Window.

The ANOVA Procedure provides for push button data analysis. It calculates Confidence Intervals and an Analysis of Variance of simulation results. Normally, during an experiment, you fill a special global Matrix Entity called a Result Matrix with the results of the simulations and then pass it as an argument to the ANOVA Procedure.

A Result Matrix is built according to a few simple rules. :

1.The Matrix Entity must be in Global Scope, i.e. cannot be a TEMPORARY MATRIX.

2.The Matrix must have between 1 and 5 dimensions, inclusively, for the factors of the experiment with exactly one additional dimension (the last) for replicates.

3.When the Matrix is defined, each dimension must declare the maximum number of treatment levels for each factor, with the last dimension declaring the maximum number of replicates within each level.

Therefore a Result Matrix can have up to 6 dimensions, supporting a maximum of a 5 factor multiway experiment. (GPSS World Version 4.0 supports only one way ANOVA)

It is up to you to keep track which matrix index values are to be used for each level of each factor when you record a result into the matrix. For example, suppose we wanted to build a Result Matrix for an experiment which examined the effect of the number of bank tellers on customer waiting time. Since Matrix indices are 1-relative we could simply use the number of tellers. In that case we would place 3 replicates of simulating two tellers into the following Matrix elements:

ResultMatrix[2,1], ResultMatrix[2,2], and ResultMatrix[2,3]

Usually though, it won't be so easy, and we will have to associate factor levels with distinct index values. If the factor levels to be used were 12 tellers and 16 tellers, we could associate the 12 teller level with the index value of 1, and the 16 teller level with the index of 2. This is arbitrary. The above three Matrix Elements would then take the replicates simulating the effects of 16 tellers. Qualitative factors such as brand name would always need to be encoded in a similar way.

Another point concerns the type of numerical result expected by ANOVA. In general, it is best to use calculated averages from the simulation as result metrics. The reason for this is that an average of

about 20 or more individual values tends to be Normally distributed according to the Central Limit Theorem of Statistics. Drastic departures from normality in the chosen result metrics should be avoided because they violate the assumptions of the Analysis of Variance and the calculations of Confidence Intervals.

An example of a PLUS Experiment and ANOVA can be found in the OneWay.gps sample Model, which is discussed in detail in Lesson 19 of the GPSS World Tutorial Manual.

We now turn to a sample report generated by passing a completed Result Matrix to the ANOVA Procedure. Then, the ANOVA table is automatically printed in the Simulation's Journal Window. If sufficient data has been read, descriptive statistics for each treatment level, including a 95% confidence interval is calculated. Also, if there is sufficient data, an ANOVA table is built. These calculations are displayed at the bottom of the ANOVA Window.

∙If there are fewer than 2 treatment levels, only the descriptive statistics, and not the ANOVA table, will be written.

∙There must be at least 2 replications in each treatment level. Otherwise only the descriptive statistics, and not the ANOVA table, will be written.

Here is an example of the use of the ANOVA Procedure.

_____________________________________________________________________________

ANOVA

_____________________________________________________________________________

_____________________________________________________________________________

_____________________________________________________________________________

___________________________________________________________________________

Figure 12—1. ANOVA Results.

The ANOVA results in the Journal Window displays descriptive statistics under the ANOVA table. These values are calculated for each treatment level, and include:

∙Treatment - Numeric treatment level.

∙Count - Number of result values in the treatment level.

∙Mean - The mean of result values in the treatment level.

∙Std. Dev. - The standard deviation of the results in the treatment level.

∙Minimum - The least value of results in the treatment level.

∙Maximum - the greatest value of results in the treatment level.

∙95% Conf. - An approximate half-range for a 95% confidence interval for the mean of the treatment level. For example, the

95% confidence interval for the mean result in treatment 2, above, would be (190.13 - 12.75, 190.13 + 12.75) or (177.38, 202.88).

In the ANOVA table, we first determine the degrees of Freedom of the Error and Treatments to be 4 and 1, respectively. Then we take the critical F value from row 4, column 1, in the following table. The critical value of F, at the 95% level, is 7.71.

Table 12—3. Critical values of F, at 95% Level

Since our calculated F value of 1329.059 is larger than 7.71, we conclude that the difference between treatments is significant.

If your results are not significant, you should consider increasing the length of the simulation runs, or increasing the number of replications of each treatment level, changing only the random number seeds. This often reduces the noise level sufficiently to expose real treatment effects, but may be futile if no real effect exists. You should consider variance reduction techniques to improve your results. On the other hand, if the treatments are indistinguishable, any detectable difference will be due only to a statistical "beta" error which will appear about

5% of the time.

One final tip. If you wish to exclude the effects of starting conditions from your final simulation, you should use the

RESET Command to begin the measurement period after transient effects have disappeared. The RESET Command is discussed in Chapter 6. Plot Windows are useful for observing the convergence of a simulation to steady state conditions.

12.2. Space-Time Products

A space-time product is a time duration multiplied by a count.

Space-time products are used in the calculation of several kinds of useful statistics. For example, to calculate the wages due to a labor force you could use the number of people who worked each given number of hours. To calculate the total hours worked, you could multiply the hours times the number of people to form a space-time product for each number of hours worked. You could then add up all the space time products in order to calculate the total person-hours. Similarly, many statistics reported in the Standard Reports are accumulations of space-time products.

Facility, Queue, Storage, and Userchain entities have SNAs which require space-time products in their evaluation. For example, the average storage in use is a time weighted average which gives more weight to those numbers which have the longest durations. The accumulated space-time product is divided by the simulated time duration in order to calculate the average storage in use.

Facility, Queue and Userchain entities also have space-time products. They are used to calculate average content via a corresponding SNA. The Facility space-time product is the accumulation of total busy time. The other space-time products are equal to the area under the graph of Queue content or

Userchain content.

The RESET command may be used to begin a new measurement period. A RESET command sets the space-time product to zero and the total count equal to the current count. This allows new space-time products to be accumulated. In the SNAs based on space-time product calculations, this method of initialization may introduce a small bias on the low side.

The following table shows the SNAs calculated from space-time

products.

Table 12—5. Space-Time System Numeric Attributes