gpss_manual

Figure 8—16. The Negative Binomial Distribution

Notes

The Negative Binomial Distribution degenerates to the Geometric when the SuccessCount argument is 1. That is, NegBinom( Stream, 1, Probability ) is distributed as Geometric( Stream, Probability ).

17. Normal

Syntax

Real = NORMAL( Stream, Mean,

StdDev )

Arguments

Stream - The random number generator entity number. Required. Coerced to integer. Must be greater than or equal to 1. The argument must be Expression.

Mean - The mean value of the distribution. Required. Coerced to real. The argument must be Expression.

StdDev - The standard deviation of the distribution. Must be strictly positive. Required. Coerced to real. The argument must be Expression.

Return Value

Real - The real value generated as a single instance of the probability distribution.

Probability Density Function

Figure 8—17. The Normal Distribution

18. Pareto

Syntax

Real = PARETO( Stream, Locate,

Scale )

Arguments

Stream - The random number generator entity number. Required. Coerced to integer. Must be greater than or equal to 1. The argument must be Expression.

Locate - The shift value used to position the distribution. Must be strictly positive. Required. Coerced to real. The argument must be Expression.

Scale - The compression value used to expand or contract the distribution. Must be strictly positive. Required. Coerced to real. The argument must be Expression.

Return Value

Real - The real value generated as a single instance of the probability distribution.

Probability Density Function

Figure 8—18. The Pareto Distribution

19. Pearson Type V

Syntax

Real = PEARSON5( Stream, Locate, Scale, Shape )

Arguments

Stream - The random number generator entity number. Required. Coerced to integer. Must be greater than or equal to 1. The argument must be Expression.

Locate - The shift value used to position the distribution. Required. Coerced to real. The argument must be Expression.

Scale - The compression value used to expand or contract the distribution. Must be strictly positive. Required. Coerced to real. The argument must be Expression.

Shape - The selection value used to choose from a family of shapes. Required. Coerced to real. Must be strictly positive. The argument must be Expression.

Return Value

Real - The real value generated as a single instance of the probability distribution.

Probability Density Function

Figure 8—19. The Pearson Type V Distribution

20. Pearson Type VI

Syntax

Real = PEARSON6( Stream, Locate, Scale, Shape1, Shape2 ) Arguments

Stream - The random number generator entity number. Required. Coerced to integer. Must be greater than or equal to 1. The argument must be Expression.

Locate - The shift value used to position the distribution. Required. Coerced to real. The argument must be Expression.

Scale - The compression value used to expand or contract the distribution. Must be strictly positive. Required. Coerced to real. The argument must be Expression.

Shape1 - The first selection value used to choose from a family of shapes. Required. Coerced to real. Must be strictly positive. The argument must be Expression.

Shape2 - The second selection value used to choose from a family of shapes. Required. Coerced to real. Must be strictly positive. The argument must be Expression.

Return Value

Real - The real value generated as a single instance of the probability distribution.

Probability Density Function

Figure 8—20. The Pearson Type VI Distribution

21. Poisson

Syntax

Integer = POISSON( Stream, Mean )

Arguments

Stream - The random number generator entity number. Required. Coerced to integer. Must be greater than or equal to 1. The argument must be Expression.

Mean - The mean number of events to occur. Required. Must be strictly positive. Coerced to real. The argument must be Expression.

Return Value

Integer - The integer value generated as a single instance of the probability distribution.

Probability Mass Function

Figure 8—21. The Poisson Distribution

22. Triangular

Syntax

Real = TRIANGULAR( Stream, Min, Max, Mode )

Arguments

Stream - The random number generator entity number. Required. Coerced to integer. Must be greater than or equal to 1. The argument must be Expression.

Locate - The shift value used to position the distribution. Required. Coerced to real. The argument must be Expression.

Min - The smallest value to be drawn from the distribution. Must be less than mode. Required. Coerced to real. The argument must be Expression.

Max - The largest value to be drawn from the distribution. Must be greater than mode. Required. Coerced to real. The argument must be Expression.

Mode - The most frequent value of the distribution. Must be greater than min and less than max. Required. Coerced to real. The argument must be Expression.

Return Value

Real - The real value generated as a single instance of the probability distribution.

Probability Density Function

Figure 8—22. The Triangular Distribution

Notes

"Right" triangular distributions can be generated as Beta distributions.

23. Uniform

Syntax

Real = UNIFORM( Stream, Min, Max )

Arguments

Stream - The random number generator entity number. Required. Coerced to integer. Must be greater than or equal to 1. The argument must be Expression.

Min - The smallest value to be drawn from the distribution. Must be less than max. Required. Coerced to real. The argument must be Expression.

Max - The largest value to be drawn from the distribution. Must be greater than min. Required. Coerced to real. The argument must be Expression.

Return Value

Real - The real value generated as a single instance of the probability distribution.

Probability Density Function

Figure 8—23. The Uniform Distribution

Notes

The Beta Distribution degenerates to the Uniform when the shape arguments are 1. That is, Beta( Stream, Min, Max, 1, 1 ) is distributed as Uniform( Stream, Min, Max ).

24. Weibull

Syntax

Real = WEIBULL( Stream, Locate, Scale, Shape )

Arguments

Stream - The random number generator entity number. Required. Coerced to integer. Must be greater than or equal to 1. The argument must be Expression.

Locate - The shift value used to position the distribution. Required. Coerced to real. The argument must be Expression.

Scale - The compression value used to expand or contract the distribution. Must be strictly positive. Required. Coerced to real. The argument must be Expression.

Shape - The selection value used to choose from a family of shapes. Required. Coerced to real. Must be strictly positive. The argument must be Expression.

Return Value

Real - The real value generated as a single instance of the probability distribution.

Probability Density Function

Figure 8—24. The Weibull Distribution

Notes

The Weibull Distribution degenerates to the Exponential when the shape argument is 1. That is, Weibull( stream, Locate, Scale, 1 ) is distributed as Exponential( Stream, Locate, Scale ).

Weibull( Stream, Locate, Scale, 2 ) is known as the Rayleigh distribution.

Chapter 9 - Advanced

Topics

9.1. Transaction Chains

Transactions are temporarily bound to other entities by occupying linked lists called chains. Some entities, such as

Facilities, have several chains. Other entities have just a single

Retry Chain. Each Transaction may be on any number of chains. However, occupying one kind of chain sometimes precludes occupancy by the same Transaction on another. For example, a Transaction on one or more Interrupt Chains cannot be on the Future Events Chain.

A Transaction can be on no more than one of the following chains:

∙Future Events Chain

∙Current Events Chain

∙Facility or Storage Delay Chain

∙Facility Pending Chain

∙User Chain

A Transaction may be waiting for any number of conditions to occur, can be in any number of Transaction Groups, and may be preempted from any number of Facilities at any one time.

This means that any single Transaction can be on any number of Interrupt Chains and any number of Group Chains and any number of Retry Chains at the same time.

Current Events Chain

The Current Events Chain (CEC) is a linked list of ready

Transactions which have Blocks yet to be entered before simulated time advances. Although the CEC is kept in priority order, the Active Transaction is usually returned to the CEC ahead of its peers. For this reason, once a Transaction starts to move in the simulation, it tends to keep moving, unless a higher priority Transaction is reactivated.

When the Active Transaction comes to rest on some Transaction Chain, the highest priority Transaction remaining on the CEC becomes the Active Transaction. If the CEC is empty, the most imminent Transaction on the Future Events

Chain is moved to the CEC.