Online Supplement to Nelson and Taaffe (2004)

"The Ph_t / Ph_t / ∞ queueing system: Part I - The single node" and
"The Ph_t / Ph_t / ∞ queueing system: Part II - The multiclass network"

Proofs

Maple Procedures

The software is distributed "as is," without warranties of any kind, either express or implied. Please report problems to nelsonb@northwestern.edu. or taaffe@vt.edu. The software is copyrighted by Barry L. Nelson and Michael R. Taaffe 1999, 2000, 2002, 2003, 2004. The authors grant permission for unlimited personal use of this software without fee. However, no derivative works based on the software may be prepared, including embedding any portion of it in another software product, without permission of the authors.

Software

Maple V

• Maple V Procedures for the single-queue case:
  • PhPhInfSymbolic: Procedure to produce a symbolic representation of the moment differential equations for the queue when initial conditions are empty and idle.

  • PhPhInfNumericEmpty: Procedure to evaluate the moment differential equations for the queue when the initial conditions are empty and idle.

  • PhPhInfNumericInit: Procedure to evaluate the moment differential equations for the queue with arbitrary initial conditions.

  • PhPhInfMoments Procedure to plot the mean and variance of the number in the queue when the initial conditions are empty and idle. This procedure calls PhPhInfNumericEmpty which must be loaded first.

  • PhPhInfSojourn: Procedure to compute the mean and variance of the sojourn time of a virtual customer arriving at an arbitrary time, and generate a plot of the sojourn time cdf. This procedure calls PhPhInfNumericInit which must be loaded first.

  • Example Maple Worksheet (in .mws format): This worksheet illustrates the use of each procedure (notice that you must replace the path in any read statement with the location of the procedures on your computer). If you do not have Maple V, you can view the worksheet in html format HERE.

• Maple V Procedures for the network case:
  • PhPhInfMCNNumeric evaluates the moment differential equations for the multiclass network when initial conditions are empty and idle. This routine calls support routines PhPhInfNetNumeric and PhPhInfNumericEmpty, which must be loaded first.

  • PhPhInfMCNSymbolic produces a symbolic representation of the moment differential equations for the multiclass network. This routine calls support routines PhPhInfNetSymbolic and PhPhInfSymbolic, which must be loaded first.

  • PhPhInfMCNMoments plots the mean and variance of the number in the network and at the individual nodes by entity class when the initial conditions are empty and idle. This procedure calls support routines PhPhInfNetMoments, PhPhInfNetNumeric, PhPhInfMoments, and PhPhInfNumericEmpty, which must be loaded first.

  • PhPhInfMCNSojourn computes the mean and variance of the sojourn time, by class, of a virtual entity arriving at an arbitrary time, and generates a plot of the sojourn time cdf. This procedure calls support routines PhPhInfNetSojourn, PhPhInfSojourn, and PhPhInfNumericInit, which must be loaded first.

  • Example Maple Worksheet (in .mws format): This worksheet illustrates the use of each procedure (notice that you must replace the path in any read statement with the location of the procedures on your computer). If you do not have Maple V, you can view the worksheet in html format HERE.

Maple 6/7/8

• Maple 6/7/8 Procedures for the single-queue case:
  • PhPhInfSymbolic: Procedure to produce a symbolic representation of the moment differential equations for the queue when initial conditions are empty and idle.

  • PhPhInfNumericEmpty: Procedure to evaluate the moment differential equations for the queue when the initial conditions are empty and idle.

  • PhPhInfNumericInit: Procedure to evaluate the moment differential equations for the queue with arbitrary initial conditions.

  • PhPhInfMoments Procedure to plot the mean and variance of the number in the queue when the initial conditions are empty and idle. This procedure calls PhPhInfNumericEmpty which must be loaded first.

  • PhPhInfSojourn: Procedure to compute the mean and variance of the sojourn time of a virtual customer arriving at an arbitrary time, and generate a plot of the sojourn time cdf. This procedure calls PhPhInfNumericInit which must be loaded first.

  • Example Maple Worksheet (in .mws format): This worksheet illustrates the use of each procedure (notice that you must replace the path in any read statement with the location of the procedures on your computer). If you do not have Maple 6/7/8, you can view the worksheet in html format HERE.

• Maple 6/7/8 Procedures for the network case:
  • PhPhInfMCNNumeric evaluates the moment differential equations for the multiclass network when initial conditions are empty and idle. This routine calls support routines PhPhInfNetNumeric and PhPhInfNumericEmpty, which must be loaded first.

  • PhPhInfMCNSymbolic produces a symbolic representation of the moment differential equations for the multiclass network. This routine calls support routines PhPhInfNetSymbolic and PhPhInfSymbolic, which must be loaded first.

  • PhPhInfMCNMoments plots the mean and variance of the number in the network and at the individual nodes by entity class when the initial conditions are empty and idle. This procedure calls support routines PhPhInfNetMoments, PhPhInfNetNumeric, PhPhInfMoments, and PhPhInfNumericEmpty, which must be loaded first.

  • PhPhInfMCNSojourn computes the mean and variance of the sojourn time, by class, of a virtual entity arriving at an arbitrary time, and generates a plot of the sojourn time cdf. This procedure calls support routines PhPhInfNetSojourn, PhPhInfSojourn, and PhPhInfNumericInit, which must be loaded first.

  • Example Maple Worksheet (in .mws format): This worksheet illustrates the use of each procedure (notice that you must replace the path in any read statement with the location of the procedures on your computer). If you do not have Maple 6/7/8, you can view the worksheet in html format HERE.