The mp_pfqn library offers fast C solvers for product-form queueing networks using the GNU Multiple Precision Arithmetic Library (GMP). Exact arithmetic in GMP allows to compute normalizing constants for the equilibrium state probabilities on large closed multiclass models.

• Current solvers:
  • Mean Value Analysis (MVA) [1]
  • Convolution Algorithm (CA) [2]
  • Recursion by Chain Algorithm (RECAL) [3]
  • Method of Moments (MoM) [4]
  • Class-Oriented Method of Moments (CoMoM) [5]

Run the following commands from the project root folder:

# Install all dependencies automatically (requires sudo)
sudo make install-deps

# Build the project
source ./setup-env.sh
make

# Run a solver
./bin/mva models/02_bottleneck_study.qn
./bin/ca models/02_bottleneck_study.qn
./bin/recal models/02_bottleneck_study.qn
./bin/mom models/02_bottleneck_study.qn
./bin/comom models/02_bottleneck_study.qn

If you wish to recompile after changes, run

make clean
make

Models are specified in .qn text files with the following format:

R                   # Number of job classes
N1 N2 ... NR        # Population per class
Z1 Z2 ... ZR        # Think times per class
M                   # Number of queueing stations
m1 L11 L12 ... L1R  # Queue 1: multiplicity, demands at station 1 per class
m2 L21 L22 ... L2R  # Queue 2: multiplicity, demands at station 2 per class
...
mM LM1 LM2 ... LMR  # Queue M: multiplicity, demands at station M per class

The demand Lir=Sir*Vir is the product of the mean service time Sir and mean number of visits Vir, both for class-r jobs at station i. See the routing2visits utility to convert a routing probability matrix into the corresponding Vir values.

IMPORTANT: All values must be passed as integers.

Examples are available under the models/ folders.

# Generate a random model
./bin/rndmodel M R N seed > model.qn
# Where: M = number of queues, R = number of classes, 
#        N = total population, seed = random seed

# Run different solvers
./bin/mva model.qn      # Mean Value Analysis
./bin/ca model.qn       # Convolution Algorithm
./bin/recal model.qn    # Recursion by Chain Algorithm
./bin/mom model.qn      # Method of Moments
./bin/comom model.qn    # Class-Oriented Method of Moments

All solvers support various command-line options to control their output format and behavior.

./bin/mva [options] models/02_bottleneck_study.qn

./bin/ca [options] models/02_bottleneck_study.qn

CA supports the same command-line options as MVA (see table above).

./bin/recal [options] models/02_bottleneck_study.qn

RECAL supports the same command-line options as MVA (see table above).

./bin/mom [options] models/02_bottleneck_study.qn

./bin/comom [options] models/02_bottleneck_study.qn

CoMoM supports the same command-line options as MoM (see table above). The Class-Oriented Method of Moments provides an efficient algorithm specifically designed for multiclass models with large population sizes.

# Get only throughputs
./bin/mom -t models/02_bottleneck_study.qn

# Get only queue lengths  
./bin/mom -q models/02_bottleneck_study.qn

# Get exact normalizing constant (numerator and denominator)
./bin/mom -e models/02_bottleneck_study.qn

# Get all performance metrics in exact rational form
./bin/mom -d models/02_bottleneck_study.qn
./bin/mva -d models/02_bottleneck_study.qn

# Apply perturbation for approximate solution (MoM/CoMoM)
./bin/mom -p 5 models/02_bottleneck_study.qn
./bin/comom -p 5 models/02_bottleneck_study.qn

# Apply perturbation with specific random seed (MoM/CoMoM)
./bin/mom -p 5 -s 12345 models/02_bottleneck_study.qn
./bin/comom -p 5 -s 12345 models/02_bottleneck_study.qn

Notes:

• The -d/--exact option is available in all solvers and prints performance metrics (throughputs, queue lengths, normalizing constants) in full exact precision as rational numbers (e.g., 1/3 instead of 0.333333). This is useful for verification and when exact values are required.
• The perturbation option (-p) is available in both the MoM and CoMoM solvers and is useful when the exact solution fails due to singular systems. It introduces small randomized numerical perturbations to enable approximate solutions. When perturbation is applied, model parameters are displayed as original integer values with separate perturbation annotations (e.g., 50 eps=1.0e-05). The -s option allows you to specify a random seed for reproducible perturbations.

[1]: Reiser & Lavenberg (1980), Mean-Value Analysis of Closed Multichain Queuing Networks, Journal of the ACM 27(2).

[2]: Reiser, M. and Kobayashi, H. (1974), Queuing Networks with Multiple Closed Chains: Theory and Computational Algorithms, IBM Research Report RC-4919, July, 1974.

[3]: Conway, A. E. and Georganas, N. D. (1986), RECAL—a new efficient algorithm for the exact analysis of multiple-chain closed queuing networks, J. ACM 33, 4 (Oct. 1986), 768–791.

[4]: Casale (2006), An efficient algorithm for the exact analysis of multiclass queueing networks with large population sizes, Proc. of ACM SIGMETRICS 2006.

[5]: Casale, G. (2009), CoMoM: Efficient Class-Oriented Evaluation of Multiclass Performance Models, IEEE Trans. Softw. Eng. 35, 2 (March 2009), 162–177.

This software is provided as-is for academic and research purposes and released as BSD-3.