QueueBANSim is a MATLAB-based simulator for GI/G/1 queuing systems incorporating Bounded Algorithmic Numbers (BANs), in accordance with Alpha Theory (see https://doi.org/10.1016/S0723-0869(03)80038-5 for further mathematical details). The software allows the simulation of GI/G/1 queuing processes based on five different scheduling policies, which can be chosen according to the specific use case (see below). The simulator enables numerical evaluation of performance in terms of average delay, even in the case of infinite service/arrival moments (condition of heavy-tailed traffic). This simulation approach ensures stability and rapid convergence while seamlessly handling both distributions with finite moments and those with infinite moments.
The full reference paper is available here: https://doi.org/10.1016/j.comnet.2025.111394
- Bounded Algorithmic Numbers (BANs): The simulator allows setting the interarrival and service time distributions parameters using BANs to simulate heavy-tailed traffic with infinite (non-diverging) moments (well-defined within the Alpha Theory). In the provided example, Euclidean LogNormal and Weibull distirbutions are employed for modelling interarrival and service times, respectively. See Customizing BAN Parameters for further details.
- Customizable Queue Policies: Users can choose from five distinct queuing policies for simulation:
- FIFO (First In, First Out) - File:
gg1simulation_GPDFIFO.m - LIFO (Last In, First Out) - File:
gg1simulation_GPDLIFO.m - SIRO (Service In Random Order) - File:
gg1simulation_GPDSIRO.m - SJF (Shortest Job First) - File:
gg1simulation_GPDSJF.m - SRPT (Shortest Remaining Processing Time) - File:
gg1simulation_GPDSRPT.m
- FIFO (First In, First Out) - File:
- Delay performance evaluation: The simulator provides the following outputs:
- Average queueing delay,
- Corresponding theoretical bounds and approximations,
- Average number of customers in the system.
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Clone this repository:
git clone https://github.com/francesco-fiorini/QueueBANSim.git
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Open MATLAB and navigate to the repository folder.
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Open the
SimulatorScript.mfile. -
Customize the distribution parameters for interarrival and service times as Bounded Algorithmic Numbers to simulate heavy-tailed traffic.
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Select the proper "gg1simulator" method corresponding to the desired queuing policy:
- For FIFO:
gg1simulation_GPDFIFO.m - For LIFO:
gg1simulation_GPDLIFO.m - For SIRO:
gg1simulation_GPDSIRO.m - For SJF:
gg1simulation_GPDSJF.m - For SRPT:
gg1simulation_GPDSRPT.m
- For FIFO:
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Run the main script.
Make sure MATLAB is installed on your system. To run the simulation, you should have installed BAN and BANARRAY classes in the current repository. Feel free to contact francesco.fiorini@phd.unipi.it for further details on the latter aspect.
The general interarrival and service time distributions can be customized using Bounded Algorithmic Numbers (BANs) to reflect heavy-tailed characteristics with infinite variance. Ensure you configure these parameters in the script according to your traffic model needs. The example provided refers to the case of Euclidean LogNormal and Weibull distributions for modelling interarrival and service times, respectively. For different Euclidean distributions applications, please see Contributing.
If you use this repository, please cite:
@article{fiorini2025_gig1_alpha_theory, title = {Quantitative delay analysis of GI/G/1 queues with heavy-tailed traffic by means of Alpha Theory}, author = {Fiorini, Francesco and Cococcioni, Marco and Pagano, Michele}, journal = {Computer Networks}, volume = {269}, pages = {111394}, year = {2025}, issn = {1389-1286}, doi = {10.1016/j.comnet.2025.111394} }
Paper: https://doi.org/10.1016/j.comnet.2025.111394
Contributions are welcome! Please contact francesco.fiorini@phd.unipi.it for suggested changes or questions.
This project is licensed under the MIT License - see the LICENSE file for details.