A Compositional Approach to the Simulation of Queuing Systems with Random Parameters
Keywords:
compositional approach, integral kernel, simulation modeling, random parameter, parametric uncertainty, hyper-delta probability distribution, generalized function, phase-type distribution, uniformly exponential distribution, approximation, phase function, queueing systemsAbstract
A general approach to modeling random service processes under conditions of disturbances and uncertainty of the initial data is substantiated. A compositional approach to constructing simulation models of queuing with parametric uncertainty based on phase-type distributions and phase functions is proposed. The calculation and comparison of the characteristics of the developed simulation models with analytical solutions were carried out to confirm their effectiveness and accuracy. The problems of uncertainty of the initial data and their impact on the modeling of service systems are highlighted. The importance of taking into account parametric uncertainty in simulation models is emphasized in order to increase their adequacy and applicability in practice. The study includes a description of a general approach to modeling random service processes with uncertainty, as well as methodological foundations for the application of phase distributions and functions in compositional modeling. Four classes of service models are considered, differing in the type of integral core and phase function, which makes it possible to implement a variety of random service processes, taking into account their characteristics and conditions of their occurrence. The analysis of a model with an exponential integral core and various types of phase functions is carried out, which demonstrates the flexibility and wide possibilities of the proposed compositional approach to the study and modeling of service systems. The results of simulation modeling are presented, confirming analytical studies and showing the applicability and effectiveness of the developed approach in the construction and analysis of models of service systems with random parameters. The practical significance of the compositional method for the design and modernization of information and computing systems at various stages of their development, taking into account the uncertainty of the initial data, is noted. The work is focused on the development of simulation methods for queuing systems and opens up new prospects for their research and optimization in conditions of uncertainty of initial parameters.
References
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2. Dudina O., Dudin A. Optimization of queueing model with server heating and cooling. Mathematics. 2019. vol. 7. no. 9. DOI: org/10.3390/math7090768.
3. Klimenok V., Dudin A., Dudina O., Kochetkova I. Queuing system with two types of customers and dynamic change of a priority. Mathematics. 2020. vol. 8(5). DOI: org/10.3390/math8050824.
4. Khomonenko A. Performance analysis of the multiprocessor systems with priority processing of heterogeneous requests flow. Avtomatika i Vychislitel'naya Tekhnika. 1991. no. 4. pp. 55–64.
5. Krasnov S., Lokhvitskiy V., Khabarov R. [Numerical analysis of multi-channel queuing systems with absolute priority based on phase approximation of the period of continuous employment]. Trudy Voyenno-kosmicheskoy akademii imeni A.F. Mozhayskogo – Proceedings of the Military Space Academy named after A.F. Mozhaisky. 2022. no. 682. pp. 7–20. (In Russ.).
6. Nazarov A., Strik J., Kvach A. A survey of recent results in finite-source retrial queues with collisions. Information technologies and mathematical modelling. Queueing Theory and Applications: 17th International Conference and 12th Workshop on Retrial Queues and Related Topics. 2018. vol. 912. pp. 1–15. DOI: 10.1007/978-3-319-97595-5_1.
7. Gaitonde J., Tardos E. Stability and learning in strategic queuing systems. Proceedings of the 21st ACM Conference on Economics and Computation. 2020. pp. 319–347.
8. Zayats O., Korenevskaya M., Ilyashenko A., Muliukha V. Prioritized Retrial Queueing Systems with Randomized Push-Out Mechanism. Informatics and Automation. 2024. vol. 23. no. 2. pp. 325–351. (In Russ.).
9. Buslenko N.P. Modelirovanie slozhnyh sistem [Modeling of complex systems]. М.: Nauka, 1978. 400 p. (In Russ.).
10. Ivnitskiy V. [On evaluating the accuracy of the simulation results of complex systems with inaccurate input information in the independent test scheme]. Izvestiya AN SSSR. Tekhnicheskaya kibernetika – Izvestia of the USSR Academy of Sciences. Technical cybernetics. 1974. no. 4. pp. 208–217. (In Russ.).
11. Law A. Simulation Modeling and Analysis, 6th Edition. McGraw Hill. 2024. 688 p.
12. Goncharenko V. [The formal apparatus of representation of stochastic processes of service with the disturbance and uncertainty parameters]. Trudy VKA imeni A.F. Mozhajskogo – Proceedings of Military Space Academy named A.F. Mozhaysky. 2015. vol. 648. pp. 13–18. (In Russ.).
13. Corlu C., Akcay A., Xie W. Stochastic simulation under input uncertainty: A review. Operations Research Perspectives. 2020. vol. 7. DOI: 10.1016/j.orp.2020.100162.
14. Shone R., Glazebrook K., Zografos K. Applications of stochastic modeling in air traffic management: Methods, challenges and opportunities for solving air traffic problems under uncertainty. European Journal of Operational Research. 2021. vol. 292. no. 1. pp. 1–26.
15. Xie W., Li С., Wu Y., Zhang P. A nonparametric Bayesian framework for uncertainty quantification in stochastic simulation. SIAM/ASA Journal on Uncertainty Quantification. 2021. vol. 9. no. 4. pp. 1527–1552.
16. Goncharenko V. [Models and methods of queueing systems analysis with parametric uncertainty]. Intellektual'nye tekhnologii na transporte – Intellectual Technologies on Transport. 2017. no. 4. pp. 5–11. (In Russ.).
17. Goncharenko V. [Modelling and estimation of characteristics of random flows of events in computer networks under parametric uncertainty]. Trudy VKA imeni A.F. Mozhajskogo – Proceedings of Military Space Academy named A.F. Mozhaysky. 2015. vol. 649. pp. 16–22. (In Russ.).
18. Kochegarov V., Frolov G. Proektirovanie sistem raspredelenija informacii. Markovskie i nemarkovskie modeli. [Designing of systems of information distribution.Markovian and non-Markovian models]. M.: Radio i svjaz', 1991. 216 p. (In Russ.).
19. Buranova M., Kartashevskiy V. [The Analysis of the Latency Period for Knot of Network of the G/D/1 Type at Inaccurate Knowledge of Parameters of the Traffic]. Informatsionnye tekhnologii i telekommunikatsii – Inf. Technol. Telecommunications. 2017. vol. 5. no. 1. pp. 24–33. (In Russ.).
20. Bukashkin S., Kartashevskij V., Saprykin A. [Analysis of the functioning of a network node with inaccurate knowledge of traffic parameters]. DSPA: Voprosy primeneniya cifrovoj obrabotki signalov – DSPA: Issues of application of digital signal processing. 2017. vol. 7. no. 2. pp. 14–17. (In Russ.).
21. Ryzhikov Yu. Imitacionnoe modelirovanie. Avtorskaya imitaciya sistem i setej s ocheredyami. [Simulation modeling. Author's simulation of systems and networks with queues]. St. Petersburg: Lan Publishing House, 2019. 112 p. (In Russ.).
22. Stefanov S. On the Basic Concepts of the Direct Simulation Monte Carlo Method. Physics of Fluids. 2019. vol. 31. no. 6. DOI: 10.1063/1.5099042.
23. Greshilov A. Analiz i sintez stohasticheskih sistem. Parametricheskie modeli i konflyuentnyj analiz [Analysis and synthesis of stochastic systems. Parametric models and confluent analysis]. М.: Radio i svyaz', 1990. 320 p. (In Russ.).
24. Kuznetsov V. Interval'nye statisticheskie modeli [Interval statistical models]. М.: Radio i svyaz', 1991. 452 p. (In Russ.).
25. Levin V. [Calculations under uncertainty using interval mathematics] Doneckie chteniya 2019: obrazovanie, nauka, innovacii, kul'tura i vyzovy sovremennosti. Materialy IV Mezhdunarodnoj nauchnoj konferencii [Donetsk Readings 2019: education, science, innovation, culture and modern challenges. Materials of the IV International Scientific Conference]. 2019. pp. 184–185. (In Russ.).
26. Lazarev V., Uvarov R. [The organization of adaptive management based on information criteria]. Myagkie izmereniya i vychisleniya – Soft measurements and calculations. 2023. vol. 64. no. 3. pp. 46–57. (In Russ.).
27. Zhao Y., Wu H., Yang C., Liu Z., Cheng Q. New Reliability Modeling Methods for Structural Systems with Hybrid Uncertainty. Quality and Reliability Engineering International. 2020. vol. 36. no. 6. pp. 1855–1871.
28. Gel’fand M., Shilov G. Obobshhennye funkcii. Vyp. 2. Prostranstva osnovnyh i obobshhennyh funkcij [Generalized functions. Vol 2. Spaces of the test and generalized functions.]. M.: Fizmatgiz. 1958. 307 p. (In Russ.).
29. Goncharenko V. [Composite Method of Forming Approximating Distributions with an Arbitrary Phase Function]. Trudy SPIIRAN – SPIIRAS Proc. 2016. vol. 46. no. 3. pp. 212–225. (In Russ.).
30. He Q.-M., Liu B., Wu H. Continuous Approximations of Discrete Phase-Type Distributions and Their Applications to Reliability Models. Performance Evaluation. 2022. vol. 154. DOI: 10.1016/j.peva.2022.102284.
31. Sarada Y., Shenbagam R. Approximations of Availability Function Using Phase Type Distribution. Opsearch. 2022. vol. 59. pp. 1337–1351.
32. Wang L., Li Y., Qian Y., Luo X. A Parameter Estimation Method of Shock Model Constructed with Phase-Type Distribution on the Condition of Interval Data. Mathematical Problems in Engineering. 2020. vol. 2020. no. 11. DOI: 10.1155/2020/1424105.
33. Smagin V., Filimonihin G. [About modelling of stochastic processes on a basis of hyperdelta distribution]. Avtomatika i vychislitel'naja tehnika – Automation and Computer Engineering. 1990. no. 1. pp. 25–31. (In Russ.).
34. Buranova M., Kartashevsky V. [Recursive selection of parameters of hyperexponential distributions in the approximation of distributions with "heavy tails"]. Trudy uchebnyh zavedenij svyazi – Proceedings of educational institutions of communication. 2023. vol. 9. no. 2. pp. 40–46. (In Russ.).
35. Dokuchaeva A. [Monte-Carlo Simulation of the Queuing Systems with Parametric Uncertainty by the Dynamic Simplified Models]. Sistemy upravleniya i informacionnye tekhnologii – Control systems and information technologies. 2019. no. 1(75). pp. 11–16. (In Russ.).
36. Tarasov V., Bakhareva N. [Simulation modeling of queuing systems based on composite distributions – probabilistic mixtures]. T-Comm: Telecommunications and Transport – T-Comm: Telekommunikacii i transport. 2023. vol. 17. no. 3. pp. 14–19.
37. Gofman M., Kornienko A., Glukharev M. A Method for Watermark Detection in Digital Audio Signals by Authorized Users. Automatic Control and Computer Sciences. 2021. vol. 55. no. 8. pp. 1005–1019.
38. Privalov A., Lukicheva V., Kotenko I., Saenko I. Increasing the sensitivity of the method of early detection of cyber-attacks in telecommunication networks based on traffic analysis by extreme filtering. Energies. 2020. vol. 13. no. 11.
39. Glukharev M., Solomatova M. Access Differentiation in Object-Oriented Databases Based on the Extended Object-Oriented Harrison–Ruzzo–Ullman Model. Automatic Control and Computer Sciences. 2020. vol. 54. pp. 1007–1012.
Published
2024-11-07
How to Cite
Goncharenko, V., Khomonenko, A., & Abu Khasan, R. (2024). A Compositional Approach to the Simulation of Queuing Systems with Random Parameters. Informatics and Automation, 23(6), 1577-1608. https://doi.org/10.15622/ia.23.6.1
Section
Mathematical Modeling and Applied Mathematics
Copyright (c) Владимир Анатольевич Гончаренко, Анатолий Дмитриевич Хомоненко, Рахеб Абу Хасан
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