Qualitative properties of mathematical model for data flow

Cory D. Hauck; Michael Herty; Giuseppe Visconti; Cory D. Hauck; Michael Herty; Giuseppe Visconti

doi:10.3934/nhm.2021015

Networks and Heterogeneous Media

2021, Volume 16, Issue 4: 513-533. doi: 10.3934/nhm.2021015

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Qualitative properties of mathematical model for data flow

1.
Computational and Applied Mathematics Group, Oak Ridge National Laboratory, 1 Bethel Valley Road, Bldg. 5700, Oak Ridge, TN 37831-6164, USA
2.
Department of Mathematics, University of Tennessee, 227 Ayres Hall. 1403 Circle Drive. Knoxville TN 37996-1320, USA
3.
Institut für Geometrie und Praktische Mathematik (IGPM), RWTH Aachen University, Templergraben 55, 52062 Aachen, Germany

Received: 01 November 2020 Revised: 01 May 2021 Published: 01 July 2021
35L65, 35L40

In this paper, properties of a recently proposed mathematical model for data flow in large-scale asynchronous computer systems are analyzed. In particular, the existence of special weak solutions based on propagating fronts is established. Qualitative properties of these solutions are investigated, both theoretically and numerically.
- Conservation laws,
- predictive performance,
- weak solutions,
- data flow,
- front propagation
Citation: Cory D. Hauck, Michael Herty, Giuseppe Visconti. Qualitative properties of mathematical model for data flow[J]. Networks and Heterogeneous Media, 2021, 16(4): 513-533. doi: 10.3934/nhm.2021015

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Abstract

In this paper, properties of a recently proposed mathematical model for data flow in large-scale asynchronous computer systems are analyzed. In particular, the existence of special weak solutions based on propagating fronts is established. Qualitative properties of these solutions are investigated, both theoretically and numerically.

References

[1]	Two-way multi-lane traffic model for pedestrians in corridors. Netw. Heterog. Media (2011) 6: 351-381.
[2]	A model for the dynamics of large queuing networks and supply chains. SIAM J. Appl. Math. (2006) 66: 896-920.
[3]	A scalar conservation law with discontinuous flux for supply chains with finite buffers. SIAM J. Appl. Math. (2011) 71: 1070-1087.
[4]	Derivation of continuum traffic flow models from microscopic follow-the-leader models. SIAM J. Appl. Math. (2002) 63: 259-278.
[5]	A mathematical model of asynchronous data flow in parallel computers. IMA Journal of Applied Mathematics (2020) 85: 865-891.
[6]	On the modelling crowd dynamics from scaling to hyperbolic macroscopic models. Mathematical Models and Methods in Applied Sciences (2008) 18: 1317-1345.
[7]	H. Chan, M. J. Cherukara, B. Narayanan, T. D. Loeffler, C. Benmore, S. K. Gray and S. K. R. S. Sankaranarayanan, Machine learning coarse grained models for water, Nature Communications, 10 (2019), 379. doi: 10.1038/s41467-018-08222-6
[8]	Pedestrian flow models with slowdown interactions. Mathematical Models and Methods in Applied Sciences (2014) 24: 249-275.
[9]	Polygonal approximations of solutions of the initial value problem for a conservation law. J. Math. Anal. Appl. (1972) 38: 33-41.
[10]	C. M. Dafermos, Hyperbolic Conservation Laws in Continuum Physics, vol. 325 of Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 2nd edition doi: 10.1007/3-540-29089-3
[11]	Rigorous derivation of nonlinear scalar conservation laws from follow-the-leader type models via many particle limit. Archive for Rational Mechanics and Analysis (2015) 217: 831-871.
[12]	J. Dongarra, J. Hittinger, J. Bell, L. Chacón, R. Falgout, M. Heroux, P. Hovland, E. Ng, C. Webster and S. Wild, Applied Mathematics Research for Exascale Computing, Technical report, U.S. Department of Energy, Office of Science, Advanced Scientific Computing Research Program, 2014. doi: 10.2172/1149042
[13]	L. C. Evans, Partial Differential Equations, American Mathematical Society, 2010. doi: 10.1090/gsm/019
[14]	Modeling selective local interactions with memory. Physica D: Nonlinear Phenomena (2013) 260: 176-190.
[15]	A fluid dynamic model for the movement of pedestrians. Complex Systems (1992) 6: 391-415.
[16]	Models for dense multilane vehicular traffic. SIAM J. Math. Anal. (2019) 51: 3694-3713.
[17]	C. Murray et al., Basic Research Needs for Microelectronics: Report of the Office of Science Workshop on Basic Research Needs for Microelectronics, Technical report, USDOE Office of Science (SC)(United States), 2018.
[18]	J. S. Vetter et al., Extreme Heterogeneity 2018-Productive Computational Science in the Era of Extreme Heterogeneity: Report for DOE ASCR Workshop on Extreme Heterogeneity, Technical report, USDOE Office of Science (SC), Washington, DC (United States), 2018. doi: 10.2172/1473756
[19]	Roofline: An insightful visual performance model for multicore architectures. Communications of the ACM (2009) 52: 65-76.

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