Nonlinear approximation of characteristics of a fork-join queueing system with Pareto service as a model of parallel structure of data processing

被引：1

作者：

Gorbunova, A. V. ^{[1
]}

Lebedev, A. V. ^{[2
]}

机构：

[1] Russian Acad Sci, VA Trapeznikov Inst Control Sci, Moscow, Russia

[2] Lomonosov Moscow State Univ, Fac Mech & Math, Dept Probabil Theory, Moscow, Russia

来源：

MATHEMATICS AND COMPUTERS IN SIMULATION | 2023年 / 214卷

关键词：

Parallel computations; Queueing system; System with parallel task processing; Mean response time; Linear regression; OPTIMIZATION;

D O I：

10.1016/j.matcom.2023.07.029

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

A fork-join system with Pareto service time distribution is considered as a model of a parallel structure of data processing. For an approximation of the mean response time of the system and its standard deviation, we apply the approach based on a combination of simulation with linear regression and the method of nonlinear Nelder-Mead optimization. Previously, no analysis of fork-join queueing systems with M|G|1 subsystems was carried out due to the complexity of its implementation. Nevertheless, the approach proposed here is capable of delivering approximations of various types of the correlation coefficients of the sojourn times of subtasks in a given system. The analytic expressions derived below are shown to deliver good approximations to these characteristics, as evidenced by numerical experiments. Application of the proposed approach can be extended to systems with more involved architecture, and, in particular, to systems with non-Poisson input flow and various options of distributing of service times of tasks.& COPY; 2023 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

引用

页码：409 / 428

页数：20

共 44 条

[1] Infocommunication Networks Design with Self-Similar Traffic [J].

Ageyev, Dmytro ;

Mohsin, Aram ;

Radivilova, Tamara ;

Kirichenko, Lyudmyla .

2019 IEEE 15TH INTERNATIONAL CONFERENCE ON THE EXPERIENCE OF DESIGNING AND APPLICATION OF CAD SYSTEMS (CADSM'2019), 2019,

[2]

Alesawi S, 2019, INT CONF COMPUT NETW, P265, DOI [10.1109/ICCNC.2019.8685505, 10.1109/iccnc.2019.8685505]

[3]

Balsamo S., 1995, Performance Evaluation Review, V23, P305, DOI 10.1145/223586.223623

[4] Bound performance models of heterogeneous parallel processing systems [J].

Balsamo, S ;

Donatiello, L ;

Van Dijk, NM .

IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, 1998, 9 (10) :1041-1056

[5]

Balsamo S, 1997, LECT NOTES COMPUT SC, V1245, P218, DOI 10.1007/BFb0022209

[6] CAN MACHINES SOLVE GENERAL QUEUEING PROBLEMS? [J].

Baron, Opher ;

Krass, Dmitry ;

Sherzer, Eliran ;

Senderovich, Arik .

2022 WINTER SIMULATION CONFERENCE (WSC), 2022, :2830-2841

[7]

Crovella M. E., 1996, Performance Evaluation Review, V24, P160, DOI 10.1145/233008.233038

[8]

David Herbert A., 2004, Order Statistics

[9] A neural network approach to performance analysis of tandem lines: The value of analytical knowledge [J].

Dieleman, N. A. ;

Berkhout, J. ;

Heidergott, B. .

COMPUTERS & OPERATIONS RESEARCH, 2023, 152

[10] Estimation of the Optimal Threshold Policy in a Queue with Heterogeneous Servers Using a Heuristic Solution and Artificial Neural Networks [J].

Efrosinin, Dmitry ;

Stepanova, Natalia .

MATHEMATICS, 2021, 9 (11)

← 1 2 3 4 5 →