Computer Science

Computer Science ›› 2022, Vol. 49 ›› Issue (7): 304-309.doi: 10.11896/jsjkx.210500218

• Computer Network • Previous Articles     Next Articles

Dependence Analysis Among Service Stations in Tandem Queueing Systems

GAO Ya1, ZHAO Ning2, LIU Wen-qi2   

  1. 1 Faculty of Science,Kunming University of Science and Technology,Kunming 650500,China
    2 Data Science Research Center,Kunming University of Science and Technology,Kunming 650500,China
  • Received:2021-05-31 Revised:2021-12-08 Online:2022-07-15 Published:2022-07-12
  • About author:GAO Ya,born in 1996,postgraduate.Her main research interests include queueing network and so on.
    ZHAO Ning,born in 1980,Ph.D,asso-ciate professor,Ph.D supervisor.Her main research interests include que-ueing theory and stochastic service systems.
  • Supported by:
    National Natural Science Foundation of China(61573173).

PDF (PC)

420

Abstract: There is dependence among stations in tandem queueing systems.Deep analysis of the influence of the upward station on the downward station is important for studying of the performance of the tandem queueing systems.However,the departure process of the upward station is usually non-renewal process,which causes the dependence among stations is difficult to be analyzed theoretically.This paper adopts performance ratio to study the dependence among stations.By simulations,the relationship between performance ratio and system parameters are analyzed.It is found that the upward station could magnify or reduce the mean waiting time of the downward station.The performance ratio increases with the square variation coefficient of the service time at the upward station.When the performance ratio is greater than 1,it increases with the ratio of the mean service time of the upward station to the downward station.When the performance ratio is less than 1,it decreases with the ratio of the mean service time of the upward station to the downward station.The mean waiting time of the downward station could be changed by adjusting mean or square variation coefficient of the service time at the upward station.

Key words: Dependence, Performance ratio, Simulation, Tandem queueing system, Waiting time

CLC Number: 

  • O226
[1]BOXMA O,DADUNA H.The cyclic queue andthe tandemqueue[J].Queueing Systems,2014,77(3):275-295.
[2]ALFA A,LIU B.Performance analysis of a mobile communication network:the tandem case[J].Computer Communications,2004,27(3):208-221.
[3]YANG Z X,LIU W,XU D.Study of cloud service queuingmodel based on imbedding Markov chain perspective[J].Cluster Computing,2018,21(1):837-844.
[4]MARTON L.Switching control analysis and design in queuenetworks[J].Journal of the Franklin Institute,2020,357(1):19-38.
[5]HUANG D B,WANG Y F.A two-stage queueing model for coordinating the product entry-exit service of manufactures' warehouse[J].Operation Research and Mangement Science,2016,25(6):250-257.
[6]LI R,ZHAO N,LIU W Q.Optimization of buffer for series production systems with waiting timeconstraints[J].Control and Decision,2018,32(2):345-350.
[7]WANG X P,QI H,XIAO H H,et al.Co scheduling model of three gorges-gezhou dam based on series queueing network[J].Journal of Traffic and Transportation Engineering,2006,6(3):82-86.
[8]PENA L D L,FREIER M J,LOPEZ B.New queuing theory applied to port terminals and proposal for practical application in container and bulk terminals[J].Journal of Waterway,Port,Coastal and Ocean Engineering,2020,146(1):1-7.
[9]JOSEPH W J.Queuing theory and modeling emergency department resource utilization[J].Emergency Medicine Clinics of North America,2020,38(3):563-572.
[10]LUO R,SHI Y.Analysis and optimization of supermarket ope-ration mode based on queuing theory:queuingand pricing of personalized service[C]//International Conference on Management Engineering,Software Engineering and Service Sciences.2020:221-224.
[11]FRIEDMAN H.Reduction methods for tandem queueing sys-tems[J].Operations Research,1965,13(1):121-131.
[12]PINEDO M,WOLFF R.A comparison between tandem queues with dependent and independent service times[J].Operations Research,1982,30(3):464-479.
[13]GUO Z T,ZHANG W L,CHEN M Y.Network service tail latency analysis based on M/M/1 queuing model[J].Computer Science,2020,47(11):286-293.
[14]PRIYA B,RAJENDRAN P.Performance measures of parallel tandem open queueing network[J].International Journal of Pervasive Computing and Communications,2021,17(1):37-48.
[15]BLANC J,IASNOGORODSKI R,NAIN P H.Analysis of theM/G/1→./M/1 queue model[J].Queueing Systems,1988,3:129-156.
[16]WU D L,ZHAO N,LIU W Q.Mean waiting time approximation of tandem queueing systems based on performance ratio[J].Journal of Nanjing University of Aeronautics & Astronautics,2020,52(4):644-649.
[17]GUO Y J,LI Z Z.Asymptotic variability analysis for a two-stage tandem queue,part I:the functional law of the iterated logarithm[J].Journal of Mathematical Analysis and Applications,2017,450(2):1479-1509.
[18]CIVELEK I,BILLER B,WOLF A.Impact of dependence on single-server queueing systems[J].European Journal of Opera-tional Research,2021,290(3):1031-1045.
[19]WU K,ZHAO N.Dependence among single stations in series and its applications in productivity improvement[J].European Journal of Operational Research,2015,247(1):245-258.
[20]WU K,MCGINNIS L.Interpolation approximations for queuesin series[J].IISE Transactions,2013,45(3):273-290.
[1] DOU Jia-wei. Privacy-preserving Hamming and Edit Distance Computation and Applications [J]. Computer Science, 2022, 49(9): 355-360.
[2] GUO Zheng-wei, FU Ze-wen, LI Ning, BAI Lan. Study on Acceleration Algorithm for Raw Data Simulation of High Resolution Squint Spotlight SAR [J]. Computer Science, 2022, 49(8): 178-183.
[3] LI Tang, QIN Xiao-lin, CHI He-yu, FEI Ke. Secure Coordination Model for Multiple Unmanned Systems [J]. Computer Science, 2022, 49(7): 332-339.
[4] ZHANG Ming-xin. Conceptual Model for Large-scale Social Simulation [J]. Computer Science, 2022, 49(4): 16-24.
[5] YANG Lin, WANG Yong-jie, ZHANG Jun. FAWA:A Negative Feedback Dynamic Scheduling Algorithm for Heterogeneous Executor [J]. Computer Science, 2021, 48(8): 284-290.
[6] SONG Yuan-long, LYU Guang-hong, WANG Gui-zhi, JIA Wu-cai. SDN Traffic Prediction Based on Graph Convolutional Network [J]. Computer Science, 2021, 48(6A): 392-397.
[7] CHENG Yu, LIU Tie-jun, TANG Yuan-gui, WANG Jian, JIANG Zhi-bin, QI Sheng. Underwater Robert Visual Simulation Based on UNITY3D [J]. Computer Science, 2021, 48(6A): 281-284.
[8] YANG Lin, WANG Yong-jie. Application and Simulation of Ant Colony Algorithm in Continuous Path Prediction of Dynamic Network [J]. Computer Science, 2021, 48(6A): 485-490.
[9] XIANG Chang-sheng, CHEN Zhi-gang. Chaotic Prediction Model of Network Traffic for Massive Data [J]. Computer Science, 2021, 48(5): 289-293.
[10] ZENG Wei-liang, HAN Yu, HE Jin-yuan, WU Miao-sen, SUN Wei-jun. Simulation Analysis on Dynamic Ridesharing Efficiency of Shared Autonomous Taxi [J]. Computer Science, 2021, 48(2): 257-263.
[11] KANG Yan, XIE Si-yu, WANG Fei, KOU Yong-qi, XU Yu-long, WU Zhi-wei, LI Hao. Traffic Prediction Model Based on Dual Path Information Spatial-Temporal Graph Convolutional Network [J]. Computer Science, 2021, 48(11A): 46-51.
[12] JIANG Hua-nan, ZHANG Shuai, LIN Yu-fei, LI Hao. Simulation Optimization and Testing Based on Gazebo of MPI Distributed Parallelism [J]. Computer Science, 2021, 48(11A): 672-677.
[13] MAO Ying-chi, ZHOU Tong, LIU Peng-fei. Multi-user Task Offloading Based on Delayed Acceptance [J]. Computer Science, 2021, 48(1): 49-57.
[14] CUI Xiang, LI Xiao-wen, CHEN Yi-feng. Communication Optimization Method of Heterogeneous Cluster Application Based on New Language Mechanism [J]. Computer Science, 2020, 47(8): 17-15.
[15] CHENG Sheng-gan, YU Hao-ran, WEI Jian-wen, James LIN. Design and Optimization of Two-level Particle-mesh Algorithm Based on Fixed-point Compression [J]. Computer Science, 2020, 47(8): 56-61.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
渝ICP备16013121号-4
Add:18# Honghu West Rd., Yubei ,Chongqing,China    Post Code: 401121
Tel: 023-63500828/023-67039612/023-67039623
E-mail: jsjkx12@163.com
Powered by Beijing Magtech Co., Ltd.