JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2023, Vol. 58 ›› Issue (11): 45-52.doi: 10.6040/j.issn.1671-9352.0.2022.212

Previous Articles     Next Articles

Analysis for the M/M/c+m queueing model with non-preemptive priority and contact matching

Yuting TAN1(),Xiuli XU1,*(),Rui ZHENG2   

  1. 1. School of Science, Yanshan University, Qinhuangdao 066004, Hebei, China
    2. School of Economics and Management, Yanshan University, Qinhuangdao 066004, Hebei, China
  • Received:2022-04-04 Online:2023-11-20 Published:2023-11-07
  • Contact: Xiuli XU E-mail:1176878197@qq.com;xxl-ysu@163.com

RichHTML

7

PDF (PC)

458

Abstract:

The M/M/c+m queueing model with non-preemptive priority contact matching is established, and the state transition rule and infinitesimal generator matrix of the quasi-birth-and-death process are obtained. Then, the steady-state equilibrium condition, steady-state probability distribution, and main performance indices of the system are given by using the matrix geometric solution method. Finally, numerical examples are presented to discuss the influence of system parameters on the performance indices.

Key words: queueing model, contact matching, preemptive priority, steady-state probability

CLC Number: 

  • O226

Fig.1

State transition figure of quasi birth and death processes of two-dimensional Markov chains"

Fig.2

Impact of lq with a"

Fig.3

Change of E(K) with a"

Fig.4

Impact of Lq with λ"

Fig.5

Impact of E(K) with λ"

1 KENDALL D G . Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded Markov chain[J]. Annals of Mathematical Statistics, 1953, 24 (3): 338- 354.
doi: 10.1214/aoms/1177728975
2 NEUTS M F . Matrix-geometric solutions in stochastic models[M]. Baltimore: Johns Hopkins University Press, 1981.
3 田乃硕, 岳德权. 拟生灭过程与矩阵几何解[M]. 北京: 科学出版社, 2002.
TIAN Naishuo , YUE Dequan . The quasi birth and death process and matrix-geometric solution[M]. Beijing: Science Press, 2002.
4 卢一强, 王念平, 李云强. 多服务台并联排队系统的随机模拟[J]. 数学的实践与认识, 2021, 51 (4): 200- 206.
LU Yiqiang , WANG Nianping , LI Yunqiang . Stochastic simulation of queue system with multiple parallel service desks[J]. Mathematics in Practice and Theory, 2021, 51 (4): 200- 206.
5 马占友, 王文博, 郑晓铭. 带抢占优先权和同步多重工作休假的M/M/c排队模型[J]. 重庆师范大学学报(自然科学版), 2018, 35 (3): 96- 100.
MA Zhanyou , WANG Wenbo , ZHENG Xiaoming . The M/M/c queueing model with preemptive priority and multiple synchronous working vacation[J]. Journal of Chongqing Normal University (Natural Science), 2018, 35 (3): 96- 100.
6 张雪梅, 岳德权, 张玉英. 具有不耐烦顾客的MX/M/1多重工作休假排队系统[J]. 工程数学学报, 2019, 36 (3): 285- 297.
ZHANG Xuemei , YUE Dequan , ZHANG Yuying . Analysis of customers' impatience in an MX/M/1 queue with multiple working vacations[J]. Chinese Journal of Engineering Mathematics, 2019, 36 (3): 285- 297.
7 王鲁, 杨玉中. 基于排队论的专项汽修厂维修台配置数量研究[J]. 数学的实践与认识, 2021, 51 (3): 143- 151.
WANG Lu , YANG Yuzhong . Research on the quantity of maintenance stations in special auto repair plant based on queueing theory[J]. Mathematics in Practice and Theory, 2021, 51 (3): 143- 151.
8 关银银, 李凯. 考虑顾客时间敏感的差异化排队策略[J]. 合肥工业大学学报(自然科学版), 2021, 44 (3): 421- 427.
GUAN Yinyin , LI Kai . Differential queueing strategy considering customer time sensitivity[J]. Journal of Hefei University of Technology(Natural Science), 2021, 44 (3): 421- 427.
9 孙敬煊, 高郡, 张峻川, 等. 带接触匹配的M/M/c排队模型[J]. 数学的实践与认识, 2020, 50 (19): 186- 192.
SUN Jingxuan , GAO Jun , ZHANG Junchuan , et al. M/M/c queueing model with the state of matching and abandoning[J]. Mathematics in Practice and Theory, 2020, 50 (19): 186- 192.
10 BAI Jiaru , SO K C , TANG C S , et al. Coordinating supply and demand on an on-demand service platform with impatientcustomers[J]. Manufacturing and Service Operations, 2017, 21 (3): 556- 570.
[1] Jiaxin DING,Yongfeng GUO,Lina MI. Transition behavior of underdamped periodic potential system driven by Gaussian noise and Lévy noise [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(8): 111-117.
[2] ZHANG Lei, WANG Yu, L Sheng-li, MA Zhan-you. Analysis of the M／M／m／k-m preemptive priority queuing system with negative customers [J]. J4, 2011, 46(11): 105-111.
[3] TIAN Rui-ling, YUE De-quan, HU Lin-min. M／Hk／1 Queue with balking, state-dependent and multiple vacations [J]. J4, 2010, 45(5): 89-94.
[4] FAN Jian-Wu, DIAO Xiao-Hua, TIAN Ai-Shuo, YUAN Xiao-Jing. The M／M／1／N queuing system with negative customers and a single working vacation [J]. J4, 2009, 44(8): 68-73.
[5] ZHAO Xiao-hua,FAN Jian-wu,TIAN Nai-shuo,TIAN Rui-ling .

The M／M／1／N queuing system with balking, reneging and multiple working vacations

[J]. J4, 2008, 43(10): 46-51 .
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
[1] GONG Yan-xiang,LI Feng . The orbit deflection of the photon in the Reissner-Nordstro¨m metric[J]. J4, 2008, 43(10): 80 -84 .
[2] ZHANG Zhuan, YUAN Jian-Li, CHEN Jian-Jin. An algorithm based on the boundary-added decomposition matrix for ternary ECL circuits[J]. J4, 2010, 45(3): 45 -49 .
[3] ZHANG Fengxia1,　LI Ying1,2,　GUO Wenbin1, ZHAO Jianli1. Extremal ranks for block Hermitian and skew-Hermitian matrices[J]. J4, 2010, 45(4): 106 -110 .
[4] LIU Ru-jun,CAO Yu-xia,ZHOU Ping . Anti-control for discrete chaos systems by small feedback[J]. J4, 2007, 42(7): 30 -32 .
[5] WU Song-li1,2, CHEN Gui-you3*. Outer-disturbances and attributes conjunctive shrink#br# law mining and separating[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(06): 1 -5 .
[6] BI Xiao-dong . Free product of left quasi-normal bands[J]. J4, 2008, 43(6): 83 -86 .
[7] HUANG Chong-zheng,WU Yuan-xi,CHEN Hong . An efficient algorithm for current frequent sequence mining in data stream[J]. J4, 2007, 42(11): 37 -39 .
[8] Ma Jia-sai,ZHANG Yong-jun . An optimized method for minimal cubing approach[J]. J4, 2006, 41(3): 104 -107 .
[9] HU Chun-mei，LIU Xiao-ji*. A splitting for the W-weighted Drazin inverse of a linear operator on Banach space[J]. J4, 2010, 45(10): 24 -26 .
[10] JIN Yong-gang, WANG Fan, HU Xiao-peng. Contour matching method based on curvature scale space[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2014, 49(12): 43 -48 .
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd