January  2010, 6(1): 57-71. doi: 10.3934/jimo.2010.6.57

Analysis on a queue system with heterogeneous servers and uncertain patterns

1. 

Department of Applied Statistics, National Taichung Institute of Technology, Taiwan

2. 

Department of Computer Science and Information Engineering, National Taichung Institute of Technology, Taiwan

3. 

Graduate School of Computer and Information Technology, National Taichung Institute of Technology, Taiwan

Received  August 2008 Revised  August 2009 Published  November 2009

This work constructs the membership functions of the system characteristics of a heterogeneous-server queueing model with fuzzy customer arrival and service rates. The $\alpha$-cut approach is used to transform a fuzzy queue into a family of conventional crisp queues in this context. By means of the membership functions of the system characteristics, a set of parametric nonlinear programs is developed to describe the family of crisp heterogeneous-server queues. A numerical example is solved successfully to illustrate the validity of the proposed approach. By extending this model to the fuzzy environment, the system characteristics are expressed and governed by the membership functions, and more information is provided for use by designers and practitioners.
Citation: Jau-Chuan Ke, Hsin-I Huang, Chuen-Horng Lin. Analysis on a queue system with heterogeneous servers and uncertain patterns. Journal of Industrial & Management Optimization, 2010, 6 (1) : 57-71. doi: 10.3934/jimo.2010.6.57
[1]

Zengjing Chen, Yuting Lan, Gaofeng Zong. Strong law of large numbers for upper set-valued and fuzzy-set valued probability. Mathematical Control & Related Fields, 2015, 5 (3) : 435-452. doi: 10.3934/mcrf.2015.5.435

[2]

Harish Garg, Dimple Rani. Multi-criteria decision making method based on Bonferroni mean aggregation operators of complex intuitionistic fuzzy numbers. Journal of Industrial & Management Optimization, 2021, 17 (5) : 2279-2306. doi: 10.3934/jimo.2020069

[3]

Tayel Dabbous. Adaptive control of nonlinear systems using fuzzy systems. Journal of Industrial & Management Optimization, 2010, 6 (4) : 861-880. doi: 10.3934/jimo.2010.6.861

[4]

Shige Peng. Law of large numbers and central limit theorem under nonlinear expectations. Probability, Uncertainty and Quantitative Risk, 2019, 4 (0) : 4-. doi: 10.1186/s41546-019-0038-2

[5]

Peng Sun. Exponential decay of Lebesgue numbers. Discrete & Continuous Dynamical Systems, 2012, 32 (10) : 3773-3785. doi: 10.3934/dcds.2012.32.3773

[6]

Danny Calegari, Alden Walker. Ziggurats and rotation numbers. Journal of Modern Dynamics, 2011, 5 (4) : 711-746. doi: 10.3934/jmd.2011.5.711

[7]

Xavier Buff, Nataliya Goncharuk. Complex rotation numbers. Journal of Modern Dynamics, 2015, 9: 169-190. doi: 10.3934/jmd.2015.9.169

[8]

Bao Qing Hu, Song Wang. A novel approach in uncertain programming part I: new arithmetic and order relation for interval numbers. Journal of Industrial & Management Optimization, 2006, 2 (4) : 351-371. doi: 10.3934/jimo.2006.2.351

[9]

Dequan Yue, Jun Yu, Wuyi Yue. A Markovian queue with two heterogeneous servers and multiple vacations. Journal of Industrial & Management Optimization, 2009, 5 (3) : 453-465. doi: 10.3934/jimo.2009.5.453

[10]

Peng Cheng, Yanqing Liu, Yanyan Yin, Song Wang, Feng Pan. Fuzzy event-triggered disturbance rejection control of nonlinear systems. Journal of Industrial & Management Optimization, 2021, 17 (6) : 3297-3307. doi: 10.3934/jimo.2020119

[11]

Jin-Zi Yang, Yuan-Xin Li, Ming Wei. Fuzzy adaptive asymptotic tracking of fractional order nonlinear systems with uncertain disturbances. Discrete & Continuous Dynamical Systems - S, 2021  doi: 10.3934/dcdss.2021144

[12]

Takao Komatsu, Bijan Kumar Patel, Claudio Pita-Ruiz. Several formulas for Bernoulli numbers and polynomials. Advances in Mathematics of Communications, 2021  doi: 10.3934/amc.2021006

[13]

Dmitry Krachun, Zhi-Wei Sun. On sums of four pentagonal numbers with coefficients. Electronic Research Archive, 2020, 28 (1) : 559-566. doi: 10.3934/era.2020029

[14]

Michael Björklund, Alexander Gorodnik. Central limit theorems in the geometry of numbers. Electronic Research Announcements, 2017, 24: 110-122. doi: 10.3934/era.2017.24.012

[15]

Wen Zhang, Lily Li Liu. Asymptotic normality of associated Lah numbers. Mathematical Foundations of Computing, 2021, 4 (3) : 185-191. doi: 10.3934/mfc.2021011

[16]

Jiaquan Zhan, Fanyong Meng. Cores and optimal fuzzy communication structures of fuzzy games. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 1187-1198. doi: 10.3934/dcdss.2019082

[17]

Xiaodong Liu, Wanquan Liu. The framework of axiomatics fuzzy sets based fuzzy classifiers. Journal of Industrial & Management Optimization, 2008, 4 (3) : 581-609. doi: 10.3934/jimo.2008.4.581

[18]

Tien-Fu Liang, Hung-Wen Cheng. Multi-objective aggregate production planning decisions using two-phase fuzzy goal programming method. Journal of Industrial & Management Optimization, 2011, 7 (2) : 365-383. doi: 10.3934/jimo.2011.7.365

[19]

Ali Mahmoodirad, Harish Garg, Sadegh Niroomand. Solving fuzzy linear fractional set covering problem by a goal programming based solution approach. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020162

[20]

Juan J. Nieto, M. Victoria Otero-Espinar, Rosana Rodríguez-López. Dynamics of the fuzzy logistic family. Discrete & Continuous Dynamical Systems - B, 2010, 14 (2) : 699-717. doi: 10.3934/dcdsb.2010.14.699

2020 Impact Factor: 1.801

Metrics

  • PDF downloads (76)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]