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Research on Geo/Geo/1 Retrial Queue with Working Vacation Interruption and Nonpersistent Customers

  • Mingcong Wu
  • Yong HuangEmail author
  • Yang Song
  • Liang Zhao
  • Jian Liu
Conference paper
Part of the Lecture Notes on Multidisciplinary Industrial Engineering book series (LNMUINEN)

Abstract

Queueing phenomenon is prevalent in all areas of society and a reasonable queueing design can improve service efficiency and customer satisfaction. In order to adapt to the new requirements of web service system, this paper studies a Geo/Geo/1 retrial queue with working vacation interruption and nonpersistent customers. Firstly, a series of assumptions about the queueing system are put forward and the corresponding transition probability matrix is obtained. Then the stationary condition of the queueing system is derived. After that, the stationary distribution and the performance measures are obtained by using the matrix-analytic method. Finally, numerical analysis is conducted to discuss the effect of parameters on performance measures, furthermore, the performance of the queueing model is optimized to obtain the best parameters and the minimum cost.

Keywords

Web service Discrete-time queueing system Retrial Working vacation interruption Nonpersistent customers 

References

  1. 1.
    Burr T (2001) Introduction to matrix analytic methods in stochastic modeling. Technometrics 95(3):1379Google Scholar
  2. 2.
    Dimitriou I (2015) A retrial queue for modeling fault-tolerant systems with checkpointing and rollback recovery. Comput Ind Eng 79:156–167CrossRefGoogle Scholar
  3. 3.
    Kobayashi H, Konheim AG (1977) Queueing models for computer communications system analysis. IEEE Trans Commun 25(1):2–29MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Kosten L (1947) On the influence of repeated calls in the theory of probabilities of blocking. De Ingenieur 49(1):947Google Scholar
  5. 5.
    Li J, Tian N (2007) The discrete-time GI/Geo/1 queue with working vacations and vacation interruption. Appl Math Comput 185(1):1–10Google Scholar
  6. 6.
    Li J, Tian N (2007) The M/M/1 queue with working vacations and vacation interruptions. J Syst Sci Syst Eng 16(1):121–127Google Scholar
  7. 7.
    Li J, Tian N (2008) Analysis of the discrete time Geo/Geo/1 queue with single working vacation. Qual Technol Quant Manage 5(1):77–89MathSciNetCrossRefGoogle Scholar
  8. 8.
    Li T, Wang Z, Liu Z (2012) Geo/Geo/1 retrial queue with working vacations and vacation interruption. J Appl Math Comput 39(1):131–143MathSciNetCrossRefzbMATHGoogle Scholar
  9. 9.
    Liu Z, Song Y (2013) Geo/Geo/1 retrial queue with non-persistent customers and working vacations. J Appl Math Comput 42(1):103–115MathSciNetCrossRefzbMATHGoogle Scholar
  10. 10.
    Meisling T (1958) Discrete-time queuing theory. Oper Res 6(1):96–105MathSciNetCrossRefGoogle Scholar
  11. 11.
    Palm C (1953) Methods of judging the annoyance caused by congestion. Tele 4(189208):4–5Google Scholar
  12. 12.
    Phung-Duc T (2014) Multiserver retrial queues with two types of nonpersistent customers. Asia Pac J Oper Res 31(2):144–171MathSciNetzbMATHGoogle Scholar
  13. 13.
    Rajadurai P (2015) Analysis of M [X]/G/1 retrial queue with two phase service under bernoulli vacation schedule and random breakdown. In J Math Oper Res 7(1):19–41MathSciNetCrossRefGoogle Scholar
  14. 14.
    Servi LD, Finn SG (2002) M/M/1 queues with working vacations (M/M/1/WV). Perform Eval 50(1):41–52CrossRefGoogle Scholar
  15. 15.
    Tao L, Zhang L, Xu X (2013) An M/G/1 queue with single working vacation and vacation interruption under Bernoulli schedule. Appl Math Model 37(3):1564–1579Google Scholar
  16. 16.
    Tian N, Zhang Z (2006) Vacation queueing models: theory and applications. Springer, New YorkCrossRefzbMATHGoogle Scholar
  17. 17.
    Tian N, Ma Z, Liu M (2008) The discrete time Geom/Geom/1 queue with multiple working vacations. Appl Math Model 32(12):2941–2953MathSciNetCrossRefzbMATHGoogle Scholar
  18. 18.
    Yang T, Li H (1995) On the steady-state queue size distribution of the discrete-time Geo/G/1 queue with repeated customers. Queueing Syst 21(1):199–215MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • Mingcong Wu
    • 1
  • Yong Huang
    • 1
    Email author
  • Yang Song
    • 2
  • Liang Zhao
    • 1
  • Jian Liu
    • 1
  1. 1.Business SchoolSichuan UniversityChengduPeople’s Republic of China
  2. 2.Department of MathematicsNanjing University of Aeronautics and AstronauticsNanjingPeople’s Republic of China

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