The Journal of Analysis

, Volume 27, Issue 1, pp 209–232 | Cite as

Fuzzy analysis of bulk arrival two phase retrial queue with vacation and admission control

  • J. Ebenesar Anna BagyamEmail author
  • K. Udaya Chandrika
Original Research Paper


In this paper state dependent batch arrival two phase retrial queue is considered. Admission of each individual customer to the system depends upon the state of the server. The server provides first essential service to all the admitted customers. After completion of essential service the customer may opt second optional service or leave the system. However, if the customer is dissatisfied with the essential service he can immediately join the orbit as a feedback customer. After providing service to a customer, the server may either wait for a new customer or take one of the multi-optional vacations. For the proposed model, steady state performance characteristics are derived. Numerical results are presented. The model is further analysed under fuzzy environment by using Zadeh’s extension principle.


Fuzzy retrial queue Admission control Two stage service and vacation 

Mathematics Subject Classification

60K20 60K25 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Informed consent

Informed consent was obtained from all individual participants included in the study.


  1. 1.
    Alnowibet, K., and L. Tadj. 2007. A quorum queueing system with bernoulli vacation schedule and restricted admissibility. Advanced Modelling and Optimization 9 (1): 171–180.zbMATHGoogle Scholar
  2. 2.
    Badamchi Zadeh, A. 2009. An MX/(G1, G2)/1/G(Bs)Vs with optional second services and admissibility restricted. International Journal of Information and Management Sciences 20: 305–316.MathSciNetzbMATHGoogle Scholar
  3. 3.
    Choudhury, G. 2008. A note on the MX/G/1 queue with a random setup time under a restricted admissibility policy with a Bernoulli vacatoin schedule. Statistical Methodology 5 (1): 21–29.MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Ebenesar Anna Bagyam, J., and K. Udaya Chandrika. 2013. Multi-stage retrial queueing system with bernoulli feedback. International Journal of Scientific and Engineering Research 4 (9): 496–499.zbMATHGoogle Scholar
  5. 5.
    Erlang, A.K. 1909. Probability and telephone calls. Nyt Tidsskr Krarup Mat Ser B 20: 33–39.Google Scholar
  6. 6.
    Jain, M., and P.K. Agrawal. 2010. Policy for state dependent batch arrival queueing system with l-stage service and modified Bernoulli schedule vacation. Quality Technology and Quantitative Management 7 (3): 215–230.CrossRefGoogle Scholar
  7. 7.
    Jeeva, M., and E. Rathnakumari. 2012. Fuzzy retrial queue with heterogeneous service and generalised vacatoin. International Journal of Recent Scientific Research 3 (9): 753–757.Google Scholar
  8. 8.
    Kalyanaraman, R., N. Thillaigovindan, and G. Kannadasan. 2010. A single server fuzzy queue with unreliable server. Internatinal Journal of Computational Cognition 8 (1): 1–4.Google Scholar
  9. 9.
    Ke, J.C., H.I. Huang, and C.H. Lin. 2007. On retrial queueing model with fuzzy parameters. Physica A: Statistical Mechanics and its Applications 374: 272–280.CrossRefGoogle Scholar
  10. 10.
    Khodadadi, S.B., and F. Jolai. 2012. A fuzzy based threshold policy for a single server retrial queue with vacations. Central European Journal of Operations Research 20 (2): 281–297.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Krishna Kumar, B., S. Pavai Madheswari, and A. Vijayakumar. 2002. The M/G/1 retrial queue with feedback and starting failures. Applied Mathematical Modelling 26: 1057–1075.CrossRefzbMATHGoogle Scholar
  12. 12.
    Krishna Kumar, B., R. Rukmani, and V. Thangaraj. 2009. On multiserver feedback retrial queue with buffer. Applied Mathematical Modelling 33: 2062–2083.MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Krishna Kumar, B., G. Vijayalakshmi, A. Krishnamoorthy, and S. Sadiq Basha. 2010. A single server feedback retrial queue with collisions. Computers and Operations Research 37 (7): 1247–1255.MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Lee, Y.W., and Y.H. Jang. 2009. The M/G/1 feedback retrial queue with Bernoulli schedule. Journal of Applied Mathematics and Informatics 27 (1–2): 259–266.Google Scholar
  15. 15.
    Madan, K.C. 2010. Steady state analysis of an MX/\( \left[ {\begin{array}{*{20}c} {{\text{G}}_{{ 1 {\text{A}}}} } & {G_{2A} } \\ {G_{1B} } & {G_{2B} } \\ \end{array} } \right] \)/1 queue with restricted admissibility of arriving batches and modified bernoulli schedule server vacations based on a single vacation policy. Applied Mathematical Sciences 4(26):2271–2292.Google Scholar
  16. 16.
    Madan, K.C., and W. Abu-Dayyeh. 2002. Steady state analysis of a single server bulk queue with general vacation time and restricted admissibility of arriving batches. Revista Investigation Operational 24 (2): 113–123.MathSciNetzbMATHGoogle Scholar
  17. 17.
    Mahesh, G., S. Yeshwanth, and Gowrishankar. 2014. Fuzzy logic based call admission control for next generation wireless networks. International Journal of Advanced Research in Computer and Communication Engineering 3 (8): 7731–7737.Google Scholar
  18. 18.
    Mokaddis, G.S., S.A. Metwally, and B.M. Zaki. 2007. A feedback retrial queueing system with starting failures and single vacation. Tamkang Journal of Science and Engineering 10 (3): 183–192.Google Scholar
  19. 19.
    Noora, A.A., G.R. Jahanshahloo, S. Fanati Rashidi, and M. Moazami Godarzi. 2011. A study of discrete-time multi server retrial queue with finite population and fuzzy parameters. African Journal of Business Management 5 (6): 2426–2431.Google Scholar
  20. 20.
    Singh, C.J., M. Jain, and B. Kumar. 2011. Queueing model with state dependent bulk arrival and second optional service. International Journal of Mathematics in Operational Research 3 (3): 322–340.MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Stephen Vincent, G., and S. Bhuvaneswari. 2011. On fuzzy retrial queue with priority subscribers. International Journal of Mathematics in Operational Research 4 (1): 9–20.Google Scholar
  22. 22.
    Suhasini, A.V.S., K. Srinivasa Rao, and P.R.S. Reddy. 2012. Transient analysis of tandem queueing model with non-homogeneous poisson bulk arrivals having state dependent service rates. International Journal of Advanced Computer and Mathematical Sciences 3 (2): 272–289.Google Scholar
  23. 23.
    Tokpo Ovengalt, C.B., K. Djouani, and A. Kurien. 2014. A fuzzy approach for call admission control in LTE networks. Procedia Computer Science 32: 237–244.CrossRefGoogle Scholar
  24. 24.
    Upadhyaya, S. 2013. Bernoulli vacation policy for a bulk retrial queue with fuzzy parameters. International Journal of Applied Operational Research 3 (3): 1–14.Google Scholar
  25. 25.
    Wang, J., and P.F. Zhou. 2010. A batch arrival retrial queue with starting failures, feedback and admission control. Journal of System Science and Engineering 19 (3): 306–320.CrossRefGoogle Scholar
  26. 26.
    Zadeh, L.A. 1978. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1: 3–28.MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Forum D'Analystes, Chennai 2018

Authors and Affiliations

  1. 1.Department of MathematicsAvinashilingam Institute for Home Science and Higher Education for WomenCoimbatoreIndia
  2. 2.Department of MathematicsAvinashilingam Institute for Home Science and Higher Education for WomenCoimbatoreIndia

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