Skip to main content
SpringerLink
Log in

An M/M/2 Heterogeneous Service Markovian Feedback Queuing Model with Reverse Balking, Reneging and Retention of Reneged Customers

  • Conference paper
  • First Online:
Advances in Computing and Intelligent Systems

Part of the book series: Algorithms for Intelligent Systems ((AIS))

Abstract

To stay ahead in today’s competitive business environment, understanding the behavior of the customer in advance is of utmost importance for every organisation. Mathematical queuing model developed in this paper can help organisations to theoretically derive the performance measures of the system in advance taking into consideration various customer behaviors. The model developed in this paper is solved iteratively to derive various probabilistic measures and performance measures of the system. Results obtained from the model with above-mentioned contemporary issues presented in this paper are of enormous use for designing effective strategies for efficient and smooth functioning of the system.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Ancker, C. J., Jr., & Gafarian, A. V. (1963). Some queuing problems with balking and reneging I. Operations Research, 11, 88–100.

    Google Scholar 

  2. Ancker, C. J., Jr., & Gafarian, A. V. (1963). Some queuing problems with balking and reneging II. Operations Research, 11, 928–937.

    Google Scholar 

  3. Haight, F. A. (1957). Queuing with balking I. Biometriika, 44, 360–369.

    Article  MathSciNet  Google Scholar 

  4. Jain, N. K., Kumar, R., & Som, B. K. (2014). An M/M/1/N queuing system with reverse balking. American Journal of Operational Research, 4(2), 17–20.

    Google Scholar 

  5. Haight, F. A. (1959). Queuing with reneging. Metrila, 2, 186–197.

    MATH  Google Scholar 

  6. Robert, E. (1979). Reneging phenomenon of single channel queues. Mathematics of Operations Research, 4(2), 162–178.

    Article  MathSciNet  Google Scholar 

  7. Baccelli, F., Boyer, I. P., & Hebuterne, G. (1984). Single-server queues with impatient customers. Advances in Applied Probability, 16, 887–905.

    Article  MathSciNet  Google Scholar 

  8. Wang, K., Li, N., & Jiang, Z. (2010). Queuing system with impatient customers: A review. In 2010 IEEE International Conference on Service Operations and Logistics and Informatics (pp. 82–87), July 15–17, 2010, Shandong.

    Google Scholar 

  9. Takács, L. (1963). A single-server queue with feedback. Bell System Technical Journal, 42(2), 505–519.

    Article  MathSciNet  Google Scholar 

  10. Davignon, G. R., & Disney, R. L. (1976). Single server queue with state dependent feedback. INFOR, 14, 71–85.

    MathSciNet  Google Scholar 

  11. Santhakumaran, A., & Thangaraj, V. (2000). A single server queue with impatient and feedback customers. Information and Management Science, 11, 71–79.

    MathSciNet  MATH  Google Scholar 

  12. Kumar, R., & Sharma, S. K. (2012). M/M/1/N queuing system with retention of reneged customers. Pakistan Journal of Statistics and Operation Research, 8(4), 719–735.

    MathSciNet  Google Scholar 

  13. Kumar, R., & Sharma, S. K. (2012). An M/M/1/N queuing model with retention of reneged customers and balking. American Journal of Operational Research, 2(1), 1–5.

    Article  Google Scholar 

  14. Kumar, R., & Sharma, S. K. (2012). A Markovian feedback queue with retention of reneged customers. AMO-Advanced Modelling and Optimization, 14(3), 673–679.

    MathSciNet  MATH  Google Scholar 

  15. Kumar, R., & Sharma, S. K. (2012). A Markovian feedback queue with retention of reneged customers and balking. AMO-Advanced Modelling and Optimization, 14(3), 681–688.

    MathSciNet  MATH  Google Scholar 

  16. Kumar, R., & Sharma, S. K. (2013). An M/M/c/N queuing system with reneging and retention of reneged customers. International Journal of Operational Research, 17, 333–340.

    Google Scholar 

  17. Morse, P. M. (1958). Queues, inventories and maintenance. New York: Willey.

    Book  Google Scholar 

  18. Krishanamoorthy, B. (1963). On Poisson queues with heterogeneous servers. Operations Research, 11, 321–330.

    Article  MathSciNet  Google Scholar 

  19. Singh, V. P. (1970). Two-server Markovian queues with balking: Heterogeneous vs homogeneous servers. Operations Research, 18, 145–159.

    Article  MathSciNet  Google Scholar 

  20. Som, B. K., & Seth, S. (2017). An M/M/2/N queuing system with encouraged arrivals, heterogenous service and retention of impatient customers. Advanced Modelling and Optimization, 19, 97–104.

    MATH  Google Scholar 

  21. Som, B. K., & Seth, S. (2018). M/M/c/N queuing systems with encouraged arrivals, reneging, retention and feedback customers. Yugoslav Journal of Operations Research, 28(3), 333–344.

    Article  MathSciNet  Google Scholar 

  22. Kumar, R., & Som, B. K. (2015). An M/M/1/N feedback queuing system with reverse balking, reverse reneging and retention of reneged customers. Indian Journal of Industrial and Applied Mathematics, 6(2), 173–183.

    Article  Google Scholar 

  23. Som, B. K., & Seth, S. (2017). A multi-server infinite capacity markovian feedback queuing system with reverse balking. In Fifth International Conference on Business Analytics and Intelligence, December 11–13, 2017, IIM Bangalore.

    Google Scholar 

  24. Som, B. K., & Seth, S. (2018). A stochastic multi-server infinite capacity feedback queuing system with reverse balking, customer impatience and retention of impatient customers. In The 13th International Conference on Queuing Theory and Network Applications (QTNA2018), July 25–27, 2018, Tsukuba, Japan.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Jagan Institute of Management Studies, Rohini Sec 5, Delhi, India

    Bhupender Kumar Som & Sunny Seth

  2. Jagannath University, Jaipur, Rajasthan, India

    Vivek Kumar Sharma

Authors
  1. Bhupender Kumar Som
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Vivek Kumar Sharma
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sunny Seth
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sunny Seth .

Editor information

Editors and Affiliations

  1. Rajasthan Technical University, Kota, Rajasthan, India

    Harish Sharma

  2. University of Southern Denmark, Odense, Denmark

    Kannan Govindan

  3. Amity University, Jaipur, Rajasthan, India

    Ramesh C. Poonia

  4. Amity University, Jaipur, Rajasthan, India

    Sandeep Kumar

  5. University of Bahrain, Zallaq, Bahrain

    Wael M. El-Medany

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Som, B.K., Sharma, V.K., Seth, S. (2020). An M/M/2 Heterogeneous Service Markovian Feedback Queuing Model with Reverse Balking, Reneging and Retention of Reneged Customers. In: Sharma, H., Govindan, K., Poonia, R., Kumar, S., El-Medany, W. (eds) Advances in Computing and Intelligent Systems. Algorithms for Intelligent Systems. Springer, Singapore. https://doi.org/10.1007/978-981-15-0222-4_25

Download citation

Publish with us

Policies and ethics

Search

Navigation