• P-ISSN 0974-6846 E-ISSN 0974-5645

Indian Journal of Science and Technology


Indian Journal of Science and Technology

Year: 2021, Volume: 14, Issue: 11, Pages: 915-931

Original Article

A Two-State Retrial Queueing Model with Feedback having Two Identical Parallel Servers

Received Date:17 July 2020, Accepted Date:26 February 2021, Published Date:09 April 2021


Objective: In this study we consider a two-state retrial queueing system with feedback having two identical parallel servers. Transient state probabilities for exact number of arrivals and departures from the system will be obtained when both, one or none of the servers is busy. Numerical and graphical solutions will also be obtained. Methods: The difference-differential equations governing the system are solved recursively, Laplace transform is then used to obtain the transient state probabilities for exact number of arrivals and departures from the system. Findings: Time dependent probabilities are obtained when both, one and none of the servers is busy. Numerical and Graphical solutions are also obtained using MATLAB programming. Novelty: In past research, models considered arrivals and departures from the orbit whereas in present model arrivals and departures from the system are studied along with the concept of feedback. Applications: This type of model is implemented in computer systems. Mathematics Subject Classification: 60K25, 90B22, 60M20

Keywords: Arrivals; Departures; Queueing; Retrial; Feedback


  1. Cohen JW. Basic problems of telephone traffic theory and the influence of repeated calls. Philips Telecommunication Review . 1957;18(2):49–100.
  2. Yang T, Templeton JGC. A survey on retrial queues. Queueing Systems. 1987;2:201–233. Available from: https://dx.doi.org/10.1007/bf01158899
  3. Artalejo JR, Gomez-Corral A. A Computational Approach. In: Retrial queueing systems (1). (pp. XIII-318) 1999. https://doi.org/10.1007/978-3-540-78725-9
  4. Artalejo J, Falin G. Standard and retrial queueing systems: a comparative analysis. Revista Matemática Complutense. 2002;15(1):101–129. Available from: https://dx.doi.org/10.5209/rev_rema.2002.v15.n1.16950
  5. Finch PD. Cyclic Queues with Feedback. Journal of the Royal Statistical Society: Series B (Methodological). 1959;21(1):153–157. Available from: https://dx.doi.org/10.1111/j.2517-6161.1959.tb00323.x
  6. Takacs L. 1963. Available from: https://doi.org/10.1002/j.1538-7305.1963.tb00510.x
  7. Lee YW. The M/G/1 feedback retrial queue with two types of customers. Bulletin of the Korean Mathematical Society. 2005;42(4):875–887.
  8. Mokaddis G, Metwally S, Zaki B. A feedback retrial queuing system with starting failures and single vacation. Tamkang Journal of Science and Engineering. 2007;10(3):183–192.
  9. Kumar BK, Vijayalakshmi G, Krishnamoorthy A, Basha SS. A single server feedback retrial queue with collisions. Computers & Operations Research. 2010;37(7):1247–1255. Available from: https://dx.doi.org/10.1016/j.cor.2009.04.019
  10. Shekhar C, Jain M. Finite Queueing Model with Multitask Servers and Blocking. American Journal of Operational Research. 2013;3(2A):17–25.
  11. Yang DY, Ke JC, Wu CH. The multi-server retrial system with Bernoulli feedback and starting failures. International Journal of Computer Mathematics. 2015;92(5):954–969.
  12. Pegden CD, Rosenshine M. Some New Results for theM/M/1 Queue. Management Science. 1982;28(7):821–828. Available from: https://dx.doi.org/10.1287/mnsc.28.7.821
  13. Singla N, Kalra S. Performance Analysis of a Two-State Queueing Model with Retrials Journal of Rajasthan . Academy of Physical Sciences. 2018;17(1 & 2):81–100.
  14. Singla N, Kalra S. A Two-State Multiserver Queueing System with Retrials. International Journal of Open Problems in Computer Science & Mathematics. 2019;12(3):62–75.
  15. Falin G, Templeton JG. Retrial queues. (Vol. 75) CRC Press. 1997.
  16. Sztrik J. Basic Queueing Theory. 1986.


© 2021 Singla & Kaur.This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee).


Subscribe now for latest articles and news.