MODELING AND ANALYZING A COMPLEX FEEDBACK QUEUE NETWORK MODEL WITH PRIORITY HAVING BI-TANDEM AND PARALLEL SERVERS IN STOCHASTIC ENVIRONMENT

Preeti; Deepak  Gupta; Vandana  Saini

doi:10.5269/bspm.78998

Preeti Maharishi Markandeshwar Engineering College- M.M.(Deemed to be University) Mullana, Ambala
Deepak Gupta
Vandana Saini

Résumé

The current study examines a complex queueing network model having three parallel subsystems.
The first subsystem comprises of biserial service channels, while the second involves parallel service channels,
which are linked in series with a third common subsystem. A distinctive feature of this model is the possibility
of customer feedback, allowing customers to re-enter the system after service, based on a defined transition
probability tied to their satisfaction. The system prioritizes the first and second subsystems, with customer
arrivals occurring independently at the other subsystems. Both arrival and service processes are modeled
using poisson distributions. The steady-state behavior is analyzed through differential difference equations
utilizing generating function techniques. This paper investigate the impact of feedback-priority mechanism on
the system’s performance and a parametric analysis is conducted to further explore the model’s applicability
in real-world situations. The results, are presented both numerically and graphically, effectively validating the
model’s behavior under different settings.

Téléchargements

Les données sur le téléchargement ne sont pas encore disponible.

Références

1. A. Cobham, Priority assignment in waiting line problems, J. Oper. Res. Soc. Am. 2, 70-76, (1954).
2. P. L. Maggu, Phase type service queues with two servers in biseries, J. Oper. Res. Soc. Japan 13, 1-6, (1970).
3. D. Gupta, T. P. Singh and R. Kumar, Analysis of a network queue model comprised of biserial and parallel channel
linked with a common server, ULTRA Science, 407-418, (2007).
4. D. Gupta, S. Sharma and N. Gulati, On steady state behaviour of a network queuing model with biserial and parallel
channels linked with a common server, Comput. Eng. Intell. Syst. 2, 11-22, (2011).
5. S. Sharma, D. Gupta and S. Sharma, Analysis of network of biserial queues linked with a common server, Int. J.
Comput. Sci. Math. 5, 293-324, (2014).
6. Y. Chun, Queueing problems with two parallel servers, in: Advances in Mathematics, Springer, Berlin, 141-157, (2016).
7. S. K. Agrawal and B. K. Singh, Development and analysis of generalized queuing model, Int. J. Comput. Sci. Eng. 6,
15-32, (2018).
8. R. Gupta and D. Gupta, Analysis of steady state behaviour of biserial and parallel queue network model with batch
arrival, J. Comput. Theor. Nanosci. 17, 5032-5036, (2020).
9. D. Gupta and R. Gupta, Time independent analysis of biserial and parallel queuing models with batch arrival, Arya
Bhatta J. Math. Inform. 13, 83-90, (2021).
10. V. Saini, D. Gupta and A. K. Tripathi, Analysis of a feedback bi-tandem queue network in fuzzy environment, Int. J.
Math. Trends Technol. 68, (2022).
11. D. Gupta, A. Saini and A. K. Tripathi, Mathematical analysis of priority bi-serial queue network model, Math. Sci.
10, 981-987, (2022).
12. A. Saini, D. Gupta and A. K. Tripathi, Performance analysis of priority queue network consisting biserial and parallel
channel, AIP Conf. Proc. 2916, 1-7, (2023).
13. V. Saini, D. Gupta and A. K. Tripathi, Analytical study of a complex feedback semi bi-tandem queue system differ in
transition probabilities, Arya Bhatta J. Math. Inform. 14, 41-54, (2022).
14. A. D. Gbadebo, A. T. Akinwale, A. S. Sodiya and S. A. Akinleye, An optimal jobs’ admission control system for
priority-based queue network, SN Comput. Sci. 5, 998, (2024).
15. I. A. Adeleke, A. D. Gbadebo and E. O. Oyebode, Packet management system in single-server queue networks with
Poisson arrivals using a treap-based model, Fac. Nat. Appl. Sci. J. Math. Model. Numer. Simul. 2, 1-13, (2024).
16. A. Tamuli, D. Das and A. Choudhury, Optimizing the performance of multi-server heterogeneous queueing systems
with dynamic customer behaviour, Sankhya B 86, 366-414, (2024).
17. K. Dayana, T. Poongodi and B. Vennila, Study on single server finite capacity neutrosophic queueing model, Comput.
Appl. Math. 44, 1-30, (2025).
18. Preeti, D. Gupta and V. Saini, Mathematical analysis of feedback queue network model with priority comprised of two
serial channels within stochastic conditions, J. Mech. Continua Math. Sci. 20(7), 154-170, (2025).
19. Preeti, D. Gupta and V. Saini, Analytical study of heterogeneous feedback queue model with priority and atmost
one-time revisit facility, Arya Bhatta J. Math. Inform. 17(1), 103-118, (2025).