Mathematical Study Of Waiting Time Of Service In Four Server Hierarchical Structured Feedback Queuing System With Revisit At Most Once To Any Of The Servers
Keywords:
Feedback, Queuing System, Poisson Process, Four Server, Waiting Time.
Abstract
The present paper deals with the study of mathematical and graphical study of waiting time of service of a customer. The queuing system has four servers for the service of customers in hierarchical order. A customer, after getting service from a server may leave the system or may go for further service to the higher order server depending upon the need of service but cannot go for service more than two times.
The arrival and service pattern are assumed to follow the Poisson process. The waiting time of customer for the service has been calculated from the mean queue length obtained by using generating function technique.
References
Chaudhry M et al. A Novel Computational Procedure for the Waiting-Time Distribution (In the Queue) for Bulk-Service Finite-Buffer Queues with Poisson Input; Mathematics. 2023; 11, 1142.
https://doi.org/10.3390/math11051142.
(2) Dudin S A, Dudina O S and Kostyukova O I. Analysis of a Queuing System with Possibility of Waiting Customers Jockeying between Two Groups of Servers; Mathematics. 2023; 11, 1475. https://doi.org/10.3390/math11061475.
(3) Khan I E and Paramasivam R. Reduction in Waiting Time in an M/M/1/N Encouraged Arrival Queue with Feedback, Balking and Maintaining of Reneged Customers; Symmetry. 2022; 14, 1743. https://doi.org/10.3390/sym14081743.
(4) Adeniran A M, Burodo M S and Suleiman S. Application of Queuing Theory and Management of Waiting Time Using Multiple Server Model: Empirical Evidence From Ahmadu Bello University Teaching Hospital, Zaria, Kaduna State, Nigeria; International Journal of Scientific and Management Research . 2022; 5(4), 159-174, http://doi.org/10.37502/IJSMR.2022.5412.
(5) Deena M C K and Haridass M. Analysis of Flexible Batch Service Queueing System to Constrict Waiting Time of Customers; Mathematical Problems in Engineering. 2021; https://doi.org/10.1155/2021/3601085.
(6) Bonomo O L, Pal A and Reuveni S. Mitigating Long Queues and Waiting Times With Service Resetting; PNAS Nexus. 2022; 1, 1-15, https:// doi.org/10.1093 / pnasnexus/pgac070.
(7) Kumari S. Waiting Time Analysis of Queueing System Having Combination of Six Servers Centrally Linked With a Common Server; International Journal of Innovations & Research Analysis . 2022; 2(2II), 233-237.
(8) Datt K, Kumar S, and Bhatia V. Mathematical Analysis of Waiting Time in a Feedback Queuing Model With Three Servers and Chances of Revisits of Customer Atmost Once to Any Server; International Journal of Creative Research Thoughts . 2022; 10(1), f590-f596.
(9) Datt K, Kumar S, and Bhatia V. Waiting Time Analysis of an Hierarchical Structured Queuing System with Feedback and Revisit of Customer at Most Once to Any of the Servers ; International Journal of Research and Analytical Reviews. 2022; 9(2), 778-783.
(10) Kamal. Mathematical modeling of some feedback queueing systems. Ph. D. Thesis. Baba Mastnath University, Asthal Bohar, Rohtak, Haryana. 2023.
https://doi.org/10.3390/math11051142.
(2) Dudin S A, Dudina O S and Kostyukova O I. Analysis of a Queuing System with Possibility of Waiting Customers Jockeying between Two Groups of Servers; Mathematics. 2023; 11, 1475. https://doi.org/10.3390/math11061475.
(3) Khan I E and Paramasivam R. Reduction in Waiting Time in an M/M/1/N Encouraged Arrival Queue with Feedback, Balking and Maintaining of Reneged Customers; Symmetry. 2022; 14, 1743. https://doi.org/10.3390/sym14081743.
(4) Adeniran A M, Burodo M S and Suleiman S. Application of Queuing Theory and Management of Waiting Time Using Multiple Server Model: Empirical Evidence From Ahmadu Bello University Teaching Hospital, Zaria, Kaduna State, Nigeria; International Journal of Scientific and Management Research . 2022; 5(4), 159-174, http://doi.org/10.37502/IJSMR.2022.5412.
(5) Deena M C K and Haridass M. Analysis of Flexible Batch Service Queueing System to Constrict Waiting Time of Customers; Mathematical Problems in Engineering. 2021; https://doi.org/10.1155/2021/3601085.
(6) Bonomo O L, Pal A and Reuveni S. Mitigating Long Queues and Waiting Times With Service Resetting; PNAS Nexus. 2022; 1, 1-15, https:// doi.org/10.1093 / pnasnexus/pgac070.
(7) Kumari S. Waiting Time Analysis of Queueing System Having Combination of Six Servers Centrally Linked With a Common Server; International Journal of Innovations & Research Analysis . 2022; 2(2II), 233-237.
(8) Datt K, Kumar S, and Bhatia V. Mathematical Analysis of Waiting Time in a Feedback Queuing Model With Three Servers and Chances of Revisits of Customer Atmost Once to Any Server; International Journal of Creative Research Thoughts . 2022; 10(1), f590-f596.
(9) Datt K, Kumar S, and Bhatia V. Waiting Time Analysis of an Hierarchical Structured Queuing System with Feedback and Revisit of Customer at Most Once to Any of the Servers ; International Journal of Research and Analytical Reviews. 2022; 9(2), 778-783.
(10) Kamal. Mathematical modeling of some feedback queueing systems. Ph. D. Thesis. Baba Mastnath University, Asthal Bohar, Rohtak, Haryana. 2023.
Published
2023-09-12
How to Cite
Surender Kumar, & Nidhi Sharma. (2023). Mathematical Study Of Waiting Time Of Service In Four Server Hierarchical Structured Feedback Queuing System With Revisit At Most Once To Any Of The Servers. Revista Electronica De Veterinaria, 24(3), 627-633. https://doi.org/10.69980/redvet.v24i3.1850
Issue
Section
Articles
