Analysis of Bulk Queueing Model with Load Balancing and Vacation
Data center architecture plays an important role in effective server management network systems. Load balancing is one such data architecture used to efficiently distribute network traffic to the server. In this paper, we incorporated the load-balancing technique used in cloud computing with power b...
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2024-12-01
|
| Series: | Axioms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2075-1680/14/1/18 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832589140857716736 |
|---|---|
| author | Subramani Palani Niranjan Suthanthiraraj Devi Latha Sorin Vlase Maria Luminita Scutaru |
| author_facet | Subramani Palani Niranjan Suthanthiraraj Devi Latha Sorin Vlase Maria Luminita Scutaru |
| author_sort | Subramani Palani Niranjan |
| collection | DOAJ |
| description | Data center architecture plays an important role in effective server management network systems. Load balancing is one such data architecture used to efficiently distribute network traffic to the server. In this paper, we incorporated the load-balancing technique used in cloud computing with power business intelligence (BI) and cloud load based on the queueing theoretic approach. This model examines a bulk arrival and batch service queueing system, incorporating server overloading and underloading based on the queue length. In a batch service system, customers are served in groups following a general bulk service rule with the server operating between the minimum value <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="bold-italic">‘</mi><mi mathvariant="bold-italic">a</mi><mi mathvariant="bold-italic">’</mi></mrow></semantics></math></inline-formula> and the maximum value <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="bold-italic">‘</mi><mi>b</mi><mi mathvariant="bold-italic">’</mi></mrow></semantics></math></inline-formula>. But in certain situations, maintaining the same extreme values of the server is difficult, and it needs to be changed according to the service request. In this paper, server load balancing is introduced for a batch service queueing model, which is the capacity of the server that can be adjusted, either increased or decreased, based upon the service request by the customer. On service completion, if the service request is not enough to start any of the services, the server will be assigned to perform a secondary job (vacation). After vacation completion based upon the service request, the server will start regular service, overload or underload. Cloud computing using power BI can be analyzed based on server load balancing. The function that determines the probability of the queue size at any given time is derived for the specified queueing model using the supplementary variable technique with the remaining time as the supplementary variable. Additionally, various system characteristics are calculated and illustrated with suitable numerical examples. |
| format | Article |
| id | doaj-art-b751a17a5ea84cc6b0177caa00f063e8 |
| institution | Kabale University |
| issn | 2075-1680 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj-art-b751a17a5ea84cc6b0177caa00f063e82025-01-24T13:22:09ZengMDPI AGAxioms2075-16802024-12-011411810.3390/axioms14010018Analysis of Bulk Queueing Model with Load Balancing and VacationSubramani Palani Niranjan0Suthanthiraraj Devi Latha1Sorin Vlase2Maria Luminita Scutaru3Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600062, IndiaDepartment of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology, Chennai 600062, IndiaDepartment of Mechanical Engineering, Transilvania University of Brasov, Romania, B-dul Eroilor, 29, 500036 Brașov, RomaniaDepartment of Mechanical Engineering, Transilvania University of Brasov, Romania, B-dul Eroilor, 29, 500036 Brașov, RomaniaData center architecture plays an important role in effective server management network systems. Load balancing is one such data architecture used to efficiently distribute network traffic to the server. In this paper, we incorporated the load-balancing technique used in cloud computing with power business intelligence (BI) and cloud load based on the queueing theoretic approach. This model examines a bulk arrival and batch service queueing system, incorporating server overloading and underloading based on the queue length. In a batch service system, customers are served in groups following a general bulk service rule with the server operating between the minimum value <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="bold-italic">‘</mi><mi mathvariant="bold-italic">a</mi><mi mathvariant="bold-italic">’</mi></mrow></semantics></math></inline-formula> and the maximum value <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi mathvariant="bold-italic">‘</mi><mi>b</mi><mi mathvariant="bold-italic">’</mi></mrow></semantics></math></inline-formula>. But in certain situations, maintaining the same extreme values of the server is difficult, and it needs to be changed according to the service request. In this paper, server load balancing is introduced for a batch service queueing model, which is the capacity of the server that can be adjusted, either increased or decreased, based upon the service request by the customer. On service completion, if the service request is not enough to start any of the services, the server will be assigned to perform a secondary job (vacation). After vacation completion based upon the service request, the server will start regular service, overload or underload. Cloud computing using power BI can be analyzed based on server load balancing. The function that determines the probability of the queue size at any given time is derived for the specified queueing model using the supplementary variable technique with the remaining time as the supplementary variable. Additionally, various system characteristics are calculated and illustrated with suitable numerical examples.https://www.mdpi.com/2075-1680/14/1/18overloadingunderloadingload balancingbatch servicesupplementary variable technique |
| spellingShingle | Subramani Palani Niranjan Suthanthiraraj Devi Latha Sorin Vlase Maria Luminita Scutaru Analysis of Bulk Queueing Model with Load Balancing and Vacation Axioms overloading underloading load balancing batch service supplementary variable technique |
| title | Analysis of Bulk Queueing Model with Load Balancing and Vacation |
| title_full | Analysis of Bulk Queueing Model with Load Balancing and Vacation |
| title_fullStr | Analysis of Bulk Queueing Model with Load Balancing and Vacation |
| title_full_unstemmed | Analysis of Bulk Queueing Model with Load Balancing and Vacation |
| title_short | Analysis of Bulk Queueing Model with Load Balancing and Vacation |
| title_sort | analysis of bulk queueing model with load balancing and vacation |
| topic | overloading underloading load balancing batch service supplementary variable technique |
| url | https://www.mdpi.com/2075-1680/14/1/18 |
| work_keys_str_mv | AT subramanipalaniniranjan analysisofbulkqueueingmodelwithloadbalancingandvacation AT suthanthirarajdevilatha analysisofbulkqueueingmodelwithloadbalancingandvacation AT sorinvlase analysisofbulkqueueingmodelwithloadbalancingandvacation AT marialuminitascutaru analysisofbulkqueueingmodelwithloadbalancingandvacation |