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Title: :  Ultrametric hierarchical resource utilization model using p-adic numbers
PaperId: :  17706
Published in:   International Journal Of Advance Research And Innovative Ideas In Education
Publisher:   IJARIIE
e-ISSN:   2395-4396
Volume/Issue:    Volume 8 Issue 4 2022
DUI:    16.0415/IJARIIE-17706
Licence: :   IJARIIE is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Author NameAuthor Institute
Toky Basilide RAVALIMINOARIMALALASONUniversity of Antananarivo
Falimanana RANDIMBINDRAINIBEUniversity of Antananarivo

Abstract

Computer Engineering, cognitive science, telecommunication, mathematical
hierarchical, p-adic, resource, utilization, ultrametric
We present a new model of resource utilization which we call the ultrametric model. It is based on a modeling of hierarchical resource utilization by p-adic numbers. This model can be used on a system with several resources which can be classified in order of importance. The state of such a system is a p-adic number. We define an elementary resource utilization as this state of the system, and a representation of the uses in the form of balls in the set of p-adic numbers has been advanced. From these models, and using state transitions at each change in resource utilization whether it is the arrival of a new customer, or a departure, we can demonstrate that the probability of resource utilization is governed by a Cauchy problem: a fractional differential equation, and more particularly, with the Vladimirov operator.

Citations

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IJARIIE Toky Basilide RAVALIMINOARIMALALASON, and Falimanana RANDIMBINDRAINIBE. "Ultrametric hierarchical resource utilization model using p-adic numbers" International Journal Of Advance Research And Innovative Ideas In Education Volume 8 Issue 4 2022 Page 566-576
MLA Toky Basilide RAVALIMINOARIMALALASON, and Falimanana RANDIMBINDRAINIBE. "Ultrametric hierarchical resource utilization model using p-adic numbers." International Journal Of Advance Research And Innovative Ideas In Education 8.4(2022) : 566-576.
APA Toky Basilide RAVALIMINOARIMALALASON, & Falimanana RANDIMBINDRAINIBE. (2022). Ultrametric hierarchical resource utilization model using p-adic numbers. International Journal Of Advance Research And Innovative Ideas In Education, 8(4), 566-576.
Chicago Toky Basilide RAVALIMINOARIMALALASON, and Falimanana RANDIMBINDRAINIBE. "Ultrametric hierarchical resource utilization model using p-adic numbers." International Journal Of Advance Research And Innovative Ideas In Education 8, no. 4 (2022) : 566-576.
Oxford Toky Basilide RAVALIMINOARIMALALASON, and Falimanana RANDIMBINDRAINIBE. 'Ultrametric hierarchical resource utilization model using p-adic numbers', International Journal Of Advance Research And Innovative Ideas In Education, vol. 8, no. 4, 2022, p. 566-576. Available from IJARIIE, https://ijariie.com/AdminUploadPdf/Ultrametric_hierarchical_resource_utilization_model_using_p_adic_numbers_ijariie17706.pdf (Accessed : 14 March 2024).
Harvard Toky Basilide RAVALIMINOARIMALALASON, and Falimanana RANDIMBINDRAINIBE. (2022) 'Ultrametric hierarchical resource utilization model using p-adic numbers', International Journal Of Advance Research And Innovative Ideas In Education, 8(4), pp. 566-576IJARIIE [Online]. Available at: https://ijariie.com/AdminUploadPdf/Ultrametric_hierarchical_resource_utilization_model_using_p_adic_numbers_ijariie17706.pdf (Accessed : 14 March 2024)
IEEE Toky Basilide RAVALIMINOARIMALALASON, and Falimanana RANDIMBINDRAINIBE, "Ultrametric hierarchical resource utilization model using p-adic numbers," International Journal Of Advance Research And Innovative Ideas In Education, vol. 8, no. 4, pp. 566-576, Jul-Aug 2022. [Online]. Available: https://ijariie.com/AdminUploadPdf/Ultrametric_hierarchical_resource_utilization_model_using_p_adic_numbers_ijariie17706.pdf [Accessed : 14 March 2024].
Turabian Toky Basilide RAVALIMINOARIMALALASON, and Falimanana RANDIMBINDRAINIBE. "Ultrametric hierarchical resource utilization model using p-adic numbers." International Journal Of Advance Research And Innovative Ideas In Education [Online]. volume 8 number 4 (14 March 2024).
Vancouver Toky Basilide RAVALIMINOARIMALALASON, and Falimanana RANDIMBINDRAINIBE. Ultrametric hierarchical resource utilization model using p-adic numbers. International Journal Of Advance Research And Innovative Ideas In Education [Internet]. 2022 [Cited : 14 March 2024]; 8(4) : 566-576. Available from: https://ijariie.com/AdminUploadPdf/Ultrametric_hierarchical_resource_utilization_model_using_p_adic_numbers_ijariie17706.pdf
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