Queueing Systems With Fractional Number of Servers: Analysis and Practical Implementation of the Erlang-B Traffic Model
In this paper, both the achievement and practical implementation of a fractional number of servers in queueing systems is proposed. The Erlang-B traffic model is considered to demonstrate how the fractional number of servers can be physically realized and incorporated into teletraffic analysis. Whil...
Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
IEEE
2024-01-01
|
| Series: | IEEE Access |
| Subjects: | |
| Online Access: | https://ieeexplore.ieee.org/document/10742361/ |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1846163876121411584 |
|---|---|
| author | Felipe A. Cruz-Perez Sandra Lirio Castellanos-Lopez Genaro Hernandez-Valdez |
| author_facet | Felipe A. Cruz-Perez Sandra Lirio Castellanos-Lopez Genaro Hernandez-Valdez |
| author_sort | Felipe A. Cruz-Perez |
| collection | DOAJ |
| description | In this paper, both the achievement and practical implementation of a fractional number of servers in queueing systems is proposed. The Erlang-B traffic model is considered to demonstrate how the fractional number of servers can be physically realized and incorporated into teletraffic analysis. While mathematical extensions of the Erlang-B formula to consider fractional number of servers have been explored in the literature, neither the practical realization nor the insensitivity property of such models has been extensively studied. In this paper, an approach is presented to effectively achieve fractional number of servers by considering, upon the arrival of service requests, the existence of <inline-formula> <tex-math notation="LaTeX">$\lfloor s\rfloor +1$ </tex-math></inline-formula> servers at times, and only <inline-formula> <tex-math notation="LaTeX">$\lfloor s\rfloor $ </tex-math></inline-formula> servers at other times. The strength of this approach lies in its easy integration into the Call Admission Control (CAC) strategy of real queueing systems. Utilizing a fractional number of servers enables precise adjustment of blocking probability, facilitating a fair and adequate performance comparison among different resource management strategies and evaluation scenarios. Additionally, the insensitivity property of the considered Erlang-B model with fractional number of servers is demonstrated. Finally, to illustrate the practical benefits and advantages of considering a fractional number of servers in the CAC and performance evaluation, numerical examples of the proposed concepts are provided and discussed, specifically within the context of a cellular system with VoIP traffic. |
| format | Article |
| id | doaj-art-f30f086c5f964f20ad7c910625744fe3 |
| institution | Kabale University |
| issn | 2169-3536 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | IEEE |
| record_format | Article |
| series | IEEE Access |
| spelling | doaj-art-f30f086c5f964f20ad7c910625744fe32024-11-19T00:01:27ZengIEEEIEEE Access2169-35362024-01-011216626816628010.1109/ACCESS.2024.349163710742361Queueing Systems With Fractional Number of Servers: Analysis and Practical Implementation of the Erlang-B Traffic ModelFelipe A. Cruz-Perez0https://orcid.org/0000-0001-8328-3760Sandra Lirio Castellanos-Lopez1https://orcid.org/0000-0002-3873-8129Genaro Hernandez-Valdez2https://orcid.org/0000-0002-1280-3527Electrical Engineering Department, CINVESTAV-IPN, Mexico City, MexicoElectronics Department, Azcapotzalco Metropolitan Autonomous University (UAM-A), Mexico City, MexicoElectronics Department, Azcapotzalco Metropolitan Autonomous University (UAM-A), Mexico City, MexicoIn this paper, both the achievement and practical implementation of a fractional number of servers in queueing systems is proposed. The Erlang-B traffic model is considered to demonstrate how the fractional number of servers can be physically realized and incorporated into teletraffic analysis. While mathematical extensions of the Erlang-B formula to consider fractional number of servers have been explored in the literature, neither the practical realization nor the insensitivity property of such models has been extensively studied. In this paper, an approach is presented to effectively achieve fractional number of servers by considering, upon the arrival of service requests, the existence of <inline-formula> <tex-math notation="LaTeX">$\lfloor s\rfloor +1$ </tex-math></inline-formula> servers at times, and only <inline-formula> <tex-math notation="LaTeX">$\lfloor s\rfloor $ </tex-math></inline-formula> servers at other times. The strength of this approach lies in its easy integration into the Call Admission Control (CAC) strategy of real queueing systems. Utilizing a fractional number of servers enables precise adjustment of blocking probability, facilitating a fair and adequate performance comparison among different resource management strategies and evaluation scenarios. Additionally, the insensitivity property of the considered Erlang-B model with fractional number of servers is demonstrated. Finally, to illustrate the practical benefits and advantages of considering a fractional number of servers in the CAC and performance evaluation, numerical examples of the proposed concepts are provided and discussed, specifically within the context of a cellular system with VoIP traffic.https://ieeexplore.ieee.org/document/10742361/Call admission controlErlang-B formulafractional number of serversconnection-level analysisblocking probabilityinsensitivity property |
| spellingShingle | Felipe A. Cruz-Perez Sandra Lirio Castellanos-Lopez Genaro Hernandez-Valdez Queueing Systems With Fractional Number of Servers: Analysis and Practical Implementation of the Erlang-B Traffic Model IEEE Access Call admission control Erlang-B formula fractional number of servers connection-level analysis blocking probability insensitivity property |
| title | Queueing Systems With Fractional Number of Servers: Analysis and Practical Implementation of the Erlang-B Traffic Model |
| title_full | Queueing Systems With Fractional Number of Servers: Analysis and Practical Implementation of the Erlang-B Traffic Model |
| title_fullStr | Queueing Systems With Fractional Number of Servers: Analysis and Practical Implementation of the Erlang-B Traffic Model |
| title_full_unstemmed | Queueing Systems With Fractional Number of Servers: Analysis and Practical Implementation of the Erlang-B Traffic Model |
| title_short | Queueing Systems With Fractional Number of Servers: Analysis and Practical Implementation of the Erlang-B Traffic Model |
| title_sort | queueing systems with fractional number of servers analysis and practical implementation of the erlang b traffic model |
| topic | Call admission control Erlang-B formula fractional number of servers connection-level analysis blocking probability insensitivity property |
| url | https://ieeexplore.ieee.org/document/10742361/ |
| work_keys_str_mv | AT felipeacruzperez queueingsystemswithfractionalnumberofserversanalysisandpracticalimplementationoftheerlangbtrafficmodel AT sandraliriocastellanoslopez queueingsystemswithfractionalnumberofserversanalysisandpracticalimplementationoftheerlangbtrafficmodel AT genarohernandezvaldez queueingsystemswithfractionalnumberofserversanalysisandpracticalimplementationoftheerlangbtrafficmodel |