Research Article
Asymptotic Analysis of Modified Erlang-B System with Sensing Time and Stochastic Loss of Secondary Users
@INPROCEEDINGS{10.1007/978-3-031-31234-2_5, author={Kazuma Abe and Tuan Phung-Duc}, title={Asymptotic Analysis of Modified Erlang-B System with Sensing Time and Stochastic Loss of Secondary Users}, proceedings={Performance Evaluation Methodologies and Tools. 15th EAI International Conference, VALUETOOLS 2022, Virtual Event, November 2022, Proceedings}, proceedings_a={VALUETOOLS}, year={2023}, month={5}, keywords={Retrial Queue Cognitive wireless networks (CRN) Erlang-B model ODE}, doi={10.1007/978-3-031-31234-2_5} }- Kazuma Abe
Tuan Phung-Duc
Year: 2023
Asymptotic Analysis of Modified Erlang-B System with Sensing Time and Stochastic Loss of Secondary Users
VALUETOOLS
Springer
DOI: 10.1007/978-3-031-31234-2_5
Abstract
This paper considers a modified Erlang-B model for cognitive radio networks with both primary users (PUs) and secondary users (SUs). PUs have absolute priority over SUs, and are blocked whenever all channels are used by other PUs upon their arrivals. SUs must sense an idle channel upon their arrivals. If, after sensing, an SU finds an idle channel, it can occupy the channel immediately; otherwise, the SU may either sense again or leave the system forever. Under Poisson arrival assumptions (both PUs and SUs) and exponential sensing and service times, we formulate the system as a three-dimensional Markov chain, and consider an asymptotic regime when the sensing rate is extremely low. We prove that a scaled version of the number of sensing SUs converges to a deterministic process. Furthermore, we prove that the deterministic process has a unique stationary point which we use to approximate the mean number of sensing SUs and the distribution of the states of the channels. Numerical examples reveal that these approximations are highly accurate when the sensing rate is low.
