Analysis of Queues Fed by Lognormal Distributed Arrivals for IoT Network Traffic

Abstract

Statistical analysis of IoT network traffic establishes the presence of lognormal distributed inter-arrivals. This letter presents analysis of LN/M/1 queueing model using approximate results of Laplace-Stieltjes transformation of lognormal distribution in terms of Lambert ${{\mathcal { W}}}$ (.) function. The comparative performance evaluation of the LN/M/1 model with traditional M/M/1 model reveals that the quality of service metrics of LN/M/1 model mostly remain lower than M/M/1 implying that less number of buffers are required in IoT systems driven by such traffic. The asymptotic expressions for loss probability are derived using finite capacity LN/M/1/N model for different values of traffic intensity.