IEEE Access (Jan 2025)
Count and Teletraffic Analysis of G/M/1 Queueing Systems With Log-Normal Interarrival Time of Bursty IoT Traffic
Abstract
In this paper, both performance analysis of finite and infinite buffer G/M/1 queueing systems and count analysis using Log-Normally distributed interarrival times to model highly variable Internet of Things (IoT) traffic are addressed. These mathematical analyses require either exact or approximate expressions for the Laplace-Stieltjes Transform (LT) of the interarrival time density function. Due to non-existence of closed-form LT for the Log-Normal (LN) distribution, count analysis is mathematically infeasible. Furthermore, analysis of finite buffer G/M/1/N queue systems is complex, with only asymptotic results available in the literature; and Markovian teletraffic analysis for LN interarrival time cannot be used. To address these challenges, two novel approaches are proposed. First, a new method to numerically calculate the parameter $\sigma $ (probability of experiencing delay) in the infinite buffer G/M/1 system is introduced. Second, the LN interarrival time distribution is approximated by Hyper-Exponential (HE) distributions of varying order. Then, a novel birth-and-death process-based teletraffic analysis for the HE/M/1/N system is developed to approximate the LN/M/1/N system’s performance. The mathematical expressions and performance evaluations presented here focus on relevant metrics, such as expected queue length, packet arrival rate, packet dropping probability, and mean packet delay, which were not addressed in prior related studies of finite buffer G/M/1 queue systems. Additionally, the HE approximation approach facilitates the development of analytical tools to quantify traffic burstiness. Numerical results show that 4th-order HE distribution provides performance metrics with less than 3% difference relative to those of the LN/M/1 queueing systems, and these metrics correlate strongly with count metrics.
Keywords
