Recent investigations of Internet of Things network traffic suggest the failure of traditionally used Poisson process-based models. The paper substantiates this finding by performing statistical analysis of packets inter-arrival time in publicly available datasets of IoT-based sensor data traffic. It is observed that gamma distribution fits well to the inter-arrival time of packets. Motivated by this outcome, a detailed performance evaluation of Gamma/M/1 model is carried out. The closed form expressions of mean queue length, mean waiting time in the queue and overflow probability are derived. Numerical computations show that the mean queue length of Gamma/M/1 model explodes much faster than Poisson process based M/M/1 model when its shape parameter is low and scale parameter is high, whereas, the opposite is observed when the values of parameters are reversed. Monte-Carlo simulation of the Gamma/M/1 model also validates these findings. These results will be useful in dimensioning resources like buffers and in designing congestion-control algorithms for IoT systems.

中文翻译：

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基于物联网的传感器数据流量的 Gamma/M/1 模型性能分析

最近对物联网网络流量的调查表明，传统上使用的基于泊松过程的模型失败了。该论文通过对基于 IoT 的传感器数据流量的公开可用数据集中的数据包到达间隔时间进行统计分析来证实这一发现。据观察，伽马分布非常适合数据包的到达间隔时间。受此结果的启发，对 Gamma/M/1 模型进行了详细的性能评估。推导出平均队列长度、平均队列等待时间和溢出概率的闭式表达式。数值计算表明，Gamma/M/1 模型的平均队列长度在其形状参数低和尺度参数高时比基于泊松过程的 M/M/1 模型爆炸快得多，而，当参数值颠倒时观察到相反的情况。Gamma/M/1 模型的蒙特卡罗模拟也验证了这些发现。这些结果将有助于确定缓冲区等资源的尺寸以及为物联网系统设计拥塞控制算法。