Application of Non-Homogeneous Poisson Process Modeling to Containership Arrival Rate
ABSTRACT Estimating containership arrival rate is a key element in harbor operation and management; however, it is not easy to be described because of a wide range of external factors. Most of the literature discussing arrival processes is based on a homogeneous Poisson process, which is unable to describe the fluctuation status of growth or recession. In the paper, we propose the Non-Homogeneous Poisson Process to analyze the arrival process of containership. The Maximum Likelihood Method is used to estimate the parameters and the performance of the models. Finally, a real case of Taichung Harbor in Taiwan is taken as an example. The result shows that power law intensity function and logarithmic linear intensity function models all estimate that the containership arrival shows slow growth trend. Relative to power law intensity function, logarithmic linear intensity function is a model with better goodness-of-fit.
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ABSTRACT: The exponential growth of reliable IP networks provides a suitable and cost-efficient replacement for the legacy TDM based voice networks. In this paper we propose a new framework for modeling Voice over IP (VoIP) traffic based on a non-homogeneous Poisson process (NHPP). We show that the NHPP can provide an exact fit for the call arrival data, and can also be approximated to a normal model under heavy traffic condition. The overall goal of traffic engineering is to minimize call blocking and maximize system resource utilization. Our study which is based on hundreds of millions of call arrival information shows that the Poisson process fails to model the traffic behavior of modern IP-based telecommunication systems. This failure is due to using fixed call arrival rate and static resource allocation scheme. Our proposed framework solves the two problems by modeling call arrivals as a function of time. This time-dependent function supports a dynamic resource allocation mechanism that can be easily applied to converged IP networks. The proposed model is validated by real traffic data, and is also applied to predict the behavior of future data. We conducted statistical tests which demonstrate the validity of our model and the goodness-of-fit of predicted data and actual data. Our statistical results also show that the NHPP can safely be approximated by a normal process under heavy traffic conditions.