Poisson Process and Its Application to the Storm Water Overflows

Abstract

The homogenous Poisson process is often used to describe the event arrivals. Such Poisson process has been applied in various areas. This study focuses on the arrival pattern of storm water overflows. A set of overflow data was obtained from the storm water pipeline of a municipality. The aim is to verify the overflow arrival pattern and check whether the Poisson process can be applied. The adopted method is the analysis over the inter-arrival times. The exponential distribution test is conducted on the annual data set as well as the entire data set. The results show that all data sets follow the exponential distribution. With the verification of Poisson process, specific examples are also given to show how the Poisson process properties can be used in the management of storm water pipeline management. For other data that are featured with various heterogeneities, the homogenous Poisson process might not be able to be verified and used. Under such circumstances, non-homogenous survival model can be used to simulate the arrival process.