On Coxian phased distributions to approximate the border crossing port of entry (POE)

In 2010, the combined trade was $914 billion within North American nations, with 80% transported by commercial trucks through one of over 150 major border crossings called "ports of entry (POE)". Recently, securing our southwest border from undocumented immigrants, terrorist interventions and the illegal flow of drugs and guns has dominated the need to efficiently and effectively process people, goods and traffic through the POEs. Increasing security and inspection requirements are seriously affecting transit times. Each POE is configured as a multi-commodity, prioritized queueing network which rarely, if ever, operates in steady state. Previous analytical models of the border crossing process assume a Markovian distribution for service time. However, security procedures, like dog sniffing, create dependencies, and other research suggests that failure to recognize such correlations in model development may lead to significant inaccuracies. This paper presents and evaluates an analytical model of the border crossing process with an approximation of the general distribution service time by applying Mixture of Generalized Erlang (MGE) distributions, also known as Coxian k-phased distributions. The implementation of the Coxian k-phased approximation will follow the work from Altiok (1996) and Curry and Feldman (2011), with accompanying results.

On Coxian phased distributions to approximate the border crossing port of entry (POE) Conference Paper