Border Crossing Modeling and Analysis: A Non-Stationary Dynamic Reallocation Methodology For Terminating Queueing Systems



Journal Title

Journal ISSN

Volume Title



The United States international land boundary is a volatile, security intense area. In 2010, the combined trade was $918 billion within North American nations, with 80% transported by commercial trucks. Over 50 million commercial vehicles cross the Texas/Mexico border every year, not including private vehicles and pedestrian traffic, between Brownsville and El Paso, Texas, through one of over 25 major border crossings called "ports of entry" (POE). Recently, securing our southwest border from terrorist interventions, undocumented immigrants, and the illegal flow of drugs and guns has dominated the need to efficiently and effectively process people, goods and traffic. 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. Therefore, the problem is about finding a balance between a reduction of wait time and its variance, POE operation costs, and the sustainment of a security level.

The contribution of the dissertation is three-fold. The first uses queueing theory on the border crossing process to develop a methodology that decreases border wait times without increasing costs or affecting security procedures. The outcome is the development of the Dynamic Reallocation Methodology (DRM). Currently at the POE, inspection stations are fixed and can only inspect one truck type, FAST or Non-FAST program participant. The methodology proposes moveable servers that once a threshold is met, can be switched to service the other type of truck. Particular emphasis is given to inspection (service) times under time-varying arrivals (demands).

The second contribution is an analytical model of the POE, to analyze the effects of the DRM. First assuming a Markovian service time, DRM benefits are evaluated. However, field data and other research suggest a general distribution for service time. Therefore, a Coxian k-phased approximation is implemented. The DRM is analyzed under this new baseline using expected number in the system, and cycle times.

A variance reduction procedure is also proposed and evaluated under DRM. Results show that queue length and wait time is reduced 10 to 33% depending on load, while increasing FAST wait time by less than three minutes.