This research project addresses two critical national challenges: (1) cost reduction in healthcare. and (2) sustainable transportation. Both of these problems are addressed by leveraging the common modeling framework of waiting lines or queues that are sensitive to time of day, day of week, seasonal, or annual effects. In the healthcare domain, a solution to the nursing home bed planning problem can be developed. This is an important issue due to the aging baby boomer demographic. Also hospital bed cleaning costs can be lowered by finding the most effective time to have cleaning staff available. Drivers looking for parking generate a large amount of pollution and congestion. Methods, motivated by sustainable transportation and enabled by large data sets, to reduce the amount of pollution and congestion caused by parking can be developed. This research also includes the training of graduate students and the inclusion of underrepresented minorities. The Conference for African American Researchers in the Mathematical Sciences (CAARMS) came into existence in 1995 to nurture and promote African American researchers in the mathematical sciences. Both PIs have given lectures and tutorials at CAARMS to share with the community of African-American mathematicians and aspiring students some of their latest research work.
This project develops dynamic performance models and dynamic optimization solution techniques based on a rich class of time dependent stochastic network models called Markovian service networks. This modeling and optimization framework captures the stochastic dynamics of the system that cannot be found in the static, long term, steady state behavior. Using this framework, solutions to critical challenges in both healthcare and sustainable transportation can be developed. These solutions address problems such as emergency room cost stabilization to handle the payments from the costs of unforeseen medical emergencies. The aging baby boomer demographic is the impetus for this work on nursing home bed planning. Hospital bed cleaning costs can be minimized by finding the most effective time to have cleaning staff available. On the average, 30% of the drivers in central business districts are searching for a parking space. This leads to a dramatic increase in air pollution and congestion. Using a big data set from a large scale parking pricing experiment, parking prices can be set to minimize pollution. This queueing analysis can also be used for a dynamic priority policy for electric car charging stations.
