Runaway and homeless youth (RHY) are a group of youth and young adults who are at high risk of being exploited through human trafficking. Although access to housing and support services is an effective way to decrease their vulnerability to being exploited, research reveals that coordination of these services provided to RHY by non-profit and government organizations is neither standardized, nor efficient. This situation often causes decreased, delayed, and inequitable access to these scarce housing resources. In this study, we aim to increase the housing system efficiency and reduce the barriers that are contributing to inequitable access to housing through simulation modeling and analyses. Specifically, we simulate a set of crisis and emergency shelters in New York City, funded by a single governmental organization, considering a queuing network with pools of multiple parallel servers, servers with demographic eligibility criteria, stochastic RHY arrival, impatient youth behaviour (possibility of abandonment), and a decision-maker (coordinator) that determines which server pool RHY is routed to. This simulation allows us to evaluate the impact of different queue routing strategies. Our simulation results show that by changing the way RHY is routed to shelters, we can reduce the average wait time by approximately a day and decrease the proportion of RHY abandoning the shelters by 13%.