A PACKAGE ORDEAL: APPLYING QUEUING THEORY TO MODEL PRINCETON PACKAGE ROOM OPERATIONS

Abstract

The operations of the Princeton Package Room, which receives, processes, tracks, stores, and then delivers all incoming packages to students was modeled using a two queue in series queuing model. Arrival and departure time data for 2012 was fit with distributions to model daily package volume, first daily arrival time, daily processing rate, nights elapsed prior to retrieval, and time of retrieval. Distributions were used to generate random samples in simulating full years of package arrival and departure times. Results were compared with historical data and found to fit well in terms of average queue length and frequency of overcapacity. Modifications were then programmed to replicate scenarios of increased daily volume, capped retrieval times, and extended hours of operations. Simulated results indicate that if daily volumes increase 10% annually, occasions of overcapacity (when queue length exceeded 1000 packages) would multiply by over 2.5 times. If students were required to pick up packages within three days, occasions of overcapacity would be nearly eradicated, whereas opening for pick-ups on Sundays was not found to have an impact. For next steps, larger data sets should be analyzed and variables such as package size and pickup location should be accounted for. Implications of research may be very beneficial to organizations implementing delay-oriented distribution systems.