“Network-theoretic” queuing delay estimation in theme park attractions

Queuing is a common phenomenon in theme parks which negatively affects visitor experience and revenue yields. There is thus a need for park operators to infer the real queuing delays without expensive investment in human effort or complex tracking infrastructure. In this paper, we depart from the classical queuing theory approach and provide a data-driven and online approach for estimating the time-varying queuing delays experienced at different attractions in a theme park. This work is novel in that it relies purely on empirical observations of the entry time of individual visitors at different attractions, and also accommodates the reality that visitors often perform other unobserved activities between moving from one attraction to the next. We solve the resulting inverse estimation problem via a modified Expectation Maximization (EM) algorithm. Experiments on data obtained from, and modeled after, a real theme park setting show that our approach converges to a fixed-point solution quite rapidly, and is fairly accurate in identifying the per-attraction mean queuing delay, with estimation errors of 7-8% for congested attractions.