The Impact of Queue Length Rounding and Delayed App Information on Disney World Queues

Nirenberg, Samantha; Daw, Andrew; Pender, Jamol

doi:10.1109/wsc.2018.8632436

Cited by 17 publications

(11 citation statements)

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“…For example, it would be informative to know the size of the amplitude and the frequency of the mean-field limit when the arrival rate is periodic. One way to analyze the amplitude and the frequency is to exploit methods from non-linear dynamics like Lindstedt's method and the two-variable expansion method in Pender et al [30,31], Nirenberg et al [22], and Novitzky et al [23].…”

Section: Discussionmentioning

confidence: 99%

A Stochastic Analysis of Bike-Sharing Systems

Tao¹,

Pender²

2020

Prob. Eng. Inf. Sci.

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As more people move back into densely populated cities, bike sharing is emerging as an important mode of urban mobility. In a typical bike-sharing system (BSS), riders arrive at a station and take a bike if it is available. After retrieving a bike, they ride it for a while, then return it to a station near their final destinations. Since space is limited in cities, each station has a finite capacity of docks, which cannot hold more bikes than its capacity. In this paper, we study BSSs with stations having a finite capacity. By an appropriate scaling of our stochastic model, we prove a mean-field limit and a central limit theorem for an empirical process of the number of stations with k bikes. The mean-field limit and the central limit theorem provide insight on the mean, variance, and sample path dynamics of large-scale BSSs. We also leverage our results to estimate confidence intervals for various performance measures such as the proportion of empty stations, the proportion of full stations, and the number of bikes in circulation. These performance measures have the potential to inform the operations and design of future BSSs.

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Section: Discussionmentioning

confidence: 99%

A Stochastic Analysis of Bike-Sharing Systems

Tao¹,

Pender²

2020

Prob. Eng. Inf. Sci.

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“…The phenomenon called 'spontaneous symmetry breaking' occurs in an equivariant dynamical system when the symmetry of a solution of a system is smaller than the symmetry of the system itself [14,21]. As shown in the top row of Figure 1, when τ < τ c , the system (2) has the stable equilibrium solution E * = (5, 5) whose symmetry group is Γ ∼ = Z 2 because it satisfies the condition given in Equation (3). In this case, the symmetry of the solution is the same as the symmetry of the system.…”

Section: The Symmetric Casementioning

confidence: 99%

“…However, when τ > τ c , the system (2) has the stable limit-cycle solution (x(t), y(t)), as shown in the bottom row of Figure 1. Here, x(t) and y(t) are oscillating completely out of phase and do not satisfy the condition given in Equation (3). In this case, the symmetry of the solution is no longer the same as the symmetry of the system.…”

Section: The Symmetric Casementioning

confidence: 99%

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Bubbling, Bistable Limit Cycles and Quasi-Periodic Oscillations in Queues with Delayed Information

Collera

2022

Symmetry

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We consider a model describing the length of two queues that incorporates customer choice behavior based on delayed queue length information. The symmetric case, where the values of the time-delay parameter in each queue are the same, was recently studied. It was shown that under some conditions, the stable equilibrium solution becomes unstable as the common time delay passes a threshold value. This one-time stability switch occurs only at a symmetry-breaking Hopf bifurcation where a family of stable asynchronous limit-cycle solutions arise. In this paper, we examine the non-symmetric case, wherein the values of the time-delay parameter in each queue are different. We show that, in contrast to the symmetric case, the non-symmetric case allows bubbling, multiple stability switches and coexistence of distinct families of stable limit cycles. An investigation of the dynamical behavior of the non-symmetric system in a neighborhood of a double-Hopf bifurcation using numerical continuation explains the occurrence of the bistable limit cycles. Quasi-periodic oscillations were also observed due to the presence of torus bifurcations near the double-Hopf bifurcation. These identifications of the underlying mechanisms that cause unwanted oscillations in the system give a better understanding of the effects of providing delayed information and consequently help in better management of queues.

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“…Walt Disney World) offer guests a smartphone application that provides real-time information on queue lengths (with wait times rounded up to the nearest five-min interval). Nirenberg et al (2018) examined the rounding and delay effects of real-time queue information. To examine theme parks' priority entry systems from the perspective of management and customers, Hern andez-Maskivker and Ryan (2016) surveyed 1,000 customers at a theme park in Spain, interviewing ten theme park managers.…”

Section: Literature Reviewmentioning

confidence: 99%

Reducing nonpriority queues at theme parks

Sakamoto

2020

JHTI

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PurposeThis study examined the waiting times to board an attraction at a theme park (Tokyo DisneySea in Japan) using a simulation based on measured values. Park visitors often complain that waiting times are too long; guests (Disney's term for park visitors) must stand in long, slow-moving queues outdoors in all weather, enduring heat, cold, rain and wind. This can undermine their health and reduce customer satisfaction. To date, no research has offered a scientific approach to solve the problem in the context of theme park queues.Design/methodology/approachThe attraction examined two queues: a short waiting queue for guests with priority entry tickets and a long waiting queue for guests without priority entry tickets. The total number of guests with priority entry tickets remained a constant value, as in the current system; however, the author designed the number as a monotonically increasing function to reduce the waiting times for nonpriority entry. It was impractical to analyze queues or try to explain proposed wait time reduction methods using theories and mathematical models alone. Therefore, the author used a simulation study based on real data to demonstrate the proposed method of this study.FindingsThe simulation results indicated that the proposed method significantly decreased guests' waiting times in the nonpriority entry queue, without changing the number of guests in both priority and nonpriority entry queues.Research limitations/implicationsSimple queues can be analyzed using theoretical calculations, but complicated queue systems require simulation methods. Therefore, this paper cannot provide a theoretical basis for the method.Practical implicationsThe proposed method offers benefits to managers of any event or location seeking to manage queue times and not just theme parks (e.g. exhibitions, concerts, etc.). Advance tickets are equivalent to priority entry tickets, so applying the proposed method can shorten waiting times on the day of the event.Originality/valueThis study has important practical implications for queues management, and the proposed approach is a unique system that reduces waiting times, thus increasing customer satisfaction. The proposed method can be applied to similar types of priority entry systems.

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The Impact of Queue Length Rounding and Delayed App Information on Disney World Queues

Cited by 17 publications

References 0 publications

A Stochastic Analysis of Bike-Sharing Systems

A Stochastic Analysis of Bike-Sharing Systems

Bubbling, Bistable Limit Cycles and Quasi-Periodic Oscillations in Queues with Delayed Information

Reducing nonpriority queues at theme parks

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