Trading Time in a Congested Environment

Abstract

The first in, first out (FIFO) queue discipline respects the order of arrivals, but is not efficient when customers have heterogeneous waiting costs. Priority queues, in which customers with higher waiting costs are served first, are more efficient but usually involve undesirable queue-jumping behaviors that violate bumped customers’ property rights over their waiting spots. To have the best of both worlds, we propose time-trading mechanisms, in which customers who are privately informed about their waiting costs mutually agree on the ordering in the queue by trading positions. If a customer ever moves back in the queue, she will receive an appropriate monetary compensation. Customers can always decide not to participate in trading and retain their positions as if they are being served FIFO. We design the optimal mechanisms for the social planner, the service provider, and an intermediary who might mediate the trading platform. Both the social planner’s and the service provider’s optimal mechanisms involve a flat admission fee and an auction that implements strict priority. If a revenue-maximizing intermediary operates the trading platform, it should charge a trade participation fee and implement an auction with some trade restrictions. Therefore, customers are not strictly prioritized. However, relative to a FIFO system, the intermediary delivers value to the social planner by improving efficiency, and to the service provider by increasing its revenue. This paper was accepted by Noah Gans, stochastic models and simulation.

Trading places: An experimental comparison of reallocation mechanisms for priority queuing

“…Kittsteiner and Moldovanu (2005) generalize the equilibrium analysis allowing for convex and concave waiting cost functions. Yang, Debo, and Gupta (2016) study mechanisms where queued customers compensate an intermediary for the opportunity to trade positions. See Hassin and Haviv's (2003) book for a discussion of some of this literature.…”

“…In other words, the endowment effect and the sunk-cost effect do not seem to interact. 27 See, for example, Kleinrock (1967), Lui (1985), Glazer and Hassin (1986), Rosenblum (1992), Mitra (2001), Afèche and Mendelson (2004), Kittsteiner and Moldovanu (2005), Gershkov and Schweinzer (2010), Kayı and Ramaekers (2010), and Yang et al (2016). 28 See, for example, Knetsch (1989), Kahneman et al (1990), Heyman, Orhun, andAriely (2004), and Manzur, Olavarrieta, Hidalgo, and Farías (2016).…”

“…See, for example, Kleinrock (), Lui (), Glazer and Hassin (), Rosenblum (), Mitra (), Afèche and Mendelson (), Kittsteiner and Moldovanu (), Gershkov and Schweinzer (), Kayı and Ramaekers (), and Yang et al ().…”

Invite Your Friend and You’ll Move Up in Line: Optimal Design of Referral Priority Programs

“…Afèche and Pavlin (2016) find lead-time-dependent customer types can drive the appearance of strategic delay, pooling, or pricing out the middle as the optimal scheduling structure. Yang et al (2017) consider auction mechanisms for customers to trade their waiting positions and show that partial pooling is the optimal mechanism for an intermediary in charge of the trading platform. While the above papers employ exact analysis that captures stochasticity of the queue (which is also the approach we take), others resort to fluid approximations to model kidney allocation (Su and Zenios 2006) or deterministic relaxations to characterize the behavior of large-scale systems (Maglaras et al 2018).…”

“…Specifically, we require that W agree with the realized average steady-state delays given capacity µ, a particular (nonanticipative and regenerative) scheduling policy, and customers' joining and referral decisions (α, r) induced by W . This consistency requirement is standard in the literature (Afèche 2013, Afèche and Pavlin 2016, Yang et al 2017 and is typically captured by constraints imposed on W ensuring that it must lie within the achievable region (Coffman and Mitrani 1980). is also binding, then W corresponds to a full-priority (work-conserving) scheme in which those with a successful referral can jump over all the non-referring customers.…”