Optimal Queue Length Information Disclosure When Service Quality is Uncertain

Internet-based technology enables firms to disseminate real-time delay information to delay-sensitive customers. We study how such delay announcements impact service providers in a competitive environment with two service providers who compete for market share. We model the service providers' strategies based on an endogenous timing game, investigating strategies that emerge in equilibrium. We determine the service providers' market shares under the various game outcomes by analyzing continuoustime Markov chains, which capture customers' joining decisions, and by developing a novel computational technique to analyze the intractable asymmetric Join-the-Shortest Queue system, providing bounds on the market shares. We find that only the lower capacity service provider announces its real-time delay under intermediate system loads and highly imbalanced capacities. However, for most parameter settings, the mere presence of a competitor induces both providers to announce delays in equilibrium, leaving customers better off on average. We relate our findings to the single-provider delay announcement literature by discussing the impact of competition on service providers, delay announcement technology firms, and customers. K E Y W O R D S delay announcement, endogenous timing game, Markov chain, service systems 1

Section: Delay Information Provision In Single-service Provider Settingsmentioning

confidence: 99%

Real‐time delay announcement under competition

Singh¹,

Delasay

Scheller‐Wolf

2023

“…Guo et al. (2021) consider a situation in which the queue‐disclosure behavior can serve as a signaling device, and derive pooling and separating equilibria in this setting. In particular, they find that if the system only has uninformed customers, only the pooling equilibria exist, and thus queue disclosure cannot convey quality information to customers.…”

Section: Literature Reviewmentioning

confidence: 99%

Optimal queue length information disclosure when service quality is uncertain

Guo

Haviv

Luo

et al. 2022

Self Cite

We investigate a server's best queue disclosure strategy in a single‐server service system with an uncertain quality level (which is assumed to be binary). We consider this problem from the perspective of a Bayesian persuasion game. The server first commits to a possibly mixed strategy stating the probability that the queue length will be revealed to customers on their arrival given a realized quality level. The service quality level is then realized, and the server's corresponding queue‐disclosure action is observed by customers, who then update their beliefs regarding service quality and decide whether to join the service system. We reformulate the server's decision problem as looking for the best Bayes‐plausible distribution of posterior beliefs regarding service quality. We demonstrate that the maximal expected effective arrival rate, as a function of the prior belief, can be graphed as the upper envelope of all convex combinations of any two arbitrary points on the two effective arrival rate functions of the revealed and concealed queues. We show that when the market size is sufficiently small (large), the server always conceals (reveals) the queue, regardless of the realized service quality. Numerically, we find that in a medium‐sized market, the server's optimal commitment strategy is often hybrid or mixed, that is, randomizing queue concealment and revelation. We also extend our analysis to a situation in which the server aims to maximize social welfare. We show that under certain conditions, it is always beneficial for the welfare‐maximizing social planner to randomize queue concealment and revelation, regardless of the market size.

“…Although many variants have been studied since, incorporating features like server vacations, customer abandonments, priorities, setup times, batch services, etc. (see Bountali & Economou, 2017, 2019; Burnetas & Economou, 2007; Guo et al., 2021; Guo & Hassin, 2011; Guo & Zipkin, 2007; Hassin, 2016; Hassin & Haviv, 2003; Ibrahim, 2018; Stidham, 2009; Z. Wang et. al., 2022; J. Wang & Zhang, 2013); the stream is almost exclusively focused on single‐arrivals systems.…”

Section: Introductionmentioning

confidence: 99%

Join, balk, or jettison? The effect of flexibility and ranking knowledge in systems with batch arrivals

Bountali

Burnetas

Örmeci

2022

Families that visit theme parks like Disneyland are debating on two aspects when they try to determine whether they prefer to join an activity of interest or would rather balk:(1) Is it better to join or balk as a group or allow the flexibility to get separated and jettison some members? and (2) Will it make any difference if they set a ranking among themselves beforehand as to who will be served first, second, etc.? We tackle the effect of flexibility and ranking knowledge and answer the above questions considering a single server Markovian queue with a generic batch size distribution. We consider two levels of flexibility: an inflexible setting, under which a family makes a common decision, and a flexible setting, under which each member makes her own decision. We pair each level with two sublevels with respect to the ranking knowledge: the case where the members set their ranking beforehand, and the case where they do not and assume they will be served according to a random order. We provide a full analytical characterization of the equilibrium and socially optimal strategies, and a comprehensive analysis of the intricate interplay among flexibility, ranking knowledge, and batch size variability, notions that do not exist in single-ins arrival systems. We offer insights as to under which circumstances entity jettison is preferable. We investigate the corresponding implications of the above on system throughput and social welfare and determine which setting is preferable for the customers and which for the society, depending on the objective and the system dynamics. Further, we highlight key differences between single versus batch-arrival models and provide high-level guidelines for managers and policymakers as to how they can influence customer decisions so that they move toward the preferable setting (e.g., by revealing/concealing the ranking, encouraging flexibility, pricing, etc.).