Herding in a Queue: A Laboratory Experiment

In this paper, we study how rational agents infer the quality of a good (a product or a service) by observing the queue that is formed by other rational agents to obtain the good. Agents also observe privately the realization of a signal that is imperfectly correlated with the true quality of the good. Based on the queue length information and the signal realization, agents decide whether to join the queue and obtain the good or to balk. The time to produce the good is exponentially distributed. Agents arrive according to a Poisson process at a market and are served according to a FIFO discipline. We find that when waiting costs are zero, agents receiving a bad signal join the queue only if it is long enough. When waiting costs are strictly positive, agents do not join the queue if it is too long. Furthermore, there may exist a set of isolated queue lengths ("holes") at which agents with a bad signal do not join. In equilibrium, queues are shorter for low quality goods and an agent is more likely to erroneously join a queue for a low quality good than erroneously balk from a queue for a high quality good. When decreasing the service rate, more agents may join queues for high quality goods, even when waiting is costly. *

Journal of Marketing Research, 2010

Ziv Carmon served as associate editor for this article.

Management Science, 2013

W e conduct an empirical study to analyze how waiting in queue in the context of a retail store affects customers' purchasing behavior. Our methodology combines a novel data set with periodic information about the queuing system (collected via video recognition technology) with point-of-sales data. We find that waiting in queue has a nonlinear impact on purchase incidence and that customers appear to focus mostly on the length of the queue, without adjusting enough for the speed at which the line moves. An implication of this finding is that pooling multiple queues into a single queue may increase the length of the queue observed by customers and thereby lead to lower revenues. We also find that customers' sensitivity to waiting is heterogeneous and negatively correlated with price sensitivity, which has important implications for pricing in a multiproduct category subject to congestion effects.

IJIIS: International Journal of Informatics and Information Systems, 2020

Consumers considering whether or not to queue make their decisions based on queuing size and the expecting waiting time. If a consumer is frustrated because he / she cannot know how long will wait, he / she will quit from a Consumers who are frustrated because they do not know how long they must wait will quit a queue or ask someone for help if the good is worthy to pay more money to own. If a good is worth waiting to purchase, a consumer will chose waiting or buying the privilege to get the good. However, a long wait causes customers to have negative feelings about the queue. Frustration also has a substantial effect on customer loyalty to a good. Therefore, the relationship between perceived waiting time and paying for queuers to buy the good is worth studying. Frustration is a moderating effect that is also worth studying. In the formal study, to make the frustrating emotion, the authors asked all participants to have a contest before they can take the tickets to enter a queue for taking the ticket to a famous concert in Taiwan. The questions used in the contest had different levels of difficulty. However, the difficulty of the questions must be verified before the formal experiment. Therefore, the 60 participants in this pilot study were asked 40 questions in history, mathematics, and Chinese to find the most difficult ten questions and the less difficulty ten questions for the formal test.

Management Science

We study how queue configuration affects human servers' service time by comparing dedicated with shared queues using field data from a natural experiment in a supermarket. We hypothesize that queue configuration may affect servers' service rate through several mechanisms: pooling may affects service rate directly due to social loafing effect and competition effect, and indirectly via its impact on queue length. To investigate these impacts, we take advantage of the supermarket's checkout layout, and use a data set containing both checkout transaction details and queue information collected from video recordings in the supermarket. After we control for the queue length, we find that servers in dedicated queues are about 10.7% faster than those in shared queues, mainly due to the social loafing effect. We also demonstrate that pooling has an indirect negative effect on service time through its impact on queue length. In addition, the queue configuration's direct effect and its indirect queue length effect function independently to each other. In aggregation, the social loafing effect dominates, and servers slow down (a 6.86% increase in service time) in shared queues.

They also serve who only stand and waite." John Milton (1608-1674), On His Blindness 1

2016

Delay or queue length information has the potential to influence the decision of a customer to use a service system. Thus, it is imperative for service system managers to understand how the information that they provide will affect the performance of the system. To this end, we construct and analyze two two-dimensional deterministic fluid models that incorporate customer choice behavior based on delayed queue length information. In the first fluid model, customers join each queue according to a Multinomial Logit Model, however, the queue length information the customer receives is delayed by a constant $\Delta$. We show that the delay can cause oscillations or asynchronous behavior in the model based on the value of $\Delta$. In the second model, customers receive information about the queue length through a moving average of the queue length. Although it has been shown empirically that giving patients moving average information causes oscillations and asynchronous behavior to occur...

We study how rational customers choose between two congested service facilities with finite buffer space and unknown service value when waiting is expensive. Customers observe an imperfect private signal indicating which service facility may provide more service value, as well as the queue lengths at the service facilities before making their choice. If more customers choose the same service facility because of their private information, longer queues will form at the service facility and therefore a long queue may be an indication of higher quality. On the other hand, a long queue also implies more waiting time to obtain the service. We characterize the equilibrium queue-joining behavior of arriving customers in the presence of such positive and negative externalities. We find that when the waiting costs are positive, it might be rational for customers to join the longer queue, even if the private information suggests joining the shorter queue. How the information is distributed among customers, and the buffer sizes play key roles in determining the customer choice behavior: In markets in which all of the customers have the same signal strength, there has to be enough waiting space available allowing for variability in queue length observations to make customers infer high service value from long queues. However, in markets in which customers have different signal strengths, the less informed customers join the longest queue even when there is not much variability in the queue lengths due to limited waiting space. The customers join the longer queue when the arrival rates are low as then the queue length information is the least contaminated by the spillovers due to capacity constraints. Finally, we find that depending on the arrival rate and waiting costs, these externalities provide strong incentives to both service facilities or to either the high-quality or the low-quality service facility to co-locate physically or virtually.

Management Science, 2012

We consider a firm's choice of service rate in the following environment. The firm may have high or low quality, and sells a good to consumers who are heterogeneously informed. Consumers arrive according to a Poisson process and are serviced in a random period of time. If a consumer arrives when another consumer is being serviced, he must join a queue. Consumers observe the length of the queue before making their purchasing decision. The firm may choose a fast or slow service rate. A faster rate requires a costly investment in technology. We show that, in equilibrium, informed consumers join the queue if it is below a threshold. The threshold varies with the quality of the good, so an uninformed consumer updates her belief about quality on observing the length of the queue. The strategy of an uninformed consumer has a "hole": she joins the queue at lengths both below and above the hole, but not at the hole itself. When all consumers are informed, the high-quality firm has a greater incentive to speed up than the low-quality firm. However, the high-quality firm selects a slower service rate than the low-quality firm if there are a lot of queue lengths between the hole in an uninformed consumer's strategy and the threshold at which informed consumers balk from its queue.

International Series in Operations Research & Management Science, 2003

Preface xi 1. INTRODUCTION A non-cooperative game is defined as follows. Let N = {1,. .. , n} be a finite set of players and let A i denote a set of actions available to player i ∈ N. A pure strategy for player i is an action from A i. A mixed strategy corresponds to a probability function which prescribes a randomized rule for selecting an action from A i. Denote by S i the set of strategies available to player i. A strategy profile s = (s 1 ,. .. , s n) assigns a strategy s i ∈ S i to each player i ∈ N. Each player is associated with a real payoff function F i (s). This function specifies the payoff received by player i given that the strategy profile s is adopted by the players. Denote by s −i a profile for the set of players N \ {i}. The function F i (s) = F i (s i , s −i) is assumed to be linear in s i. This means that if s i is a mixture with 1 In case of periodicity, with period d, replace the limit by averaging the limits along d consecutive periods. Note that ∞ s=0 πs(δ) does not necessarily sum up to 1. On one hand, it can be greater than 1 (in fact, can even be unbounded) when more than one recurrent chain exists, and on the other hand it may sum up to 0. An example for the latter case is when λ > µ and δ(s) = join for all s ≥ 0. x F (x, y). We are interested in cases where x(y) is continuous and strictly monotone. Figure 1.1 illustrates a situation where a strategy corresponds to a nonnegative number. It depicts one instance where x(y) is monotone decreasing and another where it is monotone increasing. We call these situations avoid the crowd (ATC) and follow the crowd (FTC), respectively. The rationale behind this terminology is that in an FTC (respectively, ATC) case, the higher the values selected by the others, the higher (respectively, lower) is one's best response. 3 An interesting generalization to this rule is proposed by Balachandran and Radhakrishnan [19]. Suppose that waiting t time units costs Ce at for given parameters C > 0 and a ≥ 0. Then, the expected waiting cost of a customer is ∞ 0 Ce at w(t) dt where w(t) is the density function of the waiting time. In an M/M/1 system w(t) = (µ − λ)e −(µ−λ)t where λ is the arrival rate and µ is the service rate. In this case the expected cost equals C µ−a−λ. Note that the case of linear waiting costs is obtained when a = 0. 4 See Deacon and Sonstelie [43] and Png and Reitman [140] for empirical studies concerning this parameter. Examples for disciplines that are strong and work-conserving are FCFS, LCFS, random order, order which is based on customers payments, and EPS. Service requirements are assumed to be independent and identically distributed. Denote by µ −1 the (common) expected service requirement (i.e., µ is the rate of service). For stability, assume that the system's utilization factor ρ = λ µ is strictly less than 1 (sometimes, when individual optimization leads to stability, this assumption is removed). The following five results hold when the arrival process is Poisson with rate λ, the service distribution is exponential (an M/M/1 model) with rate µ, and the service discipline is strong and work-conserving. They also hold for M/G/1 models when the service discipline is either EPS or LCFS-PR. The probability that n (n ≥ 0) customers are in the system (at arbitrary times as well as at arrival times) is (1 − ρ)ρ n. (1.2) 11 When 3 5λ > 1, commuters appear at a rate so low that even when all of them use the shuttle service, the individual's best response is still to use the bus service. In other words, when λ < 3 5 , using the bus service is a dominant strategy. Chapter 2 OBSERVABLE QUEUES This chapter deals with queueing systems, where an arriving customer observes the length of the queue before making his decisions.