Managing Information in Queues: The Impact of Giving Delayed Information to Customers (original) (raw)

A Stochastic Analysis of Queues with Customer Choice and Delayed Information

Mathematics of Operations Research, 2020

Many service systems provide queue length information to customers, thereby allowing customers to choose among many options of service. However, queue length information is often delayed, and it is often not provided in real time. Recent work by Dong et al. [Dong J, Yom-Tov E, Yom-Tov GB (2018) The impact of delay announcements on hospital network coordination and waiting times. Management Sci. 65(5):1969–1994.] explores the impact of these delays in an empirical study in U.S. hospitals. Work by Pender et al. [Pender J, Rand RH, Wesson E (2017) Queues with choice via delay differential equations. Internat. J. Bifurcation Chaos Appl. Sci. Engrg. 27(4):1730016-1–1730016-20.] uses a two-dimensional fluid model to study the impact of delayed information and determine the exact threshold under which delayed information can cause oscillations in the dynamics of the queue length. In this work, we confirm that the fluid model analyzed by Pender et al. [Pender J, Rand RH, Wesson E (2017) Que...

Queues with Choice via Delay Differential Equations

International Journal of Bifurcation and Chaos

Delay or queue length information has the potential to influence the decision of a customer to join a queue. Thus, it is imperative for managers of queueing systems 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 [Formula: see text]. We show that the delay can cause oscillations or asynchronous behavior in the model based on the value of [Formula: see text]. 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 asynchronou...

Breaking the Symmetry in Queues with Delayed Information

International Journal of Bifurcation and Chaos, 2021

Giving customers queue length information about a service system has the potential to influence the decision of a customer to join a queue. Thus, it is imperative for managers of queueing systems to understand how the information that they provide will affect the performance of the system. To this end, we construct and analyze a two-dimensional deterministic fluid model that incorporates customer choice behavior based on delayed queue length information. Reports in the existing literature always assume that all queues have identical parameters and the underlying dynamical system is symmetric. However, in this paper, we relax this symmetry assumption by allowing the arrival rates, service rates, and the choice model parameters to be different for each queue. Our methodology exploits the method of multiple scales and asymptotic analysis to understand how to break the symmetry. We find that the asymmetry can have a large impact on the underlying dynamics of the queueing system.

An Asymptotic Analysis of Queues with Delayed Information and Time Varying Arrival Rates

arXiv: Dynamical Systems, 2017

Understanding how delayed information impacts queueing systems is an important area of research. However, much of the current literature neglects one important feature of many queueing systems, namely non-stationary arrivals. Non-stationary arrivals model the fact that customers tend to access services during certain times of the day and not at a constant rate. In this paper, we analyze two two-dimensional deterministic fluid models that incorporate customer choice behavior based on delayed queue length information with time varying arrivals. In the first model, customers receive queue length information that is delayed by a constant Delta. In the second model, customers receive information about the queue length through a moving average of the queue length where the moving average window is Delta. We analyze the impact of the time varying arrival rate and show using asymptotic analysis that the time varying arrival rate does not impact the critical delay unless the frequency of the...

Joining Longer Queues: Information Externalities in Queue Choice

Social Science Research Network, 2008

A classic example that illustrates how observed customer behavior impacts other customers' decisions is the selection of a restaurant whose quality is uncertain. Customers often choose the busier restaurant, inferring that other customers in that restaurant know something that they do not. In an environment with random arrival and service times, customer behavior is reflected in the lengths of the queues that form at the individual servers. Therefore, queue lengths could signal two factors-potentially higher arrivals to the server or potentially slower service at the server. In this paper, we focus on both factors when customers' waiting costs are negligible. This allows us to understand how information externalities due to congestion impact customers' service choice behavior.

Measuring the Effect of Queues on Customer Purchases

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.

Licensed Under Creative Commons Attribution CC BY Customer Impatience in Multiserver Queues

2015

In the modeling of many queuing systems, it is assumed that customers who arrive stay on till they receive service. In real life, this does not always happen. Arriving customer may decide against joining the system. In queuing parlance, this is known as balking. In this paper, we shall assume that customers may balk if service is not instantly available. Even if a customer joins the system, the customer may withdraw and leave without completely receiving service. This is known as reneging. In this paper, we consider a multiserver Markovian queuing system where customers may balk as well as renege. In addition to the traditional performance measures, some freshly designed ones have also been presented. The relevance of this work stems from the fact that not withstanding related analysis of similar customer behavior already available in literature, explicit closed form expressions are still not available for M/M/k model. In this paper, we present the same. A numerical problem with des...

Analysis and Comparison of Queues with Different Levels of Delay Information

Management Science, 2007

Information about delays can enhance service quality in many industries. Delay information can take many forms, with different degrees of precision. Different levels of information have different effects on customers and so on the overall system. The goal of this research is to explore these effects. We first consider a queue with balking under three levels of delay information: No information, partial information (the system occupancy) and full information (the exact waiting time). We assume Poisson arrivals, independent, exponential service times, and a single server. Customers decide whether to stay or balk based on their expected waiting costs, conditional on the information provided. By comparing the three systems, we identify some important cases where more accurate delay information improves performance. In other cases, however, information can actually hurt the provider or the customers.

Equilibrium in Queues Under Unknown Service Times and Service Value

Operations Research, 2014

In Naor's seminal queue-joining model, queue-joining probabilities decrease monotonously in the queue length; the longer the queue, the fewer consumers join. In practice, empirical evidence indicates that queue-joining probabilities may not always be decreasing in the queue length. For example, for restaurants, long queues may sometimes be more attractive than short queues. We rationalize non-monotonic strategies by relaxing the information assumptions in Naor's model. Instead of assuming that the expected service time and service value are common knowledge, we assume that they are unknown to consumers, but positively correlated. Under such informational assumptions, we show that equilibria may emerge for which the joining probability increases in the queue length. We refer to these as "sputtering equilibria." We discuss when and why such sputtering equilibria exist for discrete as well as continuously distributed priors on the expected service time (with positively correlated service value).

To Queue or Not to Queue: Equilibrium Behavior in Queueing Systems

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.