Limiting the oscillations in queues with delayed information through a novel type of delay announcement (original) (raw)

Managing Information in Queues: The Impact of Giving Delayed Information to Customers

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\DeltaDelta. We show that the delay can cause oscillations or asynchronous behavior in the model based on the value of Delta\DeltaDelta. 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...

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...

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.

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...

Call Centers with Delay Information: Models and Insights

Manufacturing & Service Operations Management, 2011

In this paper, we analyze a call center with impatient customers. We study how informing customers about their anticipated delays affects performance. Customers react by balking upon hearing the delay announcement, and may subsequently renege, particularly if the realized waiting time exceeds the delay that has originally been announced to them. The balking and reneging from such a system are a function of the delay announcement. Modeling the call center as an M/M/s+M queue with endogenized customer reactions to announcements, we analytically characterize performance measures for this model. The analysis allows us to explore the role announcing different percentiles of the waiting time distribution, i.e., announcement coverage, plays on subsequent performance in terms of balking and reneging. Through a numerical study we explore when informing customers about delays is beneficial, and what the optimal coverage should be in these announcements. It is shown how managers of a call center with delay announcements can control the tradeoff between balking and reneging, through their choice of announcements to be made.

The effects of information on a queue with balking and phase‐type service times

Naval Research Logistics, 2008

This article generalizes the models in Guo and Zipkin, who focus on exponential service times, to systems with phasetype service times. Each arriving customer decides whether to stay or balk based on his expected waiting cost, conditional on the information provided. We show how to compute the throughput and customers' average utility in each case. We then obtain some analytical and numerical results to assess the effect of more or less information. We also show that service-time variability degrades the system's performance.

On the Benefits of Providing Timely Information in Ticket Queues with Balking and Calling Times

Mathematics

We study a phenomenon causing server time loss in ticket queues with balking and calling time. A customer who balks from the queue after printing a ticket leaves a virtual entity in the queue that requires server time to be cleared. The longer the queue, the larger the proportion of customers abandoning their place, and the larger the server time loss due to calling customers that left the queue. The solution is suggested by giving the customer the best possible estimate of her expected waiting time before printing a ticket, thus ensuring that, if she balks, no number in the queue is created that will waste server time. Although partially observable ticket queues have been studied in the literature, the addition of a calling time for absent customers creates a new type of problem that has been observed in real life but has not been formally addressed yet. We analyze this stochastic system, formulate its steady state probabilities, and calculate the system’s performance measures. The...

Improving Service by Informing Customers About Anticipated Delays

Management Science, 1999

This paper studies alternative ways to manage a multi-server system such as a telephone call center. Three alternatives can be described succinctly by: (i) blocking, (ii) reneging and (iii) balking. The first alternative -blocking -is to have no provision for waiting. The second alternative is to allow waiting, but neither inform customers about anticipated delays nor provide state information to allow arriving customers to predict delays. The second alternative tends to yield higher server utilizations. The first alternative tends to reduce to the second, without the first-come firstserved service discipline, when customers can easily retry, as with automatic redialers in telephone access. The third alternative is to both allow waiting and inform customers about anticipated delays. The third alternative tends to cause balking when all servers are busy (abandonment upon arrival) instead of reneging (abandonment after waiting). Birth-and-death process models are proposed to describe the performance with each alternative. Algorithms are developed to compute the conditional distributions of the time to receive service and the time to renege given each outcome.

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.

Nonlinear Dynamics in Queueing Theory: Determining the Size of Oscillations in Queues with Delay

SIAM Journal on Applied Dynamical Systems

Internet and mobile services often provide waiting time or queue length information to customers. This information allows a customer to determine whether to remain in line or, in the case of multiple lines, better decide which line to join. Unfortunately, there is usually a delay associated with waiting time information. Either the information itself is stale, or it takes time for the customers to travel to the service location after having received the information. Recent empirical and theoretical work uses functional dynamical systems as limiting models for stochastic queueing systems. This work has shown that if information is delayed long enough, a Hopf bifurcation can occur and cause unwanted oscillations in the queues. However, it is not known how large the oscillations are when a Hopf bifurcation occurs. To answer this question, we model queues with functional differential equations and implement two methods for approximating the amplitude of these oscillations. The first approximation is analytic and yields a closed-form approximation in terms of the model parameters. The second approximation uses a statistical technique, and delivers highly accurate approximations over a wider range of parameters.