Rouba Ibrahim

Real-Time Delay Estimation Based on Delay History

Motivated by interest in making delay announcements to arriving customers who must wait in call centers and related service systems, we study the performance of alternative real-time delay estimators based on recent customer delay experience. The main estimators considered are: (i) the delay of the last customer to enter service (LES), (ii) the delay experienced so far by the customer at the head of the line (HOL), and (iii) the delay experienced by the customer to have arrived most recently among those who have already completed service (RCS). We compare these delay-history estimators to the standard estimator based on the queue length (QL), commonly used in practice, which requires knowledge of the mean interval between successive service completions in addition to the QL. We characterize performance by the mean squared error (MSE). We do an analysis and conduct simulations for the standard GI/M/s multiserver queueing model, emphasizing the case of large s. We obtain analytical results for the conditional distribution of the delay given the observed HOL delay. An approximation to its mean value serves as a refined estimator. For all three candidate delay estimators, the MSE relative to the square of the mean is asymptotically negligible in the many-server and classical heavy-traffic (HT) limiting regimes.

Wait-Time Predictors for Customer Service Systems with Time-Varying Demand and Capacity

We develop new, improved real-time delay predictors for many-server service systems with a time-varying arrival rate, a time-varying number of servers, and customer abandonment. We develop four new predictors, two of which exploit an established deterministic fluid approximation for a many-server queueing model with those features. These delay predictors can be used to make delay announcements. We use computer simulation to show that the proposed predictors outperform previous predictors.

Real-Time Delay Estimation in Overloaded Multiserver Queues with Abandonments

We use heavy-traffic limits and computer simulation to study the performance of alternative real-time delay estimators in the overloaded GI/GI/s+GI multiserver queueing model, allowing customer abandonment. These delay estimates may be used to make delay announcements in call centers and related service systems. We characterize performance by the expected mean squared error in steady state. We exploit established approximations for performance measures with a nonexponential abandonment-time distribution to obtain new delay estimators that effectively cope with nonexponential abandonment-time distributions.

On the modeling and forecasting of call center arrivals

We review and discuss the key issues in building statistical models for the call arrival process in telephone call centers, and then we survey and compare various types of models proposed so far. These models are used both for simulation and to forecast incoming call volumes to make staffing decisions and build (or update) work schedules for agents who answer those calls. Commercial software and call center managers usually base their decisions solely on point forecasts, given in the form of mathematical expectations (conditional on current information), but distributional forecasts, which come in the form of (conditional) probability distributions, are generally more useful, in particular in the context of simulation. Building realistic models is not simple, because arrival rates are themselves stochastic, time-dependent, dependent across time periods and across call types, and are often affected by external events. As an illustration, we evaluate the forecasting accuracy of selected models in an empirical study with real-life call center data.

Does the Past Predict the Future? The Case of Delay Announcements in Service Systems

Motivated by the recent interest in making delay announcements in large service systems, such as call centers, we investigate the accuracy of announcing the waiting time of the last customer to enter service (LES). In practice, customers typically respond to delay announcements by either balking or by becoming more or less impatient, and their response alters system performance. We study the accuracy of the LES announcement in single-class, multiserver Markovian queueing models with announcement-dependent customer behavior. We show that, interestingly, even in this stylized setting, the LES announcement may not always be accurate. This motivates the need to study its accuracy carefully and to determine conditions under which it is accurate. Since the direct analysis of the system with customer response is prohibitively difficult, we focus on many-server, heavy-traffic analysis instead. We consider the quality-and-efficiency-driven and efficiency-driven many-server, heavy-traffic regimes and prove, under b...

Real-time delay estimation in call centers

We use computer simulation to study the performance of alternative real-time delay estimators in heavily loaded multiserver queueing models. These delay estimates may be used to make delay announcements in call centers and related service systems. We consider the classical delay estimator based on the queue length, QLs, which multiplies the queue length plus one times the mean interval between successive service completions, ignoring customer abandonment. We show that QLs has a superior performance in the GI/M/s model, but that there is a need to go beyond it in the GI/GI/s+GI model, allowing abandonment. To this end, we propose new, simple and effective, delay estimators based on the queue length. We also consider a delay estimator based on recent customer delay history in the system: the delay of the last customer to enter service, LES.

Inter-dependent, heterogeneous, and time-varying service-time distributions in call centers

Traditionally, both researchers and practitioners rely on standard Erlang queueing models to analyze call center operations. Going beyond such simple models has strong implications, as is evidenced by theoretical advances in the recent literature. However, there is very little empirical research to support that body of theoretical work. In this paper, we carry out a large-scale data-based investigation of service times in a call center with many heterogeneous agents and multiple call types. We observe that, for a given call type: (a) the service-time distribution depends strongly on the individual agent, (b) that it changes with time, and (c) that average service times are correlated across successive days or weeks. We develop stochastic models that account for these facts. We compare our models to simpler ones, commonly used in practice, and find that our proposed models have a better goodness-of-fit, both in-sample and out-of-sample. We also perform simulation experiments to show that the choice of model can have a significant impact on the estimates of common measures of quality of service in the call center.

Sharing delay information in service systems: a literature survey

Service providers routinely share information about upcoming waiting times with their customers, through delay announcements. The need to effectively manage the provision of these announcements has led to a substantial growth in the body of literature which is devoted to that topic. In this survey paper, we systematically review the relevant literature, summarize some of its key ideas and findings, describe the main challenges that the different approaches to the problem entail, and formulate research directions that would be interesting to consider in future work.

Delay predictors for customer service systems with time-varying parameters

Motivated by interest in making delay announcements in service systems, we develop new real-time delay predictors that effectively cope with customer abandonment and time-varying parameters. First, we focus on delay predictors exploiting recent customer delay history. We show that time-varying arrival rates can introduce significant prediction bias in delay-history-based predictors when the system experiences alternating periods of overload and underload. We then introduce a new delay-history-based predictor that effectively copes with time-varying arrival rates. Second, we consider a time-varying number of servers. We develop two new predictors which exploit an established deterministic fluid approximation for a many-server queueing model with time-varying demand and capacity. The new predictors effectively cope with those features, often observed in practice. Throughout, we use computer simulation to quantify the performance of the alternative delay predictors.

Flexible Workers or Full-Time Employees? On Staffing Systems with a Blended Workforce

The rise of the blended workforce, which is identified as one of the top workplace trends in 2017, is prompting firms to re-evaluate their staffing strategies. A blended workforce melds, as a deliberate business strategy, contingent workers, e.g., independent contractors or freelancers, with permanent employees. In this paper, we study optimal staffing decisions in service systems with a blended workforce, in the context of a queueingtheoretic framework. Because part of the workforce is flexible, the number of servers in our queueing model is random. Since the staffing problem with a random number of servers is analytically intractable, we formulate two problem relaxations, demonstrate their accuracies in large systems by relying on an asymptotic, manyserver, mode of analysis, and make staffing recommendations for systems with a blended workforce. We demonstrate that staffing decisions in such systems are not straightforward. Indeed, we characterize how these decisions depend on three main factors: (i) the supply-side uncertainty of the flexible agent pool, (ii) operating costs in the system, and (iii) fluctuations in incoming customer demand, and show that it may or may not be cost-effective to staff a blended workforce, depending on the interplay between those factors.