Publication Archive


Research papers that are using SEE Data – Technion and Out-of-Technion Publications before 2013 year, listed chronologically and alphabetically (and early publications using data that were later included in the SEE repositories)

Publication Archive (research papers from 2000-2012 years listed chronologically and alphabetically (and also early publications using data that were later included in the SEE repositories),)
catalog keyyear paper typedata typeSEEStat study name
p52012Atar R. A Diffusion Regime with Non-degenerate Slowdown, Operations Research, Vol. 60, No. 2 (March-April 2012), pp. 490-500

Abstract: We study a diffusion regime, earlier considered by Gurvich, Mandelbaum, Shaikhet and Whitt in the case of the M/M/N queue, that is, in a sense that we make precise, a midpoint between two well-known heavy traffic diffusion regimes, the conventional and the quality and efficiency driven regimes. Unlike the other two, this regime, that we call the non-degenerate slowdown regime, enjoys the property that delay and service time are of the same order of magnitude, a property that is often desirable from a modeling viewpoint. Our main result is that in the case of heterogeneous exponential multi-server systems, this regime gives rise to new limit processes for the sojourn time. In particular, the joint limit law of the delay and service time processes is identified as a reflected Brownian motion and an independent process, whose marginal is a size-biased mixture of exponentials. Our results also motivate the formulation and study of new diffusion control problems, based on sojourn time cost.

journal articlecall centersAnonymousBank
p122012Belitser E., Serra P., van Zanten H. Estimating the Period of a Cyclic Non-homogeneous Poisson Pprocess, Scandinavian Journal of Statistics, July 18, 2012

Abstract: Motivated by applications of Poisson processes for modelling periodic time-varying phenomena, we study a semi-parametric estimator of the period of cyclic intensity function of a non-homogeneous Poisson process. There are no parametric assumptions on the intensity function which is treated as an infinite dimensional nuisance parameter. We propose a new family of estimators for the period of the intensity function, address the identifiability and consistency issues and present simulations which demonstrate good performance of the proposed estimation procedure in practice. We compare our method to competing methods on synthetic data and apply it to a real data set from a call center.

journal articlecall centersUSBank
p132012Jouini O., Koole G., Roubos A. Performance Indicators for Call Centers with Impatience, July 9, 2012

Abstract: An important feature of call center modeling is the presence of impatient customers. In this paper, we consider single-skill call centers including customer abandonments. We study a number of different service level definitions, including all those used in practice, and show how to explicitly compute their performance measures. Based on data from different call centers, new models are defined that extend the common Erlang A model. We show that the new models fit reality very well.

journal articlecall centers AnonymousBank
p42012Mandelbaum A., Momcilovic P., Tseytlin Y. On Fair Routing From Emergency Departments to Hospital Wards: QED Queues with Heterogeneous Servers. Management Science, 58(7), pp. 1273-1291, July 2012

Abstract: The interface between an emergency department and internal wards is often a hospital's bottleneck. Motivated by this interaction in an anonymous hospital, we analyze queueing systems with heterogeneous server pools, where the pools represent the wards, and the servers are beds. Our queueing system, with a single centralized queue and several server pools, forms an inverted-V model. We introduce the randomized most-idle (RMI) routing policy and analyze it in the quality-and efficiency-driven regime, which is natural in our setting. The RMI policy results in the same server fairness (measured by idleness ratios) as the longest-idle-server-first (LISF) policy, which is commonly used in call centers and considered fair. However, the RMI policy utilizes only the information on the number of idle servers in different pools, whereas the LISF policy requires information that is unavailable in hospitals on a real-time basis.

journal articlehospitalsHomeHospital
p142011Aktekin T., Soyer R. Call center arrival modeling: A Bayesian state-space approach, Naval Research Logistics, Vol. 58, Issue 1, pp. 28-42, February 2011

Abstract: In this article, we introduce three discrete time Bayesian state-space models with Poisson measurements, each aiming to address different issues in call center arrival modeling. We present the properties of the models and develop their Bayesian inference. In so doing, we provide sequential updating and smoothing for call arrival rates and discuss how the models can be used for intra-day, inter-day, and inter-week forecasts. We illustrate the implementation of the models by using actual arrival data from a US commercial bank's call center and provide forecasting comparisons.

journal articlecall centersUSBank
p162011De Livera A. M., Hyndman R. J., Snyder R.D. Forecasting Time Series with Complex Seasonal Patterns using Exponential Smoothing, Journal of the American Statistical Association, Vol. 106, No. 496 (December 2011), pp. 1513-1527

Abstract: A new innovations state space modeling framework, incorporating Box-Cox transformations, Fourier series with time varying coefficients and ARMA error correction, is introduced for forecasting complex seasonal time series that cannot be handled using existing forecasting models. Such complex time series include time series with multiple seasonal periods, high frequency seasonality, non-integer seasonality and dual-calendar effects. Our new modelling framework provides an alternative to existing exponential smoothing models, and is shown to have many advantages. The methods for initialization and estimation, including likelihood evaluation, are presented, and analytical expressions for point forecasts and interval predictions under the assumption of Gaussian errors are derived, leading to a simple, comprehensible approach to forecasting complex seasonal time series. Our trigonometric formulation is also presented as a means of decomposing complex seasonal time series, which cannot be decomposed using any of the existing decomposition methods. The approach is useful in a broad range of applications, and we illustrate its versatility in three empirical studies where it demonstrates excellent forecasting performance over a range of prediction horizons. In addition, we show that our trigonometric decomposition leads to the identification and extraction of seasonal components, which are otherwise not apparent in the time series plot itself.

journal articlecall centersUSBank
p182010Aktekin T., Soyer R. Bayesian Modeling of Queues in Call Centers, February 22, 2010

Abstract: Queuing models have been extensively used in call center analysis for obtaining performance measures and for developing staffing policies. However, almost all of this work have been from a pure probabilistic point of view and have not addressed issues of statistical inference. In this paper, we develop Bayesian analysis of call center queuing models by describing uncertainty about system primitives probabilistically. We consider models with impatient customers and develop details of Bayesian inference for queues with abandonment such as the M/M/s+M model. We illustrate the implementation of the Bayesian models using actual arrival, service, and abandonment data from call centers. We compare the M/M/s+M model results with those from the M/M/s queues and discuss implications of ignoring abandonment.

technical reportcall centersAnonymousBank
p152010Bertsimas D., Doan X. V. Robust and Data-Driven Approaches to Call Centers, European Journal of Operational Research, Vol. 207, Issue 2, December 2010, pp.1007-1085 

Abstract: We propose both robust and data-driven approaches to a fluid model of call centers that incorporates random arrival rates with abandonment to determine staff levels and dynamic routing policies. We test the resulting models with real data obtained from the call center of a US bank. Computational results show that the robust fluid model is significantly more tractable as compared to the data-driven one and produces overall better solutions to call centers in most experiments.

journal articlecall centersUSBank
p22010Gans N., Liu N., Mandelbaum A., Shen H., Ye H. Service Times in Call Centers: Agent Heterogeneity and Learning with some Operational Consequences. To appear in a book on the occasion of Larry Brown’s 70th birthday, December 2010

Abstract: Telephone call centers are data-rich environments that, until recently, have not received sustained attention from academics. For about a decade now, we are fortunate to have worked with our colleague, mentor and friend, Larry Brown, on the collection and analysis of large call-center datasets. This work has provided many fascinating windows into the world of call-center operations, stimulating further research and affecting management practice. Larry's inexhaustible curiosity and creativity, sharp insight and unique technical power, have continuously been an inspiration to us. We look forward to collaborating and learning from him on many occasions to come. In this paper, we study operational heterogeneity of call center agents. Our proxy for heterogeneity is agents' service times (call durations), a performance measure that prevalently enjoys tight management control. Indeed, managers of large call centers argue that a 1-second increase/decrease in average service time can translate into additional/reduced operating costs on the order of millions of dollars per year. We are motivated by an empirical analysis of call-center data, which identifies both short- term and long-term factors associated with agent heterogeneity. Operational consequences of such heterogeneity are then illustrated via discrete event simulation. This highlights the potential benefits of analyzing individual agents' operational histories. We are thus naturally led to a detailed analysis of agents' learning-curves, which reveals various learning patterns and opens up new research opportunities.

journal articlecall centersUSBank
p172010Kearton K. Correlating Temporal Rules to Time-Series Data with Rule-Based Intuition, March 2010

Abstract: Analysts are frequently confronted with time-series data. A simple form is magnitude (or count) and time frame, whether the data is number of e-mails sent, number of cell phones called, purchases made by volume or cost, or a variety of other time-derived data. Studying the temporal dimension of data allows analysts more opportunities to find relational ties and trends in data, classify or group like activity, and even help narrow the search space of massively complex and large datasets. This thesis presents a new approach called the Rule Based Intuition (RBI) system that can evaluate time-series data by finding the best fitting rule, from a repository of known rules, to quickly infer information about the data. This approach is most applicable for analysts viewing large sets of data who wish to classify or correlate data from users’ temporal activity.

thesiscall centersAnonymousBank
p62010Khudyakov P., Feigin P., Mandelbaum A. Designing a Call Center with an IVR (Interactive Voice Response). QUESTA 2010.

Abstract: A call center is a popular term for a service operation that caters to customers’ needs via the telephone. A call center typically consists of agents that serve customers, telephone lines, an Interactive Voice Response (IVR) unit, and a switch that routes calls to agents. In this paper we study a Markovian model for a call center with an IVR. We calculate operational performance measures, such as the probability for a busy signal and the average wait time for an agent. Exact calculations of these measures are cumbersome and they lack insight. We thus approximate the measures in an asymptotic regime known as QED (Quality & Efficiency Driven) or the Halfin-Whitt regime, which accomodates moderate to large call centers. The approximations are both insightful and easy to apply (for up to 1000’s of agents). They yield, as special cases, known and novel approximations for the M/M/N/N (Erlang-B), M/M/S (Erlang-C) and M/M/S/N queue.

journal articlecall centersUSBank
p32010Khudyakov P., Gorfine M., Feigin P. Test for Equality of Baseline Hazard Functions for Correlated Survival Data using Frailty Models

Abstract: In this work we provide a new class of test statistics for hypothesis testing of the equality of the baseline hazard functions for correlated survival data under frailty models. The asymptotic distribution of the test statistics is investigated theoretically under the null hypothesis and certain local alternatives. We also provide a simple variance estimator. The properties of the test statistics, under finite sample size, is being studied by an extensive simulation study and we verify the control of Type I error and our proposed sample size formula. To the best of our knowledge, this is the first work for comparing the baseline hazard functions of correlated survival outcomes with covariates and frailty models. The utility of our proposed estimating technique is illustrated by the analysis of the call center data of an Israeli commercial company that processes up to 100,000 calls per day and the analysis of the breast cancer data of the Washington Ashkenazi Kin-Cohort family study.

journal articlecall centers
p12010Feldman Z., Mandelbaum A. Using Simulation-Based Stochastic Approximation to Optimize Staffing of Systems with Skills-Based Routing. Proceedings of the 2010 Winter Simulation Conference, December 2010

Abstract:In this paper, we consider the problem of minimizing the operational costs of systems with Skills-Based-Routing (SBR). In such systems, customers of multiple classes are routed to servers of multiple skills. In the settings we consider, each server skill is associated with a corresponding cost, and service level can either appear as a strong constraint or incur a cost.
The solution we propose is based on the Stochastic Approximation (SA) approach. Since SBR models are analytically intractable in general, we use computer simulation to evaluate service-level measures. Under the assumption of convexity of the service-level as functions in staffing levels, SA provides an analytical proof of convergence, together with a rate of convergence. We show, via numerical examples, that although the convexity assumption does not hold for all cases and all types of service-level objectives, the algorithm nevertheless identifies the optimal solution.

conference papercall centersUSBank
p72009Aldor-Noiman S., Feigin P.D., Mandelbaum A. Workload Forecasting for a Call Center: Methodology and a Case Study. The Annals of Applied Statistics, vol. 3, No.4, pp. 1403-1447, 2009 

Abstract: Today’s call center managers face multiple operational decision-making tasks. One of the most common is determining the weekly staffing levels to ensure customer satisfaction and meeting their needs while minimizing service costs. An initial step for producing the weekly schedule is forecasting the future system loads which involves predicting both arrival counts and average service times. We introduce an arrival count model which is based on a mixed Poisson process approach. The model is applied to data from an Israeli Telecom company call center. In our model, we also consider the effect of events such as billing on the arrival process and we demonstrate how to incorporate them as exogenous variables in the model. After obtaining the forecasted system load, in large call centers, a manager can choose to apply the QED (Quality-Efficiency Driven) regime’s “squareroot staffing” rule in order to balance the offered-load per server with the quality of service. Implementing this staffing rule requires that the forecasted values of the arrival counts and average service times maintain certain levels of precision. We develop different goodness of fit criteria that help determine our model’s practical performance under the QED regime. These show that during most hours of the day the model can reach desired precision levels.

journal articlecall centersILTelecom
p82009Gurvich I., Liberman P., Mandelbaum A. Empirical Analysis of Skill Based Routing in Call Centers: A Queueing-Science Perspective. 2009 MIT MSOM Conference.conference papercall centers
p222008Ausin M. C., Wiper M. P., Lillo R. E. Bayesian Prediction of the Transient Behaviour and Busy Period in Short and Long-Tailed GI/G/1 Queueing Systems, January 2008

Abstract: Bayesian inference for the transient behavior and duration of a busy period in a single server queueing system with general, unknown distributions for the interarrival and service times is investigated. Both the interarrival and service time distributions are approximated using the dense family of Coxian distributions. A suitable reparameterization allows the definition of a non-informative prior and Bayesian inference is then undertaken using reversible jump Markov chain Monte Carlo methods. An advantage of the proposed procedure is that heavy tailed interarrival and service time distributions such as the Pareto can be well approximated. The proposed procedure for estimating the system measures is based on recent theoretical results for the Coxian/Coxian/1 system. A numerical technique is developed for every MCMC iteration so that the transient queue length and waiting time distributions and the duration of a busy period can be estimated. The approach is illustrated with both simulated and real data.

journal articlecall centersAnonymousBank
p202008Goh K.I., Barabási A.L. Burstiness and memory in complex systems, EPL, Vol. 81, Num. 4, February 2008

Abstract: The dynamics of a wide range of real systems, from email patterns to earthquakes, display a bursty, intermittent nature, characterized by short timeframes of intense activity followed by long times of no or reduced activity. The understanding of the origin of such bursty patterns is hindered by the lack of tools to compare different systems using a common framework. Here we propose to characterize the bursty nature of real signals using orthogonal measures quantifying two distinct mechanisms leading to burstiness: the interevent time distribution and the memory. We find that while the burstiness of natural phenomena is rooted in both the interevent time distribution and memory, for human dynamics memory is weak, and the bursty character is due to the changes in the interevent time distribution. Finally, we show that current models lack in their ability to reproduce the activity pattern observed in real systems, opening up avenues for future work.

journal articlecall centers AnonymousBank
p192008Shen H., Huang J. Z. Interday Forecasting and Intraday Updating of Call Center Arrivals, Manufacturing & Service Operations Management, Vol. 10, No. 3, summer 2008, pp. 391–410

Abstract: Accurate forecasting of call arrivals is critical for staffing and scheduling of a telephone call center. We develop methods for interday and dynamic intraday forecasting of incoming call volumes. Our approach is to treat the intraday call volume profiles as a high-dimensional vector time series. We propose first to reduce the dimensionality by singular value decomposition of the matrix of historical intraday profiles and then to apply time series and regression techniques. Our approach takes into account both interday (or day-to-day) dynamics and intraday (or within-day) patterns of call arrivals. Distributional forecasts are also developed. The proposed methods are data driven, appear to be robust against model assumptions in our simulation studies, and are shown to be very competitive in out-of-sample forecast comparisons using two real data sets. Our methods are computationally fast; it is therefore feasible to use them for real-time dynamic forecasting.

journal articlecall centersUSBank
p212008Taylor J.W. A Comparison of Univariate Time Series Methods for Forecasting Intraday Arrivals at a Call Center, Management Science, February 2008, Vol. 54, pp. 253–265

Abstract: Predictions of call center arrivals are a key input to staff scheduling models. It is, therefore, surprising that simplistic forecasting methods dominate practice, and that the research literature on forecasting arrivals is so small. In this paper, we evaluate univariate time series methods for forecasting intraday arrivals for lead times from one half-hour ahead to two weeks ahead. We analyze five series of intraday arrivals for call centers operated by a retail bank in the UK. A notable feature of these series is the presence of both an intraweek and an intraday seasonal cycle. The methods considered include seasonal ARIMA modeling; periodic AR modeling; an extension of Holt-Winters exponential smoothing for the case of two seasonal cycles; robust exponential smoothing based on exponentially weighted least absolute deviations regression; and dynamic harmonic regression, which is a form of unobserved component state space modeling. Our results indicate strong potential for the use of seasonal ARIMA modeling and the extension of Holt-Winters for predicting up to about two to three days ahead and that, for longer lead times, a simplistic historical average is difficult to beat. We find a similar ranking of methods for call center data from an Israeli bank.

journal articlecall centersAnonymousBank
p232007Gorst-Rasmussen A., Hansen M.B. Asymptotic Inference for Waiting Times and Patiences in Queues with Abandonment, July 2007

Abstract: Motivated by applications in call center management, we propose a framework based on empirical process techniques for inference about waiting time and patience distributions in multiserver queues with abandonment. The framework rigorises heuristics based on survival analysis of independent and identically distributed observations by allowing correlated waiting times. Assuming a regenerative structure of offered waiting times, we establish asymptotic properties of estimators of limiting distribution functions and derived functionals. We discuss construction of bootstrap confidence intervals and statistical tests, including a simple bootstrap two-sample test for comparing patience distributions. A small simulation study and a real data example are presented.

journal articlecall centersAnonymousBank
p262006Huang J. Z., Liu N., Pourahmadi M., Liu L. Covariance Matrix Selection and Estimation via Penalized Normal Likelihood, Biometrika (March 2006), Vol. 93, No. 1, pp. 85–98

Abstract: We propose a nonparametric method for identifying parsimony and for producing a statistically efficient estimator of a large covariance matrix. We reparameterise a covariance matrix through the modified Cholesky decomposition of its inverse or the one-step-ahead predictive representation of the vector of responses and reduce the nonintuitive task of modelling covariance matrices to the familiar task of model selection and estimation for a sequence of regression models. The Cholesky factor containing these regression coefficients is likely to have many off-diagonal elements that are zero or close to zero. Penalised normal likelihoods in this situation with L1 and L2 penalties are shown to be closely related to Tibshirani’s (1996) LASSO approach and to ridge regression. Adding either penalty to the likelihood helps to produce more stable estimators by introducing shrinkage to the elements in the Cholesky factor, while, because of its singularity, the L1 penalty will set some elements to zero and produce interpretable models. An algorithm is developed for computing the estimator and selecting the tuning parameter. The proposed maximum penalised likelihood estimator is illustrated using simulation and a real dataset involving estimation of a 102 x 102 covariance matrix.

journal articlecall centersUSBank
p272006Shen H., Brown L.D. Nonparametric Modeling of Time-varying Customer Service Times at a Bank Call Center, January 2006

Abstract: Call centers becoming increasingly important in our modern commerce. We are interested in modeling the time-varying pattern of average customer service times at a bank call center. Understating such a pattern is essential for efficient operation of a call center. The call service times are show to be lognormally distributed. Motivated by this observation and the important application, we propose a new method for inference about nonparametric regression curves when the errors are lognormally distributed. Estimates and pointwise confidence bands are developed. The method builds upon the special relationship between the lognormal distribution and the normal distribution, and improves upon a naïve estimation procedure that ignores this distributional structure. Our approach includes local nonparametric estimation for both the mean function and the heteroscedastic variance function of the logged data, and uses local polynomial regression as a fitting tool. A simulation study is performed to illustrate the method. We then apply the method to model the time-varying patterns of mean service times for different types of customer calls. Several operationally interesting finding are obtained and discussed.

journal articlecall centersAnonymousBank
p242006Thümmler A., Buchholz P., Telek M. A Novel Approach for Phase-Type Fitting with the EM Algorithm, July 2006

Abstract: The representation of general distributions or measured data by phase-type distributions is an important and non-trivial task in analytical modeling. Although a large number of different methods for fitting parameters of phase-type distributions to data traces exist, many approaches lack efficiency and numerical stability. In this paper, a novel approach is presented that fits a restricted class of phase-type distributions, namely mixtures of Erlang distributions, to trace data. For the parameter fitting an algorithm of the expectation maximization type is developed. The paper shows that these choices result in a very efficient and numerically stable approach which yields phase-type approximations for a wide range of data traces that are as good or better than approximations computed with other less efficient and less stable fitting methods. To illustrate the effectiveness of the proposed fitting algorithm, we present comparative results for our approach and two other methods using six benchmark traces and two real traffic traces as well as quantitative results from queueing analysis.

journal articlecall centersAnonymousBank
p252006Weinberg J., Brown L.D., Stroud J.R. Bayesian Forecasting of an Inhomogeneous Poisson Process with Applications to Call Center Data, June 2006

Abstract: A call center is a centralized hub where customer and other telephone calls are dealt with by an organization. In today’s economy, they have become the primary point of contact between customers and businesses. Accurate prediction of the call arrival rate is therefore indispensable for call center practitioners to staff their call center efficiently and cost effectively. This article proposes a multiplicative model for modeling and forecasting within-day arrival rates to a US commercial bank’s call center. Markov chain Monte Carlo sampling methods are used to estimate both latent states and model parameters. One-day-ahead density forecasts for the rates and counts are provided. The calibration of these predictive distributions is evaluated through probability integral transforms. Furthermore, we provide one-day-ahead forecasts comparisons with classical statistical models. Our predictions show significant improvements of up to 25% over these standards. A sequential Monte Carlo algorithm is also proposed for sequential estimation and forecasts of the model parameters and rates.

journal articlecall centersUSBank
p282005Bhulai S., Kan W.H., Marchiori E. Nearest Neighbour Algorithms for Forecasting Call Arrivals in Call Centers, August 2005.

Abstract: In this paper we study a nearest neighbour algorithm for forecasting call arrivals to call centers. The algorithm does not require an underlying model for the arrival rates and it can be applied to historical data without pre-processing it. We show that this class of algorithms provides a more accurate forecast when compared to the conventional method that simply takes averages. The nearest neighbour algorithm with the Pearson correlation distance function is also able to take correlation structures, that are usually found in call center data, into account. Numerical experiments show that this algorithm provides smaller errors in the forecast and better staffing levels in call centers. The results can be used for a more flexible workforce management in call centers.

journal articlecall centersAnonymousBank
p92005Brown L., Gans N., Mandelbaum A., Sakov A., Shen H., Zeltyn S., Zhao L. Statistical Analysis of a Telephone Call Center : A Queueing-Science Perspective. (2005) Journal of the American Statistical Association, Vol 100: 36-50. 

Abstract: A call center is a service network in which agents provide telephone-based services. Customers who seek these services are delayed in tele-queues. This article summarizes an analysis of a unique record of call center operations. The data comprise a complete operational history of a small banking call center, call by call, over a full year. Taking the perspective of queueing theory, we decompose the service process into three fundamental components: arrivals, customer patience, and service durations. Each component involves different basic mathematical structures and requires a different style of statistical analysis. Some of the key empirical results are sketched, along with descriptions of the varied techniques required. Several statistical techniques are developed for analysis of the basic components. One of these techniques is a test that a point process is a Poisson process. Another involves estimation of the mean function in a nonparametric regression with lognormal errors. A new graphical technique is introduced for nonparametric hazard rate estimation with censored data. Models are developed and implemented for forecasting of Poisson arrival rates. Finally, the article surveys how the characteristics deduced from the statistical analyses form the building blocks for theoretically interesting and practically useful mathematical models for call center operations.

journal articlecall centersAnonymousBank
p292005Shen H., Huang J. Z. Analysis of Call Centre Arrival Data Using Singular Value Decomposition, Applied Stochastic Models in Business and Industry, May 2005.

Abstract: We consider the general problem of analysing and modelling call centre arrival data. A method is described for analysing such data using singular value decomposition (SVD). We illustrate that the outcome from the SVD can be used for data visualization, detection of anomalies (outliers), and extraction of significant features from noisy data. The SVD can also be employed as a data reduction tool. Its application usually results in a parsimonious representation of the original data without losing much information. We describe how one can use the reduced data for some further, more formal statistical analysis. For example, a short term forecasting model for call volumes is developed, which is multiplicative with a time series component that depends on day of the week. We report empirical results from applying the proposed method to some real data collected at a call center of a large-scale U.S. financial organization. Some issues about forecasting call volumes are also discussed.

journal articlecall centersUSBank
p102005Zeltyn S., Mandelbaum A. Call centers with impatient customers: many-server asymptotics of the M/M/n+G queue. QUESTA, 51 (3/4), 361-402, 2005

Abstract:The subject of the present research is the M/M/n + G queue. This queue is characterized by Poisson arrivals at rate λ, exponential service times at rate μ, n service agents and generally distributed patience times of customers. The model is applied in the call center environment, as it captures the tradeoff between operational efficiency (staffing cost) and service quality (accessibility of agents).
In our research, three asymptotic operational regimes for medium to large call centers are studied. These regimes correspond to the following three staffing rules, as λ and n increase indefinitely and μ held fixed:
Efficiency-Driven (ED): n ≈ (λ/μ)⋅(1−γ),γ>0,
Quality-Driven (QD): n ≈ (λ/μ)⋅(1+γ),γ>0, and
Quality and Efficiency Driven (QED): n ≈ λ/μ+β√(λ/μ),−∞<β<∞.

In the ED regime, the probability to abandon and average wait converge to constants. In the QD regime, we observe a very high service level at the cost of possible overstaffing. Finally, the QED regime carefully balances quality and efficiency: agents are highly utilized, but the probability to abandon and the average wait are small (converge to zero at rate 1/√n).
Numerical experiments demonstrate that, for a wide set of system parameters, the QED formulae provide excellent approximation for exact M/M/n + G performance measures. The much simpler ED approximations are still very useful for overloaded queueing systems.
Finally, empirical findings have demonstrated a robust linear relation between the fraction abandoning and average wait. We validate this relation, asymptotically, in the QED and QD regimes.

journal articlecall centersUSBank
p302004Chassioti E., Worthington D. J. A New Model for Call Centre Queue Management, The Journal of the Operational Research Society, Vol. 55, No. 12 (Dec., 2004), pp. 1352–1357.

Abstract: A new model for call centre queue management is described. It incorporates important features of call centre queues and is shown to produce results that are very different from those produced by the more usual models. The analytic approach is easy to apply, and is used to offer some interesting insights for call center queue management.

journal articlecall centersAnonymousBank
p312002Brown L. D., Zhao L. H. A Test for the Poisson Distribution, Sankhya: The Indian Journal of Statistics, 2002, Vol. 64, Series A, Pt. 3, pp. 611–625.

Abstract: We consider the problem of testing whether a sample of observations comes from a single Poisson distribution. Of particular interest is the alternative that the observations come from Poisson distributions with different parameters. Such a situation would correspond to the frequently discussed situation of overdispersion. We propose a new test for this problem that is based on Anscombe’s variance stabilizing transformation. There are a number of tests commonly proposed, and we compare the performance of these tests under the null hypothesis with that of our new test. We find that the performance of our test is competitive with the two best of these. The asymptotic distribution of the new test is derived and discussed. Use of these tests is illustrated through two examples of analysis of call-arrival times from a telephone call center. The example facilitates careful discussion of the performance of the tests for small parameter values and moderately large sample sizes.

journal articlecall centersAnonymousBank
p112001Mandelbaum A., Sakov A., Zeltyn S. Empirical Analysis of a Call Center, Technion Report, Awarded the Students' Mitchner Prize for "Quality Sciences and Quality Management", Technion, 2001

Introductiont: Call center is the common term for describing a telephone-based human-service operation. A call center provides tele-services, namely services in which the customers and the service agents are remote from each other. The agents, who sit in cubicles, constitute the physical embodiment of the call center: with numbers varying from very few to many hundreds, they serve customers over the phone, while facing a computer terminal that outputs and inputs customer data. The customers, who are only virtually present, are either being served, or they are waiting in, what we call, tele-queues: up to possibly thousands of customers sharing a phantom queue, invisible to each other and the agents serving them, waiting and accumulating impatience until one of two things happens: an agent is allocated to serve them (through a supporting software), or they abandon the tele-queue, plausibly due to impatience that has built up to exceed their anticipated worth of the service. The world of call centers is vast: some estimate that 70% of all customer-business interactions occur in call centers; that $700 billions in goods and services were sold through call centers in 1997, and this figure has been expanding 20% annually; and that 3% of the U.S. working population is currently employed in call centers. (This amounts to 1.55 million agents, and some estimates actually go up to 6 million). The leading-edge call center is a complex socio-technical system: its hundreds of agents could cater to thousands of customers per hour, in a way that the average wait is measured in a few seconds and agents' utilization exceeds 90%. Such simultaneous attainment of superb service quality with extreme resource efficiency is achievable, despite ample stochastic variability, through scale-economies of unparalleled magnitudes; and all this is possible only in the unique frictionless environment of computer-telephony integration and automatic call distribution. Some view call centers as the business frontiers and others as the sweat-shops of the 21st century. Either way, call centers provide ample uncharted challenges for researchers in multi-disciplines, from the soft (e.g. Psychology, Sociology), through functional management (e.g. Marketing, Information Systems), to the exact (e.g. Computer Science, Mathematics). One should note that the challenges are, in fact, expanding: there exist an increasing number of multi-media call centers that can provide, in addition to the telephone, also video, Internet, fax and e-mail services. (The term customer contact center has been used to accommodate this broader connotation of a tele-service.) Our paper targets primarily researchers in Statistics, Operations-Research (especially Queueing Theory, and even more so Queueing Science, Operations Management, and Industrial Engineering. We believe that it is also of interest to researchers in telecommunications, and of use to managers that either run or oversee the operations of medium to large call centers.

technion reportcall centersAnonymousBank
p321996Asmussen S., Nerman O., Olsson M. Fitting Phase-type Distributions via the EM Algorithm, Scandinavian Journal of Statistics, Vol. 23, No. 4 (Dec, 1996), pp. 419–441. (This research uses data that was later absorbed into SEE repositories.)

Abstract: Estimation from sample data and density approximation with phase-type distributions are considered. Maximum likelihood estimation via the EM algorithm is discussed and performed for some data sets. An extended EM algorithm is used to minimize the information divergence (maximize the relative entropy) in the density approximation case. Fits to Weibull, log normal, and Erlang distributions are used as illustrations of the latter.

journal articlecall centers