Modeling and forecasting call center arrivals: A literature survey and a case study

Ibrahim, Raafat N; Ye, Han; L’Ecuyer, Pierre; Shen, Haipeng

doi:10.1016/j.ijforecast.2015.11.012

Cited by 86 publications

(56 citation statements)

References 48 publications

(122 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…In those systems, Empirical evidence shows that if arrivals are from a Poisson process, the arrival rate must change with time and also be stochastic. Such evidence is given later in this paper and also in Tanir and Booth (1999), Deslauriers (2003), Avramidis et al (2004), Brown et al (2005), Steckley et al (2009), Channouf and L'Ecuyer (2012), Ibrahim et al (2015b) and references therein. If the arrival rate is taken as a deterministic function of time, the Poisson process model implies that the variance and the mean of the number of arrivals in any given time period are equal.…”

Section: Introductionsupporting

confidence: 67%

“…Although a continuous function may appear more realistic, the most popular choice by far is a piecewise-constant function, for which the day is divided into time periods of equal length (usually 30 or 15 minutes) and the arrival rate is assumed constant over each period (Gans et al 2003, Avramidis et al 2004, Brown et al 2005, Akşin et al 2007, Channouf and L'Ecuyer 2012, Koole 2013, Kim and Whitt 2014a, Ibrahim et al 2015b). There are many reasons for this.…”

Section: Introductionmentioning

confidence: 99%

“…For the day-to-day management of real-life call centers, one would also need to model the dependence across successive days, the seasonalities at weekly and yearly levels, special-day effects, and in many cases the dependence between different call types (Brown et al 2005, Jaoua et al 2013, Ibrahim et al 2015b. This is beyond the scope of the present paper, but could be done in combination with the models proposed here.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Rate-Based Daily Arrival Process Models with Application to Call Centers

Oreshkin

Réegnard

L’Ecuyer

2016

Operations Research

Self Cite

View full text Add to dashboard Cite

We propose, develop, and compare new stochastic models for the daily arrival rate in a call center. Following standard practice, the day is divided in time periods of equal length (e.g., 15 or 30 minutes), the arrival rate is assumed random but constant in time in each period, and the arrivals are from a Poisson process, conditional on the rate. The random rate for each period is taken as a deterministic base rate (or expected rate) multiplied by a random busyness factor having mean 1. Models in which the busyness factors are independent across periods, or in which a common busyness factor applies to all periods, have been studied previously. But they are not sufficiently realistic. We examine alternative models for which the busyness factors have some form of dependence across periods. Maximum likelihood parameter estimation for these models is not easy, mainly because the arrival rates themselves are never observed. We develop specialized techniques to perform this estimation. We compare the goodness-of-fit of these models on arrival data from three call centers, both in-sample and out-of-sample. Our models can represent arrivals in many other types of systems as well. Estimating a model for the vector of counts (the number of arrivals in each period) is generally easier than for the vector of rates, because the counts can be observed, but a model for the rates is often more convenient and natural, e.g., for simulation. We examine and provide insight on the relationship between these two types of modeling. In particular, we give explicit formulas for the relationship between the correlation between rates and that between counts in two given periods, and for the variance and dispersion index in a given period. These formulas imply that for a given correlation between the rates, the correlation between the counts is much smaller in low traffic than in high traffic.

show abstract

Section: Introductionsupporting

confidence: 67%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Rate-Based Daily Arrival Process Models with Application to Call Centers

Oreshkin

Réegnard

L’Ecuyer

2016

Operations Research

Self Cite

View full text Add to dashboard Cite

show abstract

“…In operational research literature, call centers are studied as queuing systems, with a view to optimize processing of the stream of call arrivals by adjusting the number and service properties of human phone operators or automated agents (e.g., recent survey [13]). From the queuing theory standpoint, the organization operates a human-staffed, multiple server system that processes inbound calls only, has a nulllength queue (an arriving call is either immediately answered or dropped), retries (a caller redials after meeting an engaged tone) and reconnects (conversations spanning more than one call).…”

Section: Introductionmentioning

confidence: 99%

Predicting Caller Type From a Mental Health and Well-Being Helpline: Analysis of Call Log Data (Preprint)

Grigorash¹,

O’Neill²,

Bond³

et al. 2018

Preprint

View full text Add to dashboard Cite

Background: The paper presents an analysis of call data records pertaining to a telephone helpline in Ireland, for those seeking mental health and wellbeing support and for those who are in a suicidal crisis. Objective: Our aim was to examine if rule sets generated from decision tree classification, trained using features derived from a caller's several initial calls could be used to predict the type of caller they would become. Methods: Machine learning techniques were applied to the call log data and five distinct patterns of caller behaviors were revealed, each impacting the helpline capacity in different ways. Results:The main findings from the paper indicate that a statistically significant model (p<0.001) for predicting caller type from call log data obtained from the first eight calls is possible. This indicates an association between caller behavior exhibited in the first number of calls and their behavior over the lifetime of using the service. Conclusions: These data-driven findings contribute to advanced workload forecasting for operational management of the telephony-based helpline and informs the literature on helpline caller behavior generally.

show abstract

“…to account for diurnal patterns) to the random environment Λ(·), the results could be generalized to a setting with nonstationary Cox arrival processes. Moreover, we could pursue to upgrade our model to not only allow for a deterministic trend, but also for dependence between arrival rates corresponding to subsequent time slots; such properties have been observed in (overdispersed) datasets, and are therefore desirable to incorporate [14]. Another challenge lies in refining the logarithmic asymptotics, as obtained in Section 4, to exact asymptotics.…”

mentioning

confidence: 99%

Scaling limits for infinite-server systems in a random environment

Heemskerk¹,

Leeuwaarden²,

Mandjes³

2017

Stoch. Syst.

View full text Add to dashboard Cite

Full terms and conditions of use: http://pubsonline.informs.org/page/terms-and-conditionsThis article may be used only for the purposes of research, teaching, and/or private study. Commercial use or systematic downloading (by robots or other automatic processes) is prohibited without explicit Publisher approval, unless otherwise noted. For more information, contact permissions@informs.org.The Publisher does not warrant or guarantee the article's accuracy, completeness, merchantability, fitness for a particular purpose, or non-infringement. Descriptions of, or references to, products or publications, or inclusion of an advertisement in this article, neither constitutes nor implies a guarantee, endorsement, or support of claims made of that product, publication, or service. Copyright © 2017, The author(s)Please scroll down for article-it is on subsequent pages INFORMS is the largest professional society in the world for professionals in the fields of operations research, management science, and analytics. This paper studies the effect of an overdispersed arrival process on the performance of an infinite-server system. In our setup, a random environment is modeled by drawing an arrival rate Λ from a given distribution every Δ time units, yielding an i.i.d. sequence of arrival rates Λ1, Λ2, . . .. Applying a martingale central limit theorem, we obtain a functional central limit theorem for the scaled queue length process. We proceed to large deviations and derive the logarithmic asymptotics of the queue length's tail probabilities. As it turns out, in a rapidly changing environment (i.e., Δ is small relative to Λ) the overdispersion of the arrival process hardly affects system behavior, whereas in a slowly changing random environment it is fundamentally different; this general finding applies to both the central limit and the large deviations regime. We extend our results to the setting where each arrival creates a job in multiple infinite-server queues.

show abstract

Modeling and forecasting call center arrivals: A literature survey and a case study

Cited by 86 publications

References 48 publications

Rate-Based Daily Arrival Process Models with Application to Call Centers

Rate-Based Daily Arrival Process Models with Application to Call Centers

Predicting Caller Type From a Mental Health and Well-Being Helpline: Analysis of Call Log Data (Preprint)

Scaling limits for infinite-server systems in a random environment

Contact Info

Product

Resources

About