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Avishai Mandelbaum

Bio: Avishai Mandelbaum is an academic researcher from Technion – Israel Institute of Technology. The author has contributed to research in topics: Queueing theory & Queue. The author has an hindex of 37, co-authored 86 publications receiving 7295 citations.


Papers
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Journal ArticleDOI
TL;DR: This work begins with a tutorial on how call centers function and proceed to survey academic research devoted to the management of their operations, which identifies important problems that have not been addressed and identifies promising directions for future research.
Abstract: Telephone call centers are an integral part of many businesses, and their economic role is significant and growing. They are also fascinating sociotechnical systems in which the behavior of customers and employees is closely intertwined with physical performance measures. In these environments traditional operational models are of great value--and at the same time fundamentally limited--in their ability to characterize system performance.We review the state of research on telephone call centers. We begin with a tutorial on how call centers function and proceed to survey academic research devoted to the management of their operations. We then outline important problems that have not been addressed and identify promising directions for future research.

1,415 citations

Journal ArticleDOI
TL;DR: An analysis of a unique record of call center operations that comprises a complete operational history of a small banking call center, call by call, over a full year is summarized.
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 ...

857 citations

Journal ArticleDOI
TL;DR: This paper analyzes the simplest abandonment model, in which customers' patience is exponentially distributed and the system's waiting capacity is unlimited ( M/ M/ N +M), and derives approximations for performance measures and proposes "rules of thumb" for the design of large call centers.
Abstract: The most common model to support workforce management of telephone call centers is theM/ M/ N/ B model, in particular its special casesM/ M/ N (Erlang C, which models out busy signals) andM/ M/ N/ N (Erlang B, disallowing waiting). All of these models lack a central prevalent feature, namely, that impatient customers might decide to leave (abandon) before their service begins.In this paper, we analyze the simplest abandonment model, in which customers' patience is exponentially distributed and the system's waiting capacity is unlimited ( M/ M/ N +M). Such a model is both rich and analyzable enough to provide information that is practically important for call-center managers. We first outline a method for exact analysis of theM/ M/ N +M model, that while numerically tractable is not very insightful. We then proceed with an asymptotic analysis of theM/ M/ N +M model, in a regime that is appropriate for large call centers (many agents, high efficiency, high service level). Guided by the asymptotic behavior, we derive approximations for performance measures and propose "rules of thumb" for the design of large call centers. We thus add support to the growing acknowledgment that insights from diffusion approximations are directly applicable to management practice.

585 citations

Journal ArticleDOI
TL;DR: The present document is an abridged version of a survey that can be downloaded from www.cs.vu.nl/obp/callcenters and ie.technion.il/∼serveng.
Abstract: This is a survey of some academic research on telephone call centers. The surveyed research has its origin in, or is related to, queueing theory. Indeed, the “queueing-view” of call centers is both natural and useful. Accordingly, queueing models have served as prevalent standard support tools for call center management. However, the modern call center is a complex socio-technical system. It thus enjoys central features that challenge existing queueing theory to its limits, and beyond. The present document is an abridged version of a survey that can be downloaded from www.cs.vu.nl/obp/callcenters and ie.technion.ac.il/∼serveng.

354 citations

Journal ArticleDOI
TL;DR: A queueing system with multitype customers and flexible (multiskilled) servers that work in parallel is considered and a very simple generalizedcµ-rule is shown to minimizes both instantaneous and cumulative queueing costs, asymptotically, over essentially all scheduling disciplines, preemptive or non-preemptive.
Abstract: We consider a queueing system with multitype customers and flexible (multiskilled) servers that work in parallel. IfQ iis the queue length of typei customers, this queue incurs cost at the rate ofC i ( Q i ), whereC i (.) is increasing and convex. We analyze the system in heavy traffic (Harrison and Lopez 1999) and show that a very simple generalizedcµ-rule (Van Mieghem 1995) minimizes both instantaneous and cumulative queueing costs, asymptotically, over essentially all scheduling disciplines, preemptive or non-preemptive. This rule aims at myopically maximizing the rate of decrease of the instantaneous cost at all times, which translates into the following: when becoming free, serverj chooses for service a typei customer such thati ? arg max i C' i ( Q i )µ ij , where µ ijis the average service rate of typei customers by serverj.An analogous version of the generalizedcµ-rule asymptotically minimizes delay costs. To this end, let the cost incurred by a typei customer be an increasing convex functionC i ( D) of its sojourn timeD. Then, serverj always chooses for service a customer for which the value ofC' i ( D) µ ijis maximal, whereD andi are the customer's sojourn time and type, respectively.

345 citations


Cited by
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Journal ArticleDOI
TL;DR: Convergence of Probability Measures as mentioned in this paper is a well-known convergence of probability measures. But it does not consider the relationship between probability measures and the probability distribution of probabilities.
Abstract: Convergence of Probability Measures. By P. Billingsley. Chichester, Sussex, Wiley, 1968. xii, 253 p. 9 1/4“. 117s.

5,689 citations

Book ChapterDOI
01 Jan 2011
TL;DR: Weakconvergence methods in metric spaces were studied in this article, with applications sufficient to show their power and utility, and the results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables.
Abstract: The author's preface gives an outline: "This book is about weakconvergence methods in metric spaces, with applications sufficient to show their power and utility. The Introduction motivates the definitions and indicates how the theory will yield solutions to problems arising outside it. Chapter 1 sets out the basic general theorems, which are then specialized in Chapter 2 to the space C[0, l ] of continuous functions on the unit interval and in Chapter 3 to the space D [0, 1 ] of functions with discontinuities of the first kind. The results of the first three chapters are used in Chapter 4 to derive a variety of limit theorems for dependent sequences of random variables. " The book develops and expands on Donsker's 1951 and 1952 papers on the invariance principle and empirical distributions. The basic random variables remain real-valued although, of course, measures on C[0, l ] and D[0, l ] are vitally used. Within this framework, there are various possibilities for a different and apparently better treatment of the material. More of the general theory of weak convergence of probabilities on separable metric spaces would be useful. Metrizability of the convergence is not brought up until late in the Appendix. The close relation of the Prokhorov metric and a metric for convergence in probability is (hence) not mentioned (see V. Strassen, Ann. Math. Statist. 36 (1965), 423-439; the reviewer, ibid. 39 (1968), 1563-1572). This relation would illuminate and organize such results as Theorems 4.1, 4.2 and 4.4 which give isolated, ad hoc connections between weak convergence of measures and nearness in probability. In the middle of p. 16, it should be noted that C*(S) consists of signed measures which need only be finitely additive if 5 is not compact. On p. 239, where the author twice speaks of separable subsets having nonmeasurable cardinal, he means "discrete" rather than "separable." Theorem 1.4 is Ulam's theorem that a Borel probability on a complete separable metric space is tight. Theorem 1 of Appendix 3 weakens completeness to topological completeness. After mentioning that probabilities on the rationals are tight, the author says it is an

3,554 citations

Book ChapterDOI
01 Jan 1998
TL;DR: In this paper, the authors explore questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties, using diffusion processes as a model of a Markov process with continuous sample paths.
Abstract: We explore in this chapter questions of existence and uniqueness for solutions to stochastic differential equations and offer a study of their properties. This endeavor is really a study of diffusion processes. Loosely speaking, the term diffusion is attributed to a Markov process which has continuous sample paths and can be characterized in terms of its infinitesimal generator.

2,446 citations

Book ChapterDOI
01 Jan 1986

2,356 citations

Journal ArticleDOI

1,484 citations