Service Engineering in Action: The Palm/Erlang-A Queue, with Applications to Call Centers

Mandelbaum, Avishai; Zeltyn, Sergey

doi:10.1007/978-3-540-29860-1_2

Cited by 103 publications

(110 citation statements)

References 19 publications

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“…In fact, a recent empirical study by Brown et al (2005) based on call center data, found that service times have a distribution which is "closer" to a lognormal, not in line with the prevalent exponential assumption. Interestingly, Mandelbaum and Zeltyn (2005) observe that the performance predicted by the Erlang A formulae are fairly close to observed performance despite the various sources of misspecification. This is consistent with the performance-based approach advocated here.…”

Section: A Call Center Staffing Problemmentioning

confidence: 53%

Testing the Validity of a Demand Model: An Operations Perspective

Besbes

Phillips

Zeevi

2010

M&SOM

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The fields of statistics and econometrics have developed powerful methods for testing the validity (specification) of a model based on its fit to underlying data. Unlike statisticians, managers are typically more interested in the performance of a decision rather than the statistical validity of the underlying model. We propose a framework and a statistical test that incorporate decision performance into a measure of statistical validity. Under general conditions on the objective function, asymptotic behavior of our test admits a sharp and simple characterization. We develop our approach in a revenue management setting and apply the test to a data set used to optimize prices for consumer loans. We show that traditional model-based goodness-of-fit tests may consistently reject simple parametric models of consumer response (e.g., the ubiquitous logit model), while at the same time these models may "pass" the proposed performance-based test. Such situations arise when decisions derived from a postulated (and possibly incorrect) model generate results that cannot be distinguished statistically from the best achievable performance-i.e., when demand relationships are fully known. We develop our approach in a revenue management setting and apply the test to a data set used to optimize prices for consumer loans. We show that traditional model-based goodness-of-fit tests may consistently reject simple parametric models of consumer response (e.g., the ubiquitous logit model), while at the same time these models may "pass" the proposed performance-based test.Such situations arise when decisions derived from a postulated (and possibly incorrect) model, generate results that cannot be distinguished statistically from the best achievable performance -i.e., when demand relationships are fully known.

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Section: A Call Center Staffing Problemmentioning

confidence: 53%

Testing the Validity of a Demand Model: An Operations Perspective

Besbes

Phillips

Zeevi

2010

M&SOM

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“…More recently, mainly triggered by the application area of the call-center industry, more authors have studied queueing models with abandonments [see e.g. Garnett et al (2002) and Mandelbaum et al (2002); Mandelbaum and Zeltyn (2007) and references therein].…”

Section: Discrete-time Models With Abandonmentsmentioning

confidence: 99%

“…Mandelbaum and Zeltyn (2007)]. This continuous-time queueing model is a variant of the well-known M/M/c model.…”

Section: A Discrete-time Delay Queueing Model With Abandonmentsmentioning

confidence: 99%

Retrial queueing models in discrete time: a short survey of some late arrival models

Nobel

2015

Ann Oper Res

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This paper presents an overview of one-server queueing models with retrials in discrete-time. In all these models the number of primary customers arriving in a time slot follows a general probability distribution and the different numbers of primary arrivals in consecutive time slots are mutually independent. Each customer requires from the server a generally distributed number of slots for his service, and the service times of the different customers are independent. Only models with delayed access are considered, and the socalled late arrival setup is chosen. For all the models the steady-state behavior is studied through the generating function of the number of customers in the orbit. From the generating function several performance measures are deduced, like the average orbit size and the mean busy period.

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“…Palm [10,11] (cited in [8] and [12]) derived the probability of abandonment and the mean waiting time for an arbitrary customer. (It is mentioned in [9, p. 169] that Engset's main model in his report from 1915 under certain conditions is identical to Palm's model.)…”

Section: Introductionmentioning

confidence: 99%

“…The distribution of the waiting time is shown in such books as Gnedenko and Kovalenko [4, p. 64] and Riordan [12, p. 109]. Lately, this system has been used widely as a basic model for the performance evaluation of a call center [8,15]. The author [13] recently presented a detailed analysis of the waiting time in the M/M/m/(m + c) queue (with a finite waiting room) with impatient customers.…”

Section: Introductionmentioning

confidence: 99%

WAITING TIME IN THE M/M/m FCFS NONPREEMPTIVE PRIORITY QUEUE WITH IMPATIENT CUSTOMERS

Takagi¹

2014

Int. J. of Pure and Appl. Math.

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As a possible model for a service center with multiple servers and prioritized impatient customers, we study an M/M/m nonpreemptive priority (first-come, first-served within the same class) queueing system with impatient customers in the steady state. We analyze the waiting time for those customers who are served successfully and the time to abandonment for those customers who leave the system while waiting. Explicit formulas are given for the probabilities of service and abandonment as well as the mean and second moment of the waiting time for customers of each class. The distribution of the waiting time is derived only for customers of the highest priority class. Numerical examples are shown in order to demonstrate the feasibility of computation from theoretical formulas.

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Service Engineering in Action: The Palm/Erlang-A Queue, with Applications to Call Centers

Cited by 103 publications

References 19 publications

Testing the Validity of a Demand Model: An Operations Perspective

Testing the Validity of a Demand Model: An Operations Perspective

Retrial queueing models in discrete time: a short survey of some late arrival models

WAITING TIME IN THE M/M/m FCFS NONPREEMPTIVE PRIORITY QUEUE WITH IMPATIENT CUSTOMERS

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