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## Contact centers with a call-back option and real-time delay information (2004)

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Venue: | Operations Research |

Citations: | 85 - 18 self |

### Citations

5089 |
Probability and Measure
- Billingsley
- 1995
(Show Context)
Citation Context ...s nonidling. Hereafter, the notation ZN i and QN i without time argument will denote the steady-state random variable. Also, the notation “⇒” is used to denote weak convergence in D�0� �� (see, e.g., =-=Billingsley 1968-=-, §§14 and 15), or convergence in distribution, and a tilde denotes that the relevant quantity is associated with the limiting system. Halfin and Whitt established the following results (see Halfin an... |

580 | Discrete Choice Theory of Product Differentiation - Anderson, Palma, et al. - 1992 |

350 | On positive harris recurrence of multiclass queueing networks: A unified approach via fluid limit models. The Annals of Applied Probability - Dai - 1995 |

268 |
Heavy-traffic limits for queues with many exponential servers
- Halfin, Whitt
- 1981
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Citation Context ...sley 1968, §§14 and 15), or convergence in distribution, and a tilde denotes that the relevant quantity is associated with the limiting system. Halfin and Whitt established the following results (see =-=Halfin and Whitt 1981-=-, Proposition 1, Theorems 2 and 3). Theorem 3.1. As N →�, lim P�wait>0�= lim N →� N →� P�ZN 1 +ZN 2 >N�=�∈�0�1�� (6) if and only if � N �= �N � a � 1 = 1 − √ + o √N N� N � � �>0 (7) (i.e., √ N�1 − �N ... |

204 |
Designing a call center with impatient customers. Manufacturing Service Oper. Management 5
- Garnett, Mandelbaum, et al.
- 2002
(Show Context)
Citation Context ...t to have used the Halfin-Whitt regime in the context of call centers; they use this asymptotic regime to characterize staffing levels with time-varying demand. Flemming et al. [9] and Garnett et al. =-=[11]-=- have added the notion of abandonment (that is, customers renege after having waited in the queue for some time). Puhalskii and Reiman [23] have analyzed multi-class systems with renewal arrival and p... |

128 |
State space collapse with application to heavy traffic limits for multiclass queueing networks
- Bramson
- 1998
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Citation Context ... (29) also goes to zero as N → ∞. This is done by analyzing a set of fluid scaled processes. 29 = 0. (29)2. Convergence of the Fluid Scale Process. This part mimics the framework proposed by Bramson =-=[5]-=-, but does not make explicit use of his results. Specifically, we will analyze the limits of the scaled queue length processes defined according to ¯Q N (·; x, y) := QN ( · √ ; x, y) N √ N . This proc... |

122 | Open queueing networks in heavy traffic - Reiman - 1984 |

118 | 2001. Dynamic scheduling of a system with two parallel servers in heavy traffic with resource pooling: Asymptotic optimality of a threshold policy - Bell, Williams |

109 | Dimensioning large call centers
- Borst, Mandelbaum, et al.
- 2004
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Citation Context ...e he/she found the system too congested, �balk = �eff�d2� − �� N 1 + �N 2 � is the fraction of customers that choose not to join the system, and $c is the operating cost per unit time per server (see =-=Borst et al. 2004-=- for a detailed analysis in this direction). We conclude with a numerical example. Suppose that customers make decisions according to the MNL model with parameters r 1 = r 2 = 1, c 1 = 0�5, c 2 = 0�02... |

67 | Server staffing to meet timevarying demand
- Jennings, Mandelbaum, et al.
- 1996
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Citation Context ...or M/M/N systems in the form of a simple diffusion process. It also provides useful insights about the scaling phenomena in these systems. This work has been extended in several ways: Jennings et. al =-=[16]-=- seem to be the first to have used the Halfin-Whitt regime in the context of call centers; they use this asymptotic regime to characterize staffing levels with time-varying demand. Flemming et al. [9]... |

66 | Existence and uniqueness of semimartingale reflecting Brownian motions in convex polyhedrons. Theory Probab - Dai, Williams - 1995 |

58 |
The pointwise stationary approximation for queues with nonstationary arrivals. Management Sci
- Green, Kolesar
- 1991
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Citation Context ...se stationary approximation, where the performance at time t, is approximated by the steady-state performance of the stationary system with constant arrival rates given by λ(t); see Green and Kolesar =-=[13]-=- and Jennings et al. [16]. Also, the approach taken by Whitt in [27] of differentiating between calls according to their level of urgency, and postponing the less pressing calls to off-peak hours in o... |

57 |
The multiclass GI/PH/N queue in the Halfin–Whitt regime
- Puhalskii, Reiman
- 2000
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Citation Context ... time-varying demand. Flemming et al. [9] and Garnett et al. [11] have added the notion of abandonment (that is, customers renege after having waited in the queue for some time). Puhalskii and Reiman =-=[23]-=- have analyzed multi-class systems with renewal arrival and phase-type processing time distributions with and without priorities. A detailed asymptotic analysis of dimensioning rules for single class ... |

50 | Discrete-review policies for scheduling stochastic networks: trajectory tracking and fluid-scale asymptotic optimality - Maglaras - 2000 |

45 |
The BIGSTEP approach to flow management in stochastic processing networks, Stochastic Networks: Theory and Applications
- Harrison
- 1996
(Show Context)
Citation Context ...ts. Our use of the term “threshold policy” is different from that appearing in, for example, Bell and Williams (2001), where thresholds are synonymous for safety stocks (see also Kelly and Laws 1993, =-=Harrison 1996-=-, Maglaras 2000, Teh and Ward 2002) that are asymptotically negligible and are used to prevent the system from incurring undesirable idleness when some of the queue lengths get depleted. Irrespective ... |

43 | A call-routing problem with service-level constraints
- Gans, Zhou
- 2003
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Citation Context ...server system, intentional idling may be desirable—or even optimal—to reserve capacity for the call-back customers that need to satisfy a qualityof-service constraint (e.g., see the policy derived by =-=Gans and Zhou 2003-=-). In contrast, in the limiting system, this quality-of-service constraint can be satisfied without incurring any idleness, which motivated the restriction to nonidling policies. The optimality of the... |

43 | Pricing and capacity sizing for systems with shared resources: Approximate solutions and scaling relations, Managm - Maglaras, Zeevi - 2003 |

43 | A model for rational abandonments from invisible queues. Queueing Systems
- Mandelbaum, Shimkin
- 2000
(Show Context)
Citation Context ...luding the scenario that leads to the limiting regime proposed by Halfin and Whitt in [14] that is also used here. Customer behavior has been analyzed by Hassin and Haviv [15], Mandelbaum and Shimkin =-=[20]-=-, and recently by Zohar et al. [29] in the context of modelling rational abandonment. In [15] rational abandonments are considered in an M/M/1 queue, and it is shown that the only rational abandonment... |

33 |
On the invariance principle for the first passage time
- Puhalskii
- 1994
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Citation Context ...contradiction. Hence, (30) is true uniformly in x, y. This establishes (28) (through (29)) and completes the proof. ⋄ Proof of Proposition 3.2 The result follows from Puhalskii’s invariance principle =-=[22]-=-. We prove it by a direct application of Lemma A.2 of Puhalskii and Reiman [23] for i = 1, 2. In the notation of [23], K N i is equal to QN i , the limits of process LNi (t) follow from the FCLT for t... |

31 | Server staffing to meet time varying demand. Management Science 42 - Jennings, Mandelbaum, et al. - 1996 |

28 | On a two-queue priority system with impatience and its applications to a call center. Methodology Comput
- Brandt, Brandt
- 1999
(Show Context)
Citation Context ...ing the service of less urgent jobs to off-peak hours can smooth out the load of the system. Two-class M/M/N systems related to ours have been studied in the following two papers. 5Brandt and Brandt =-=[6]-=- analyze the Markov chain associated with a two class system with impatient customers, fixed arrival rates, no service level guarantees, and a static priority policy that prioritize the real-time chan... |

28 |
Diffusion approximations
- Glynn
- 1990
(Show Context)
Citation Context ...rm implies weak convergence; that is, (28) implies that �X N 1 �t + bN �, X N 2 �t + bN �� ⇒ ���X�t� − ˜�� + � �X�t� + ∧ ˜��. Because t + b N → t, an application of a random time change argument (see =-=Glynn 1990-=-, Proposition 5) establishes the statement of the proposition. The next step is to show that the second term in (29) converges to 0 as N →�. This is done in two steps. First, we establish (30), and se... |

28 |
How multiserver queues scale with growing congestiondependent demand
- Whitt
(Show Context)
Citation Context ...time distributions with and without priorities. A detailed asymptotic analysis of dimensioning rules for single class call centers has been done by Borst et al. [4]. Finally, in a recent paper, Whitt =-=[28]-=- studies single-class multi-server systems in which arrival rates depend on system performance, including the scenario that leads to the limiting regime proposed by Halfin and Whitt in [14] that is al... |

23 |
Adaptive behavior of impatient customers in tele-queues: theory and empirical support
- Zohar, Mandelbaum, et al.
- 2002
(Show Context)
Citation Context ...he limiting regime proposed by Halfin and Whitt in [14] that is also used here. Customer behavior has been analyzed by Hassin and Haviv [15], Mandelbaum and Shimkin [20], and recently by Zohar et al. =-=[29]-=- in the context of modelling rational abandonment. In [15] rational abandonments are considered in an M/M/1 queue, and it is shown that the only rational abandonments are the trivial ones, that is, th... |

20 |
Insights on service system design from a normal approximation to Erlang’s delay formula
- Kolesar, Green
- 1998
(Show Context)
Citation Context ... performance of the M/M/N system that can be found in most textbooks on stochastic models. A significant fraction of recent work has been on developing good staffing rules for large call centers (see =-=Kolesar and Green 1998-=- and references therein) with particular emphasis on nonstationary arrival streams and the development of practical solutions that can be implementable in a true system with eight-hour shifts, breaks,... |

18 | Critical thresholds for dynamic routing in queueing networks
- Teh, Ward
- 2002
(Show Context)
Citation Context ...hold policy” is different from that appearing in, for example, Bell and Williams (2001), where thresholds are synonymous for safety stocks (see also Kelly and Laws 1993, Harrison 1996, Maglaras 2000, =-=Teh and Ward 2002-=-) that are asymptotically negligible and are used to prevent the system from incurring undesirable idleness when some of the queue lengths get depleted. Irrespective of the choice of �N , this policy ... |

17 |
Heavy traffic limit for a mobile phone system loss model, in
- Fleming, Stolyar, et al.
- 1994
(Show Context)
Citation Context ...16] seem to be the first to have used the Halfin-Whitt regime in the context of call centers; they use this asymptotic regime to characterize staffing levels with time-varying demand. Flemming et al. =-=[9]-=- and Garnett et al. [11] have added the notion of abandonment (that is, customers renege after having waited in the queue for some time). Puhalskii and Reiman [23] have analyzed multi-class systems wi... |

13 | Equilibrium strategies for queues with impatient customers - Hassin, Haviv - 1995 |

11 |
A call center uses simulation to drive strategic change. Interfaces
- RM, Mehrotra
(Show Context)
Citation Context ...othesized value for E W N 1 agrees with the one estimated via simulation. 9 9 Another example where simulation was used for performance analysis of a call center can be found in Saltzman and Mehrotra =-=[25]-=-, where they study a system with two classes of jobs, with static priorities. 22Ew 1 (min) 0.25 0.2 0.15 0.1 0.05 0 0 20 40 60 D (min) 2 P(w 1 > 20 sec.) 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0 20 40 60 ... |

8 | Using different response-time requirements to smooth time-varying demand for
- Whitt
- 1999
(Show Context)
Citation Context ...lti-class systems, or, more so, to networks, and it often gives numerical rather than analytic characterizations of quantities of interest. Also within the non-stationary arrivals framework, Whitt in =-=[27]-=- demonstrates how postponing the service of less urgent jobs to off-peak hours can smooth out the load of the system. Two-class M/M/N systems related to ours have been studied in the following two pap... |

7 | Admission and sequencing control under delay constraints with applications to GPS - Maglaras, Mieghem - 2004 |

6 |
Leadtime constraints in stochastic processing networks under heavy traffic conditions. Queueing Systems 39
- Plambeck, Kumar, et al.
- 2001
(Show Context)
Citation Context ...pected waiting time experienced by class 1 customers among all policies that asymptotically guarantee the delay bound for class 2; these are the so-called asymptotically compliant policies (see §3 or =-=Plambeck et al. 2001-=-). This is a threshold rule that gives priority to class 1 as long as the class 2 queue length is below an appropriately chosen threshold that is easy to specify; beyond this threshold class 2 gets pr... |

6 | Heavy traffic limits for queues: A survey - Whitt - 1974 |

4 |
Dynamic routing in open queueing models: Brownian models, cut constraints and resource pooling. Queueing Systems 13
- Kelly, Laws
- 1993
(Show Context)
Citation Context ... within �D 2 time units. Our use of the term “threshold policy” is different from that appearing in, for example, Bell and Williams (2001), where thresholds are synonymous for safety stocks (see also =-=Kelly and Laws 1993-=-, Harrison 1996, Maglaras 2000, Teh and Ward 2002) that are asymptotically negligible and are used to prevent the system from incurring undesirable idleness when some of the queue lengths get depleted... |

3 | Diffusion approximations for a Markovian service system with “guaranteed” and “best-effort” service - Maglaras, Zeevi - 2004 |

3 | A discrete choice model of yield management
- Ryzin, Talluri
- 2000
(Show Context)
Citation Context ...d through experimental evidence and for which efficient estimation procedures can be constructed. For example, the parameters of the MNL choice model are simple to estimate (see van Ryzin and Talluri =-=[26]-=- and the references therein). On the positive side, as the number of agents increases and the traffic intensity approaches one, the actual waiting times encountered by both classes of customers will d... |

2 | 1 191–210. Call center statistics. 2001. www.callcenternews.com/resources/statistics. shtml - Probab |

2 | Revenue management under a general discrete-choice model of demand. Management Sci. Forthcoming - Talluri, Ryzin - 2004 |

1 |
Revenue management for systems with shared resources: Approximate solutions and scaling relations
- Maglaras, Zeevi
(Show Context)
Citation Context ...the context of a single-class model that the economically optimal capacity level, trading-off congestion and staffing costs, puts the system in this regime. Finally, recent work by Maglaras and Zeevi =-=[19]-=- has shown that for a related model with pricing decisions this is the revenue maximizing and socially optimal regime. The remainder of this section analyzes the system of interest in the rationalized... |