#### DMCA

## Dynamic routing in large-scale service systems with heterogeneous servers (2005)

Citations: | 51 - 12 self |

### Citations

657 |
Markov Processes. Characterization and Convergence
- ETHIER, G
- 1986
(Show Context)
Citation Context ...ution is geometric. The resulting convergence as λ→∞ is then straightforward. Proof of Proposition 4.6: The proof is based on Ethier and Kurtz [21, Theorem 9.10 and Remark 9.11, p. 244]. According to =-=[21]-=- and based on our Propositions 4.1 and 4.2, it suffices to show that: 1. There exists a stationary distribution of ~Xλ(·) for all λ. 2. The sequence of stationary distributions of ~Xλ(·) is tight. We ... |

277 | Telephone call centers: tutorial, review and research prospects
- Gans, Koole, et al.
- 2003
(Show Context)
Citation Context ... in [27] and [23], respectively. The optimality of the QED regime, under revenue maximization or constraint satisfaction, is discussed in [2,3,12, 42]. Readers are referred to Sections 4 and 5.1.4 of =-=[25]-=- for a survey of the QED regime, both practically and academically. It is important to note that the QED regime differs in significant ways from the conventional (or “classical”) heavy traffic regime.... |

256 |
Heavy-traffic limits for queues with many exponential servers
- Halfin, Whitt
- 1981
(Show Context)
Citation Context ... a threshold needed in that case? The asymptotic framework considered in this paper is the many-server heavytraffic regime, first appearing in Erlang [20], and formally introduced by Halfin and Whitt =-=[32]-=-. We refer to this regime as the QED (Quality and Efficiency Driven) regime. Systems that operate in the QED regime enjoy a rare combination of high efficiencies together with high quality of service.... |

200 |
Designing a call center with impatient customers.
- Garnett, Mandelbaum, et al.
- 2002
(Show Context)
Citation Context ...t characterization is a non-trivial limit (within (0, 1)) of the fraction of delayed customers. The latter equivalence was established for GI/M/N [32], GI/D/N [36] and M/M/N with exponential patience =-=[27]-=-. More recently, this equivalence was also shown to be true in the multiple customer classes case [30], as well as in the setting considered in this paper [4]. The QED regime was explicitly recognized... |

126 |
State space collapse with application to heavy traffic limits for multiclass queueing networks.
- Bramson
- 1998
(Show Context)
Citation Context ... 1/ √ N λ .Wewill show that the fluid limit reaches the goal of x2 = 0infinite time, and hence, the diffusion limit will get there instantaneously. This argument mimics the one proposed by Bramson in =-=[13]-=-, although does not make a direct use of his results. Let ˜X λ (t) := X λ (t/ √ N λ ), then ˜X λ (t) = ( ˜X λ 1 (t), ˜X λ 2 (t)) ( √ λ Q (t/ N λ λ ) + Z1 (t/ = √ N λ ) − N λ 1 √ , N λ Z λ 2 (t/√N λ... |

112 | 2001. Dynamic scheduling of a system with two parallel servers in heavy traffic with resource pooling: Asymptotic optimality of a threshold policy
- Bell, Williams
(Show Context)
Citation Context ...éricourt and Zhou [18], Shumsky [52], and Rykov and Efrosinin [49], Asymptotic analysis—“conventional” heavy traffic: Foschini [24], Reiman [47], Kelly and Laws [38], Harrison [33], Bell and Williams =-=[10]-=-, Glazebrook and Niño-Mora [28], Teh and Ward [55], Mandelbaum and Stolyar [43] and Stolyar [53], and Asymptotic analysis—many server systems: Armony and Maglaras [2,3], Harrison and Zeevi [34], Atar ... |

107 |
Fundamentals of Queueing Networks.
- Chen, Yao
- 2001
(Show Context)
Citation Context ...entional (or “classical”) heavy traffic regime. Indeed, QED combines light and heavy traffic characteristics. For example, in conventional heavy traffic, the theory of which has been well established =-=[16,58]-=-, essentially all customers are delayed prior to service. In the QED regime, on the other hand, a non-trivial fraction is served immediately upon arrival. Also, conventional heavy traffic can be achie... |

105 | Dimensioning large call centers
- Borst, Mandelbaum, et al.
(Show Context)
Citation Context ...works, taking into account customers’ impatience, can be found in [27] and [23], respectively. The optimality of the QED regime, under revenue maximization or constraint satisfaction, is discussed in =-=[2,3,12, 42]-=-. Readers are referred to Sections 4 and 5.1.4 of [25] for a survey of the QED regime, both practically and academically. It is important to note that the QED regime differs in significant ways from t... |

105 |
Stochastic-Process Limits: An introduction to stochastic-process limits and their application to queues
- Whitt
(Show Context)
Citation Context ...entional (or “classical”) heavy traffic regime. Indeed, QED combines light and heavy traffic characteristics. For example, in conventional heavy traffic, the theory of which has been well established =-=[16,58]-=-, essentially all customers are delayed prior to service. In the QED regime, on the other hand, a non-trivial fraction is served immediately upon arrival. Also, conventional heavy traffic can be achie... |

90 | Scheduling flexible servers with convex delay costs: Heavy-traffic optimality of the generalized cµ-rule
- Mandelbaum, Stoylar
(Show Context)
Citation Context ...analysis—“conventional” heavy traffic: Foschini [24], Reiman [47], Kelly and Laws [38], Harrison [33], Bell and Williams [10], Glazebrook and Niño-Mora [28], Teh and Ward [55], Mandelbaum and Stolyar =-=[43]-=- and Stolyar [53], and Asymptotic analysis—many server systems: Armony and Maglaras [2,3], Harrison and Zeevi [34], Atar et al. [7], Atar [5,6], Gurvich [30], Gurvich, Armony and Mandelbaum [31], Wall... |

87 |
Fundamentals of Queueing Networks: Performance, Asymptotics and Optimization
- Chen, Yao
- 2001
(Show Context)
Citation Context ...entional (or “classical”) heavy traffic regime. Indeed, QED combines light and heavy traffic characteristics. For example, in conventional heavy traffic, the theory of which has been well established =-=[16, 58]-=-, essentially all customers are delayed prior to service. In the QED regime, on the other hand, a non-trivial fraction is served immediately upon arrival. Also, conventional heavy traffic can be achie... |

78 | 2004a. Contact centers with a call-back option and real-time delay information
- Armony, Maglaras
(Show Context)
Citation Context ...works, taking into account customers’ impatience, can be found in [27] and [23], respectively. The optimality of the QED regime, under revenue maximization or constraint satisfaction, is discussed in =-=[2,3,12, 42]-=-. Readers are referred to Sections 4 and 5.1.4 of [25] for a survey of the QED regime, both practically and academically. It is important to note that the QED regime differs in significant ways from t... |

66 |
Some properties of the Erlang loss function
- Jagerman
- 1974
(Show Context)
Citation Context ... motivated by AT&T call centers operating in the QED regime). A precise characterization of the asymptotic expansion of the blocking probability, for Erlang-B in the QED regime, was given in Jagerman =-=[35]-=-; see also [57], and then [44] for the analysis of finite buffers. But the operational significance of the QED regime, in particular its balancing of “service and economy” via a non-trivial delay prob... |

62 | Dynamic routing in open queueing networks: Brownian models, cut constraints and resource pooling
- Kelly, Laws
- 1993
(Show Context)
Citation Context ...iotis [41], Bhulai and Koole [11], de Véricourt and Zhou [18], Shumsky [52], and Rykov and Efrosinin [49], Asymptotic analysis—“conventional” heavy traffic: Foschini [24], Reiman [47], Kelly and Laws =-=[38]-=-, Harrison [33], Bell and Williams [10], Glazebrook and Niño-Mora [28], Teh and Ward [55], Mandelbaum and Stolyar [43] and Stolyar [53], and Asymptotic analysis—many server systems: Armony and Maglara... |

61 |
Design and Control of a Large Call Center: Asymptotic Analysis of an LP-based Method
- Bassamboo, Harrison, et al.
- 2004
(Show Context)
Citation Context ...r systems: Armony and Maglaras [2,3], Harrison and Zeevi [34], Atar et al. [7], Atar [5,6], Gurvich [30], Gurvich, Armony and Mandelbaum [31], Wallace and Whitt [56] and Bassamboo, Harrison and Zeevi =-=[8,9]-=-. 2. Model formulation Consider a service system with a single customer class and K server types (each type in its own server pool), all are capable of fully handling customers’ service requirements.... |

57 | A staffing algorithm for call centers with skill-based routing
- Wallace, Whitt
- 2005
(Show Context)
Citation Context ...53], and Asymptotic analysis—many server systems: Armony and Maglaras [2,3], Harrison and Zeevi [34], Atar et al. [7], Atar [5,6], Gurvich [30], Gurvich, Armony and Mandelbaum [31], Wallace and Whitt =-=[56]-=- and Bassamboo, Harrison and Zeevi [8,9]. 2. Model formulation Consider a service system with a single customer class and K server types (each type in its own server pool), all are capable of fully ha... |

55 |
Optimal control of a queueing system with two heterogeneous servers
- Lin, Kumar
- 1984
(Show Context)
Citation Context ...this solution is not optimal. As was shown for the two server288 ARMONY λ N 1 N 2 N 3 N K µ 1 µ 2 µ 3 µ K Figure 1. The inverted-V model—a single customer class and multiple server types. case (e.g. =-=[18,39]-=-) it is sometimes necessary to keep customers waiting even when the slower server is idle in order not to starve the faster server. Specifically, optimality is obtained by assigning customers to the s... |

51 | Heavy traffic analysis of a system with parallel servers: Asymptotic optimality of discrete-review policies - Harrison - 1998 |

50 |
Some diffusion approximations with state space collapse, Modelling and Performance Evaluation Methodology
- Reiman
- 1984
(Show Context)
Citation Context ...kov [48], Luh and Viniotis [41], Bhulai and Koole [11], de Véricourt and Zhou [18], Shumsky [52], and Rykov and Efrosinin [49], Asymptotic analysis—“conventional” heavy traffic: Foschini [24], Reiman =-=[47]-=-, Kelly and Laws [38], Harrison [33], Bell and Williams [10], Glazebrook and Niño-Mora [28], Teh and Ward [55], Mandelbaum and Stolyar [43] and Stolyar [53], and Asymptotic analysis—many server system... |

49 | Queueing Dynamics and Maximal Throughput Scheduling in Switched Processing Systems
- Armony, Bambos
- 2003
(Show Context)
Citation Context ...d routing. Examples include: Exact (non-asymptotic) analysis: Lin and Kumar [39], Kella and Yechiali [37], Federgruen and Groenvelt [22], Brandt and Brandt [14], Gans and Zhou [26], Armony and Bambos =-=[1]-=-, Rykov [48], Luh and Viniotis [41], Bhulai and Koole [11], de Véricourt and Zhou [18], Shumsky [52], and Rykov and Efrosinin [49], Asymptotic analysis—“conventional” heavy traffic: Foschini [24], Rei... |

49 |
Stability of Fluid and Stochastic Processing Networks. MaPhySto
- Dai
- 1999
(Show Context)
Citation Context ... and ¯D λ k = Dk. Note that Dλ k need not be divided by N λ , due to its definition as a Poisson process with rate µk, which is independent of λ. Using standard tools of fluid models (see for example =-=[17]-=-, Theorem 2.3.1) one can show that if ( ¯Q λ (0), ¯Z λ k (0), k = 1,...,K ) are bounded, then the process ( ¯Q λ , ¯Z λ k , ¯Y λ , Āλ , Āλ k , Āλ q , ¯B λ k , ¯T λ k , Ī λ k , ¯D λ k )ispre-compact as... |

49 | Heavy-traffic limits for the G/H∗ 2 /n/m queue
- Whitt
- 2005
(Show Context)
Citation Context ...overed and formalized by Halfin and Whitt [32]: Within the GI/M/N framework, they analyzed the scaled number of customers, both in steady-state and as a stochastic process. Recent generalizations are =-=[59,60]-=-. Convergence of the scaled queueing process, in the more general GI/PH/N setting, was established in [46]. Application of QED queues to modelling and staffing of telephone call centers and communicat... |

42 | Scheduling control for queueing systems with many servers: Asymptotic optimality in heavy traffic. The Annals of Applied Probability
- Atar
(Show Context)
Citation Context ...Niño-Mora [28], Teh and Ward [55], Mandelbaum and Stolyar [43] and Stolyar [53], and Asymptotic analysis—many server systems: Armony and Maglaras [2,3], Harrison and Zeevi [34], Atar et al. [7], Atar =-=[5,6]-=-, Gurvich [30], Gurvich, Armony and Mandelbaum [31], Wallace and Whitt [56] and Bassamboo, Harrison and Zeevi [8,9]. 2. Model formulation Consider a service system with a single customer class and K s... |

41 | Scheduling a multi class queue with many exponential servers: Asymptotic optimality in heavy traffic. The Annals of Applied Probability
- Atar, Mandelbaum, et al.
(Show Context)
Citation Context ...brook and Niño-Mora [28], Teh and Ward [55], Mandelbaum and Stolyar [43] and Stolyar [53], and Asymptotic analysis—many server systems: Armony and Maglaras [2,3], Harrison and Zeevi [34], Atar et al. =-=[7]-=-, Atar [5,6], Gurvich [30], Gurvich, Armony and Mandelbaum [31], Wallace and Whitt [56] and Bassamboo, Harrison and Zeevi [8,9]. 2. Model formulation Consider a service system with a single customer c... |

40 |
Pricing and capacity sizing for systems with shared resources: Approximate solutions and scaling relations
- Maglaras, Zeevi
- 2003
(Show Context)
Citation Context ...works, taking into account customers’ impatience, can be found in [27] and [23], respectively. The optimality of the QED regime, under revenue maximization or constraint satisfaction, is discussed in =-=[2,3,12, 42]-=-. Readers are referred to Sections 4 and 5.1.4 of [25] for a survey of the QED regime, both practically and academically. It is important to note that the QED regime differs in significant ways from t... |

39 | Piecewise-linear diffusion processes
- Browne, Whitt
- 1995
(Show Context)
Citation Context ...me. Specifically, it further follows straightforwardly from Lemma A.2 in Puhalskii and Reiman [46] (which is based on [45]), and from assumption (A3). Proof of Proposition 4.4. The proof follows from =-=[15]-=-. Note that the process X(·), restricted to [0, ∞), is a reflected Brownian motion with infinitesimal drift −δ √ µ and variance 2µ. Hence, according to [15, (18.33)], its steady-state density conditio... |

39 | Dynamic scheduling of a multiclass queue in the Halfin and Whitt heavy traffic regimes
- Harrison, Zeevi
(Show Context)
Citation Context ...lliams [10], Glazebrook and Niño-Mora [28], Teh and Ward [55], Mandelbaum and Stolyar [43] and Stolyar [53], and Asymptotic analysis—many server systems: Armony and Maglaras [2,3], Harrison and Zeevi =-=[34]-=-, Atar et al. [7], Atar [5,6], Gurvich [30], Gurvich, Armony and Mandelbaum [31], Wallace and Whitt [56] and Bassamboo, Harrison and Zeevi [8,9]. 2. Model formulation Consider a service system with a ... |

38 | A diffusion approximation for the G/GI/n/m queue
- Whitt
(Show Context)
Citation Context ...overed and formalized by Halfin and Whitt [32]: Within the GI/M/N framework, they analyzed the scaled number of customers, both in steady-state and as a stochastic process. Recent generalizations are =-=[59,60]-=-. Convergence of the scaled queueing process, in the more general GI/PH/N setting, was established in [46]. Application of QED queues to modelling and staffing of telephone call centers and communicat... |

37 | A call-routing problem with service-level constraints
- Gans, Zhou
- 2003
(Show Context)
Citation Context ...literature on skill-based routing. Examples include: Exact (non-asymptotic) analysis: Lin and Kumar [39], Kella and Yechiali [37], Federgruen and Groenvelt [22], Brandt and Brandt [14], Gans and Zhou =-=[26]-=-, Armony and Bambos [1], Rykov [48], Luh and Viniotis [41], Bhulai and Koole [11], de Véricourt and Zhou [18], Shumsky [52], and Rykov and Efrosinin [49], Asymptotic analysis—“conventional” heavy traf... |

31 |
Dynamic routing and admission control in highvolume service systems: asymptotic analysis via multi-scaled fluid limits. Queueing Systems
- Bassamboo, Harrison, et al.
- 2005
(Show Context)
Citation Context ...r systems: Armony and Maglaras [2,3], Harrison and Zeevi [34], Atar et al. [7], Atar [5,6], Gurvich [30], Gurvich, Armony and Mandelbaum [31], Wallace and Whitt [56] and Bassamboo, Harrison and Zeevi =-=[8,9]-=-. 2. Model formulation Consider a service system with a single customer class and K server types (each type in its own server pool), all are capable of fully handling customers’ service requirements.... |

30 |
On the invariance principle for the first passage time
- Puhalskii
- 1994
(Show Context)
Citation Context ...o drift and variance 2µ. Applying the continuous mapping theorem to the process X λ completes the proof of the Proposition. Proof of Proposition 4.3. The proof is a result of a corollary by Puhalskii =-=[45]-=- which deals with limits of the first passage time. Specifically, it further follows straightforwardly from Lemma A.2 in Puhalskii and Reiman [46] (which is based on [45]), and from assumption (A3). P... |

28 | A queueing model for call blending in call centers
- Bhulai, Koole
- 2003
(Show Context)
Citation Context ...sis: Lin and Kumar [39], Kella and Yechiali [37], Federgruen and Groenvelt [22], Brandt and Brandt [14], Gans and Zhou [26], Armony and Bambos [1], Rykov [48], Luh and Viniotis [41], Bhulai and Koole =-=[11]-=-, de Véricourt and Zhou [18], Shumsky [52], and Rykov and Efrosinin [49], Asymptotic analysis—“conventional” heavy traffic: Foschini [24], Reiman [47], Kelly and Laws [38], Harrison [33], Bell and Wil... |

27 | On a two-queue priority system with impatience and its applications to a call center. Methodology Comput
- Brandt, Brandt
- 1999
(Show Context)
Citation Context ...ere is an extensive literature on skill-based routing. Examples include: Exact (non-asymptotic) analysis: Lin and Kumar [39], Kella and Yechiali [37], Federgruen and Groenvelt [22], Brandt and Brandt =-=[14]-=-, Gans and Zhou [26], Armony and Bambos [1], Rykov [48], Luh and Viniotis [41], Bhulai and Koole [11], de Véricourt and Zhou [18], Shumsky [52], and Rykov and Efrosinin [49], Asymptotic analysis—“conv... |

24 |
A queueing model for telephone operator staffing
- Sze
- 1984
(Show Context)
Citation Context ...ich addresses both Erlang-B (M/M/N/N) and Erlang-C (M/M/N)292 ARMONY models. Later on, extensive related work took place in various telecom companies but little has been openly documented, as in Sze =-=[54]-=- (who was actually motivated by AT&T call centers operating in the QED regime). A precise characterization of the asymptotic expansion of the blocking probability, for Erlang-B in the QED regime, was ... |

21 |
On the rational determination of the number of circuits
- Erlang
- 1948
(Show Context)
Citation Context ...ters? Is the FSF policy optimal in that regime? Is a threshold needed in that case? The asymptotic framework considered in this paper is the many-server heavytraffic regime, first appearing in Erlang =-=[20]-=-, and formally introduced by Halfin and Whitt [32]. We refer to this regime as the QED (Quality and Efficiency Driven) regime. Systems that operate in the QED regime enjoy a rare combination of high e... |

21 |
Heavy traffic approximations for service systems with blocking
- Whitt
- 1984
(Show Context)
Citation Context ...T&T call centers operating in the QED regime). A precise characterization of the asymptotic expansion of the blocking probability, for Erlang-B in the QED regime, was given in Jagerman [35]; see also =-=[57]-=-, and then [44] for the analysis of finite buffers. But the operational significance of the QED regime, in particular its balancing of “service and economy” via a non-trivial delay probability, was fi... |

19 |
An asymptotically optimal design of the M/M/c/k queue for call centers. Queueing Systems. Forthcoming
- Massey, Wallace
- 2005
(Show Context)
Citation Context ...s operating in the QED regime). A precise characterization of the asymptotic expansion of the blocking probability, for Erlang-B in the QED regime, was given in Jagerman [35]; see also [57], and then =-=[44]-=- for the analysis of finite buffers. But the operational significance of the QED regime, in particular its balancing of “service and economy” via a non-trivial delay probability, was first discovered ... |

17 |
The multiclass GI/PH/N queue
- Puhalskii, Reiman
(Show Context)
Citation Context ...of customers, both in steady-state and as a stochastic process. Recent generalizations are [59,60]. Convergence of the scaled queueing process, in the more general GI/PH/N setting, was established in =-=[46]-=-. Application of QED queues to modelling and staffing of telephone call centers and communication networks, taking into account customers’ impatience, can be found in [27] and [23], respectively. The ... |

16 |
A diffusion model of scheduling control in queueing system with many servers
- Atar
- 2005
(Show Context)
Citation Context ...Niño-Mora [28], Teh and Ward [55], Mandelbaum and Stolyar [43] and Stolyar [53], and Asymptotic analysis—many server systems: Armony and Maglaras [2,3], Harrison and Zeevi [34], Atar et al. [7], Atar =-=[5,6]-=-, Gurvich [30], Gurvich, Armony and Mandelbaum [31], Wallace and Whitt [56] and Bassamboo, Harrison and Zeevi [8,9]. 2. Model formulation Consider a service system with a single customer class and K s... |

16 |
Heavy traffic limit for a mobile phone system loss model
- Fleming, Stolyar, et al.
- 1994
(Show Context)
Citation Context ... was established in [46]. Application of QED queues to modelling and staffing of telephone call centers and communication networks, taking into account customers’ impatience, can be found in [27] and =-=[23]-=-, respectively. The optimality of the QED regime, under revenue maximization or constraint satisfaction, is discussed in [2,3,12, 42]. Readers are referred to Sections 4 and 5.1.4 of [25] for a survey... |

16 | Monotone Control of Queueing Systems with Heterogeneous Servers”, Queueing Systems
- Rykov
- 2001
(Show Context)
Citation Context ...hes 1. In particular, in the limit, the threshold level approaches infinity. According to [19], the problem of finding an optimal policy for the general multi-heterogeneous server case (considered in =-=[41,48,49]-=-) is still open. But what about the many-server heavy-traffic regime that typifies large call centers? Is the FSF policy optimal in that regime? Is a threshold needed in that case? The asymptotic fram... |

15 | Optimal routing in output-queued flexible server systems
- Stolyar
(Show Context)
Citation Context ...ional” heavy traffic: Foschini [24], Reiman [47], Kelly and Laws [38], Harrison [33], Bell and Williams [10], Glazebrook and Niño-Mora [28], Teh and Ward [55], Mandelbaum and Stolyar [43] and Stolyar =-=[53]-=-, and Asymptotic analysis—many server systems: Armony and Maglaras [2,3], Harrison and Zeevi [34], Atar et al. [7], Atar [5,6], Gurvich [30], Gurvich, Armony and Mandelbaum [31], Wallace and Whitt [56... |

15 | Critical thresholds for dynamic routing in queueing networks
- Teh, Ward
- 2002
(Show Context)
Citation Context ...hose who wish to implement this threshold policy. Matters simplify when “conventional” heavy-traffic (traffic intensity converges to 1, but number of servers stays fixed) is considered. For this case =-=[55]-=- showed that a state-independent threshold policy is asymptotically optimal as traffic intensity approaches 1. In particular, in the limit, the threshold level approaches infinity. According to [19], ... |

14 |
Waiting Times in the Non-Preemptive Priority M/M/c Queue
- Kella, Yechiali
- 1985
(Show Context)
Citation Context ...omer classes are matched with multiple server pools. There is an extensive literature on skill-based routing. Examples include: Exact (non-asymptotic) analysis: Lin and Kumar [39], Kella and Yechiali =-=[37]-=-, Federgruen and Groenvelt [22], Brandt and Brandt [14], Gans and Zhou [26], Armony and Bambos [1], Rykov [48], Luh and Viniotis [41], Bhulai and Koole [11], de Véricourt and Zhou [18], Shumsky [52], ... |

12 |
On heavy traffic diffusion analysis and dynamic routing in packet switched networks
- Foschini
- 1977
(Show Context)
Citation Context ...ambos [1], Rykov [48], Luh and Viniotis [41], Bhulai and Koole [11], de Véricourt and Zhou [18], Shumsky [52], and Rykov and Efrosinin [49], Asymptotic analysis—“conventional” heavy traffic: Foschini =-=[24]-=-, Reiman [47], Kelly and Laws [38], Harrison [33], Bell and Williams [10], Glazebrook and Niño-Mora [28], Teh and Ward [55], Mandelbaum and Stolyar [43] and Stolyar [53], and Asymptotic analysis—many ... |

12 |
Design and control of the M/M/N queue with multitype customers and many servers, MSc
- Gurvich
- 2004
(Show Context)
Citation Context ...tter equivalence was established for GI/M/N [32], GI/D/N [36] and M/M/N with exponential patience [27]. More recently, this equivalence was also shown to be true in the multiple customer classes case =-=[30]-=-, as well as in the setting considered in this paper [4]. The QED regime was explicitly recognized already in Erlang’s 1923 paper (that appeared in [20]) which addresses both Erlang-B (M/M/N/N) and Er... |

12 |
Staffing and control of large-scale service systems with multiple customer classes and fully flexible servers. (working paper
- Gurvich, Armony, et al.
- 2004
(Show Context)
Citation Context ...olyar [43] and Stolyar [53], and Asymptotic analysis—many server systems: Armony and Maglaras [2,3], Harrison and Zeevi [34], Atar et al. [7], Atar [5,6], Gurvich [30], Gurvich, Armony and Mandelbaum =-=[31]-=-, Wallace and Whitt [56] and Bassamboo, Harrison and Zeevi [8,9]. 2. Model formulation Consider a service system with a single customer class and K server types (each type in its own server pool), all... |

11 |
2004. Dynamic scheduling of a multiclass queue in the Halfin and Whitt heavy traffic regime
- Harrison, Zeevi
(Show Context)
Citation Context ...ms [10], Glazebrook and Niño-Mora [28], Teh and Ward [55], Mandelbaum and Stolyar [43] and Stolyar [53], and Asymptotic analysis - many server systems: Armony and Maglaras [2, 3], Harrison and Zeevi =-=[34]-=-, Atar et. al. [7], Atar [5, 6], Gurvich [30], Gurvich, Armony and Mandelbaum [31], Wallace and Whitt [56] and Bassamboo, Harrison and Zeevi [8, 9]. 2 Model Formulation Consider a service system with ... |

9 | 2001. Parallel scheduling of multiclass M/M/m queues: Approximate and heavy-traffic optimization of achievable performance
- Glazebrook, Nino-Mora
(Show Context)
Citation Context ... [52], and Rykov and Efrosinin [49], Asymptotic analysis—“conventional” heavy traffic: Foschini [24], Reiman [47], Kelly and Laws [38], Harrison [33], Bell and Williams [10], Glazebrook and Niño-Mora =-=[28]-=-, Teh and Ward [55], Mandelbaum and Stolyar [43] and Stolyar [53], and Asymptotic analysis—many server systems: Armony and Maglaras [2,3], Harrison and Zeevi [34], Atar et al. [7], Atar [5,6], Gurvich... |

9 |
Necessary and sufficient conditions for delay moments in FIFO multiserver queues with an application comparing s slow servers with one fast one
- Scheller-Wolf
(Show Context)
Citation Context ...hoosing to staff the system with a non-negligible fraction of slow servers. This is to be expected given the well known tradeoff between a single fast server and multiple slower ones (see for example =-=[50]-=-). To the best of our knowledge, this is the first time such a result is shown for a heterogeneous server system. Remark 4.9 (Heterogeneity is good for wait minimization). Recall that in Corollary 4.1... |

7 |
Threshold control policies for heterogeneous server systems
- Luh, Viniotis
- 2002
(Show Context)
Citation Context ...hes 1. In particular, in the limit, the threshold level approaches infinity. According to [19], the problem of finding an optimal policy for the general multi-heterogeneous server case (considered in =-=[41,48,49]-=-) is still open. But what about the many-server heavy-traffic regime that typifies large call centers? Is the FSF policy optimal in that regime? Is a threshold needed in that case? The asymptotic fram... |

6 |
Approximation and Analysis of a Call Center with Flexible and Specialized Servers
- Shumsky
- 2004
(Show Context)
Citation Context ...i [37], Federgruen and Groenvelt [22], Brandt and Brandt [14], Gans and Zhou [26], Armony and Bambos [1], Rykov [48], Luh and Viniotis [41], Bhulai and Koole [11], de Véricourt and Zhou [18], Shumsky =-=[52]-=-, and Rykov and Efrosinin [49], Asymptotic analysis—“conventional” heavy traffic: Foschini [24], Reiman [47], Kelly and Laws [38], Harrison [33], Bell and Williams [10], Glazebrook and Niño-Mora [28],... |

5 |
On the rational determination of the number of circuits,” in The Life and Works of
- ERLANG
- 1917
(Show Context)
Citation Context ...s? Is the FSF policy optimal in that regime? Is a threshold needed in that case? The asymptotic framework considered in this paper is the many-server heavy-traffic regime, 2 first appearing in Erlang =-=[20]-=-, and formally introduced by Halfin and Whitt [32]. We refer to this regime as the QED (Quality and Efficiency Driven) regime. Systems that operate in the QED regime enjoy a rare combination of high e... |

3 |
Routing and staffing in large-scale service systems with heterogeneous servers and impatient customers
- Armony, Mandelbaum
- 2007
(Show Context)
Citation Context ...[36] and M/M/N with exponential patience [27]. More recently, this equivalence was also shown to be true in the multiple customer classes case [30], as well as in the setting considered in this paper =-=[4]-=-. The QED regime was explicitly recognized already in Erlang’s 1923 paper (that appeared in [20]) which addresses both Erlang-B (M/M/N/N) and Erlang-C (M/M/N)292 ARMONY models. Later on, extensive re... |

3 |
A routing problem for call centers with customer callbacks after service failure
- Véricourt, Zhou
- 2005
(Show Context)
Citation Context ...this solution is not optimal. As was shown for the two server288 ARMONY λ N 1 N 2 N 3 N K µ 1 µ 2 µ 3 µ K Figure 1. The inverted-V model—a single customer class and multiple server types. case (e.g. =-=[18,39]-=-) it is sometimes necessary to keep customers waiting even when the slower server is idle in order not to starve the faster server. Specifically, optimality is obtained by assigning customers to the s... |

3 |
A Note On the Incomplete Results for the MultipleServer Slow-Server Problem
- Véricourt, Zhou
- 2004
(Show Context)
Citation Context ...e [55] showed that a state-independent threshold policy is asymptotically optimal as traffic intensity approaches 1. In particular, in the limit, the threshold level approaches infinity. According to =-=[19]-=-, the problem of finding an optimal policy for the general multi-heterogeneous server case (considered in [41,48,49]) is still open. But what about the many-server heavy-traffic regime that typifies l... |

3 |
M/G/c systems with multiple customer classes: characterization and achievable performance unrder nonpreemptive priority rules
- Federgruen, Groenevelt
- 1988
(Show Context)
Citation Context ...ultiple server pools. There is an extensive literature on skill-based routing. Examples include: Exact (non-asymptotic) analysis: Lin and Kumar [39], Kella and Yechiali [37], Federgruen and Groenvelt =-=[22]-=-, Brandt and Brandt [14], Gans and Zhou [26], Armony and Bambos [1], Rykov [48], Luh and Viniotis [41], Bhulai and Koole [11], de Véricourt and Zhou [18], Shumsky [52], and Rykov and Efrosinin [49], A... |

2 |
Comparing ordered-entry queues with heterogeneous servers, Queueing Systems 2
- Shanthikumar, Yao
- 1987
(Show Context)
Citation Context ...Y (∞; π) ofY (t; π), as t→∞ (or a subsequence thereof), we have P{Y (∞; π) > y} ≥P{Y (∞; FSFP) > y}, for all y ≥ 0. Remark 3.1 (Dominance of FSF among work-conserving policies). Shanthikumar and Yaoin=-=[51]-=- show that FSF is path-wise optimal among all work-conserving policies. The optimality we establish here is weaker in the sense that it only considers the process in steady-state, but is stronger in t... |

2 |
Staffing of large service systems: The case of a single customer class and multiple server types
- Armony, Mandelbaum
- 2004
(Show Context)
Citation Context ...[36] and M/M/N with exponential patience [27]. More recently, this equivalence was also shown to be true in the multiple customer classes case [30], as well as in the setting considered in this paper =-=[4]-=-. The QED regime was explicitly recognized already in Erlang’s 1923 paper (that appeared in [20]) which addresses both Erlang-B (M/M/N/N) and Erlang-C (M/M/N) models. Later on, extensive related work ... |

2 |
Stolyar S (2004) Scheduling flexible servers with convex delay costs: Heavy-traffic optimality of the generalized c�-rule
- Mandelbaum
(Show Context)
Citation Context ...lysis - “conventional” heavy traffic: Foschini [24], Reiman [47], Kelly and Laws [38], Harrison [33], Bell and Williams [10], Glazebrook and Niño-Mora [28], Teh and Ward [55], Mandelbaum and Stolyar =-=[43]-=- and Stolyar [53], and Asymptotic analysis - many server systems: Armony and Maglaras [2, 3], Harrison and Zeevi [34], Atar et. al. [7], Atar [5, 6], Gurvich [30], Gurvich, Armony and Mandelbaum [31],... |

2 |
Wallace 2004. An optimal design of the M/M/C/K queue for call centers. Queueing Systems
- Massey, B
(Show Context)
Citation Context ...s operating in the QED regime). A precise characterization of the asymptotic expansion of the blocking probability, for Erlang-B in the QED regime, was given in Jagerman [35]; see also [57], and then =-=[44]-=- for the analysis of finite buffers. But the operational significance of the QED regime, in particular its balancing of “service and economy” via a non-trivial delay probability, was first discovered ... |

1 | Diffusion approximations, Stochastic models, Handbooks - Glynn - 1990 |

1 |
The GI/D/N queue
- Jelenkovic, Mandelbaum, et al.
- 2004
(Show Context)
Citation Context ... λ , −∞ <β<∞. (1.2) Yet another equivalent characterization is a non-trivial limit (within (0, 1)) of the fraction of delayed customers. The latter equivalence was established for GI/M/N [32], GI/D/N =-=[36]-=- and M/M/N with exponential patience [27]. More recently, this equivalence was also shown to be true in the multiple customer classes case [30], as well as in the setting considered in this paper [4].... |

1 |
A note on the incomplete results for the multiple- server slow-server problem
- Véricourt, Zhou
- 2004
(Show Context)
Citation Context ...e [55] showed that a state-independent threshold policy is asymptotically optimal as traffic intensity approaches 1. In particular, in the limit, the threshold level approaches infinity. According to =-=[19]-=-, the problem of finding an optimal policy for the general multi-heterogeneous server case (considered in [48, 41, 49]) is still open. But what about the many-server heavy-traffic regime that typifies... |