Results 1  10
of
17
On Customer Contact Centers with a CallBack Option: Customer Decisions, Routing Rules, and System Design
, 2004
"... Organizations worldwide use contact centers as an important channel of communication and transaction with their customers. This paper describes a contact center with two channels, one for realtime telephone service, and another for a postponed callback service offered with a guarantee on the maxim ..."
Abstract

Cited by 78 (13 self)
 Add to MetaCart
(Show Context)
Organizations worldwide use contact centers as an important channel of communication and transaction with their customers. This paper describes a contact center with two channels, one for realtime telephone service, and another for a postponed callback service offered with a guarantee on the maximum delay until a reply is received. Customers are sensitive to both realtime and callback delay and their behavior is captured through a probabilistic choice model. The dynamics of the system are modeled as an M/M/N multiclass system. We rigorously justify that as the number of agents increases, the system’s load approaches its maximum processing capacity. Based on this observation, we perform an asymptotic analysis in the manyserver, heavy traffic regime to find an asymptotically optimal routing rule, characterize the unique equilibrium regime of the system, approximate the system performance, and finally, propose a staffing rule that picks the minimum number of agents that satisfies a set of operational constraints on the performance of the system.
Dynamic routing in largescale service systems with heterogeneous servers
, 2005
"... Motivated by modern call centers, we consider largescale service systems with multiple server pools and a single customer class. For such systems, we propose a simple routing rule which asymptotically minimizes the steadystate queue length and virtual waiting time. The proposed routing scheme is ..."
Abstract

Cited by 51 (12 self)
 Add to MetaCart
(Show Context)
Motivated by modern call centers, we consider largescale service systems with multiple server pools and a single customer class. For such systems, we propose a simple routing rule which asymptotically minimizes the steadystate queue length and virtual waiting time. The proposed routing scheme is FSF which assigns customers to the Fastest Servers First. The asymptotic regime considered is the HalfinWhitt manyserver heavytraffic regime, which we refer to as the Quality and Efficiency Driven (QED) regime; it achieves high levels of both service quality and system efficiency by carefully balancing between the two. Additionally, expressions are provided for system limiting performance measures based on diffusion approximations. Our analysis shows that in the QED regime this heterogeneous server system outperforms its homogeneous server counterpart.
Heavy Traffic Limits for Queues with Many Deterministic Servers
"... Consider a sequence of stationary GI/D/N queues indexed by N with servers' utilization 1 #/ # N , # > 0. For such queues we show that the scaled waiting times NWN converge to the (finite) supremum of a Gaussian random walk with drift #. ..."
Abstract

Cited by 51 (5 self)
 Add to MetaCart
Consider a sequence of stationary GI/D/N queues indexed by N with servers' utilization 1 #/ # N , # > 0. For such queues we show that the scaled waiting times NWN converge to the (finite) supremum of a Gaussian random walk with drift #.
A Diffusion Approximation for Markovian Queue with Reneging
, 2002
"... Consider a singleserver queue with a Poisson arrival process and exponential processing times in which each customer independently reneges after an exponentially distributed amount of time. We establish that this system can be approximated by either a reflected OrnsteinUhlenbeck process or a refle ..."
Abstract

Cited by 43 (3 self)
 Add to MetaCart
Consider a singleserver queue with a Poisson arrival process and exponential processing times in which each customer independently reneges after an exponentially distributed amount of time. We establish that this system can be approximated by either a reflected OrnsteinUhlenbeck process or a reflected affine diffusion when the arrival rate exceeds or is close to the processing rate and the reneging rate is close to 0. We further compare the quality of the steadystate distribution approximations suggested by each diffusion.
Scheduling a multiclass queue with many exponential servers: Asymptotic optimality in heavytraffic
 THE ANNALS OF APPLIED PROBABILITY
, 2004
"... We consider the problem of scheduling a queueing system in which many statistically identical servers cater to several classes of impatient customers. Service times and impatience clocks are exponential while arrival processes are renewal. Our cost is an expected cumulative discounted function, line ..."
Abstract

Cited by 41 (14 self)
 Add to MetaCart
We consider the problem of scheduling a queueing system in which many statistically identical servers cater to several classes of impatient customers. Service times and impatience clocks are exponential while arrival processes are renewal. Our cost is an expected cumulative discounted function, linear or nonlinear, of appropriately normalized performance measures. As a special case, the cost per unit time can be a function of the number of customers waiting to be served in each class, the number actually being served, the abandonment rate, the delay experienced by customers, the number of idling servers, as well as certain combinations thereof. We study the system in an asymptotic heavytraffic regime where the number of servers n and the offered load r are simultaneously scaled up and carefully balanced: n ≈ r + β √ r for some scalar β. This yields an operation that enjoys the benefits of both heavy traffic (high server utilization) and light traffic (high service levels.)
Dynamic scheduling of a multiclass queue in the HalfinWhitt heavy traffic regime
, 2003
"... We consider a Markovian model of a multiclass queueing system in which a single large pool of servers attends to the various customer classes. Customers waiting to be served may abandon the queue, and there is a cost penalty associated with such abandonments. Service rates, abandonment rates and aba ..."
Abstract

Cited by 39 (4 self)
 Add to MetaCart
(Show Context)
We consider a Markovian model of a multiclass queueing system in which a single large pool of servers attends to the various customer classes. Customers waiting to be served may abandon the queue, and there is a cost penalty associated with such abandonments. Service rates, abandonment rates and abandonment penalties are generally different for the different classes. The problem studied is that of dynamically scheduling the various classes. We consider the HalfinWhitt heavy traffic regime, where the total arrival rate and the number of servers both become large in such a way that the system’s traffic intensity parameter approaches one. An approximating diffusion control problem is described and justified as a purely formal (i.e., non rigorous) heavy traffic limit. The HamiltonJacobiBellman equation associated with the limiting diffusion control problem is shown to have a smooth (classical) solution, and optimal controls are shown to have an extremal or “bangbang ” character. Several useful qualitative insights are derived from the mathematical analysis, including a “square root rule ” for sizing large systems and a sharp contrast between system behavior in the HalfinWhitt regime versus that observed in the “conventional ” heavy traffic regime. The latter phenomenon is illustrated by means of a numerical example having two customer classes.
Pricing and design of differentiated services: Approximate analysis and structural insights
 Operations Research
, 2005
"... We consider a Markovian service system that offers two grades of service to a market of heterogenous users: a “guaranteed ” (G) service rate to high priority users, and “besteffort” (BE) type service, in which residual capacity not allocated to Gusers is shared by the low priority users. Users, in ..."
Abstract

Cited by 27 (5 self)
 Add to MetaCart
We consider a Markovian service system that offers two grades of service to a market of heterogenous users: a “guaranteed ” (G) service rate to high priority users, and “besteffort” (BE) type service, in which residual capacity not allocated to Gusers is shared by the low priority users. Users, in turn, are sensitive to both price and congestionrelated effects. The service provider’s objective is to optimally design the system so as to extract maximum revenues. This design problem consists of optimally pricing the two service classes, and determining the mechanism by which users are informed of the state of congestion in the system. Since these objectives are difficult to address using exact analysis, we pursue approximations that are tractable and lead to structural insights. Specifically, we first solve a deterministic problem to obtain a “fluidoptimal ” solution which is subsequently evaluated and refined to account for stochastic fluctuations. Using diffusion limits, we derive large capacity approximations that yield the following structural results: (i) pricing rules derived from the deterministic analysis are “almost” optimal; (ii) the optimal operational regime for the system is close to heavytraffic, and; (iii) realtime congestion notification results in increased revenues. Numerical results illustrate the accuracy of the proposed approximations and validate the aforementioned structural insights.
Queues with Many Servers: The Virtual WaitingTime Process in the QED Regime
, 2007
"... We consider a multiserver queue (G/GI/N) in the Quality and EfficiencyDriven (QED) regime. In this regime, which was first formalized by Halfin and Whitt, the number of servers N is not small, servers ’ utilization is 1 − O(1/√N) (EfficiencyDriven) while waiting time is O(1/ N) (QualityDriven). ..."
Abstract

Cited by 22 (1 self)
 Add to MetaCart
We consider a multiserver queue (G/GI/N) in the Quality and EfficiencyDriven (QED) regime. In this regime, which was first formalized by Halfin and Whitt, the number of servers N is not small, servers ’ utilization is 1 − O(1/√N) (EfficiencyDriven) while waiting time is O(1/ N) (QualityDriven). This is equivalent to having the number of servers N being approximately equal to R + β R, where R is the offered load and β is a positive constant. For the G/GI/N queue in the QED regime, we analyze the virtual waiting time VN (t), as N increases indefinitely. Assuming that the service time distribution has a finite support, it is shown that, in the limit, the scaled virtual waiting time V̂N (t) = NVN (t)/ES is representable as a supremum over a random weighted tree (S denotes a service time). Informally, it is then argued that, for large N,
Steadystate analysis of a multiserver queue in the HalfinWhitt regime
, 2008
"... We examine a multiserver queue in the HalfinWhitt (Quality and EfficiencyDriven) regime: as the number of servers n increases, the utilization approaches 1 from below at the rate Θ(1 / √ n). The arrival process is renewal and service times have a latticevalued distribution with a finite suppor ..."
Abstract

Cited by 14 (0 self)
 Add to MetaCart
We examine a multiserver queue in the HalfinWhitt (Quality and EfficiencyDriven) regime: as the number of servers n increases, the utilization approaches 1 from below at the rate Θ(1 / √ n). The arrival process is renewal and service times have a latticevalued distribution with a finite support. We consider the steadystate distribution of the queue length and waiting time in the limit as the number of servers n increases indefinitely. The queue length distribution, in the limit as n → ∞, is characterized in terms of the stationary distribution of an explicitly constructed Markov chain. As a consequence, the steadystate queue length and waiting time scale as Θ ( √ n) and Θ(1 / √ n) as n → ∞, respectively. Moreover, an explicit expression for the critical exponent is derived for the moment generating function of a limiting (scaled) steadystate queue length. This exponent depends on three parameters: the amount of spare capacity and the coefficients of variation of interarrival and service times. Interestingly, it matches an analogous exponent corresponding to a singleserver queue in the conventional heavytraffic regime. The results are derived by analyzing Lyapunov functions.
State Space Collapse in ManyServer Diffusion Limits of Parallel Server Systems
, 2006
"... We consider a class of queueing systems that consist of server pools in parallel and multiple customer classes. Customer service times are assumed to be exponentially distributed. We study the asymptotic behavior of these queueing systems in a heavy traffic regime that is known as the Halfin and Wh ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
(Show Context)
We consider a class of queueing systems that consist of server pools in parallel and multiple customer classes. Customer service times are assumed to be exponentially distributed. We study the asymptotic behavior of these queueing systems in a heavy traffic regime that is known as the Halfin and Whitt manyserver asymptotic regime. Our main contribution is a general framework for establishing state space collapse results in this regime for parallel server systems. In our work, state space collapse refers to a decrease in the dimension of the processes tracking the number of customers in each class waiting for service and the number of customers in each class being served by various server pools. We define and introduce a “state space collapse ” function, which governs the exact details of the state space collapse. We show that a state space collapse result holds in manyserver heavy traffic if a corresponding deterministic hydrodynamic model satisfies a similar state space collapse condition. Our methodology is similar in spirit to that in Bramson [10], which focuses on the conventional heavy traffic regime. We illustrate the applications of our results by establishing state space collapse results in manyserver diffusion limits of staticbufferpriority Vparallel server systems, Nmodel parallel server systems, and minimumexpecteddelay–fasterserverfirst distributed server pools systems. We show for these systems that the condition on the hydrodynamic model can easily be checked using the standard tools for fluid models.