Results 1  10
of
118
Fluid models for multiserver queues with abandonments
 Operations Research
"... Deterministic fluid models are developed to provide simple firstorder performance descriptions for multiserver queues with abandonment under heavy loads. Motivated by telephone call centers, the focus is on multiserver queues with a large number of servers and nonexponential servicetime and ti ..."
Abstract

Cited by 43 (28 self)
 Add to MetaCart
Deterministic fluid models are developed to provide simple firstorder performance descriptions for multiserver queues with abandonment under heavy loads. Motivated by telephone call centers, the focus is on multiserver queues with a large number of servers and nonexponential servicetime and timetoabandon distributions. The first fluid model serves as an approximation for the G/GI/s + GI queueing model, which has a general stationary arrival process with arrival rate λ, independent and identically distributed (IID) service times with a general distribution, s servers and IID abandon times with a general distribution. The fluid model is useful in the overloaded regime, where λ> s, which is often realistic because only a small amount of abandonment can keep the system stable. Numerical experiments, using simulation for M/GI/s + GI models and exact numerical algorithms for M/M/s + M models, show that the fluid model provides useful approximations for steadystate performance measures when the system is heavily loaded. The fluid model accurately shows that steadystate performance depends strongly upon the timetoabandon distribution beyond its mean, but not upon the servicetime distribution beyond its mean. The second fluid model is a discretetime fluid model, which serves as an approximation for the Gt(n)/GI/s + GI queueing model, having a statedependent and timedependent arrival process. The discretetime framework is exploited to prove that properly scaled queueing processes in the queueing model converge to fluid functions as s → ∞. The discretetime framework is also convenient for calculating the timedependent fluid performance descriptions. Subject classifications: Queues, approximations: multiserver queues with abandonment. Queues, multichannel: approximation of nonMarkovian multichannel queues with customer abandonment.
Efficiencydriven heavytraffic approximations for manyserver queues with abandonments
 Management Science
, 2004
"... Motivated by the desire to understand the performance of serviceoriented call centers, which often provide lowtomoderate quality of service, this paper investigates the efficiencydriven (ED) limiting regime for manyserver queues with abandonments. The starting point is the realization that, in ..."
Abstract

Cited by 43 (28 self)
 Add to MetaCart
Motivated by the desire to understand the performance of serviceoriented call centers, which often provide lowtomoderate quality of service, this paper investigates the efficiencydriven (ED) limiting regime for manyserver queues with abandonments. The starting point is the realization that, in the presence of substantial customer abandonment, callcenter servicelevel agreements (SLA’s) can be met in the ED regime, where the arrival rate exceeds the maximum possible service rate. Mathematically, the ED regime is defined by letting the arrival rate and the number of servers increase together so that the probability of abandonment approaches a positive limit. To obtain the ED regime, it suffices to let the arrival rate and the number of servers increase with the traffic intensity ρ held fixed with ρ> 1 (so that the arrival rate exceeds the maximum possible service rate). Even though the probability of delay necessarily approaches 1 in the ED regime, the ED regime can be realistic because, due to the abandonments, the delays need not be excessively large. This paper establishes ED manyserver heavytraffic limits and develops associated approximations for performance measures in the M/M/s/r + M model, having a Poisson arrival process, exponential service times, s servers, r extra waiting spaces and exponential abandon times (the final +M). In the ED regime, essentially the same limiting behavior occurs when the abandonment rate α approaches 0 as when the number of servers s approaches ∞; indeed, it suffices to assume that s/α → ∞. The ED approximations are shown to be useful by comparing them to exact numerical results for the M/M/s/r + M model obtained using an algorithm developed in Whitt (2003), which exploits numerical transform inversion.
Dynamic routing in largescale service systems with heterogeneous servers, Queueing Systems
, 2005
"... Abstract. 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 s ..."
Abstract

Cited by 37 (12 self)
 Add to MetaCart
Abstract. 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.
A staffing algorithm for call centers with skillbased routing
 Manufacturing and Service Operations Management
, 2005
"... informs ® doi 10.1287/msom.1050.0086 © 2005 INFORMS Call centers usually handle several types of calls, butitis usually notpossible or costeffective to have every agent be able to handle every type of call. Thus, the agents tend to have different skills, in different combinations. In such an environ ..."
Abstract

Cited by 32 (7 self)
 Add to MetaCart
informs ® doi 10.1287/msom.1050.0086 © 2005 INFORMS Call centers usually handle several types of calls, butitis usually notpossible or costeffective to have every agent be able to handle every type of call. Thus, the agents tend to have different skills, in different combinations. In such an environment, it is challenging to route calls effectively and determine the staff requirements. This paper addresses both of these routing and staffing problems by exploiting limited crosstraining. Consistent with the literature on flexible manufacturing, we find that minimal flexibility can provide great benefits: Simulation experiments show that when (1) the servicetime distribution does not depend on the call type or the agent and (2) each agent has only two skills, in appropriate combinations, the performance is almost as good as when each agent has all skills. We apply this flexibility property to develop an algorithm for both routing and staffing, aiming to minimize the total staff subject to perclass performance constraints. With appropriate flexibility, it suffices to use a suboptimal routing algorithm. Simulation experiments show that the overall procedure can be remarkably effective: The required staff with limited crosstraining can be nearly the same as if all agents had all skills. Hence, the overall algorithm is nearly optimal for that scenario.
The Modern Call Center: A MultiDisciplinary Perspective on Operations Management Research
"... Call centers are an increasingly important part of today’s business world, employing millions of agents across the globe and serving as a primary customerfacing channel for firms in many different industries. Call centers have been a fertile area for operations management researchers in several dom ..."
Abstract

Cited by 32 (0 self)
 Add to MetaCart
Call centers are an increasingly important part of today’s business world, employing millions of agents across the globe and serving as a primary customerfacing channel for firms in many different industries. Call centers have been a fertile area for operations management researchers in several domains, including forecasting, capacity planning, queueing, and personnel scheduling. In addition, as telecommunications and information technology have advanced over the past several years, the operational challenges faced by call center managers have become more complicated. Issues associated with human resources management, sales, and marketing have also become increasingly relevant to call center operations and associated academic research. In this paper, we provide a survey of the recent literature on call center operations management. Along with traditional research areas, we pay special attention to new management challenges that have been caused by emerging technologies, to behavioral issues associated with both call center agents and customers, and to the interface between call center operations and sales and marketing. We identify a handful of broad themes for future investigation while also pointing out several very specific research opportunities.
Servicelevel differentiation in manyserver service systems: A solution based on fixedqueueratio routing
 OPERATIONS RESEARCH
, 2007
"... Motivated by telephone call centers, we study largescale service systems with multiple customer classes and multiple agent pools, each with many agents. For the purpose of delicately balancing service levels of the different customer classes, we propose a family of routing controls called FixedQue ..."
Abstract

Cited by 30 (18 self)
 Add to MetaCart
Motivated by telephone call centers, we study largescale service systems with multiple customer classes and multiple agent pools, each with many agents. For the purpose of delicately balancing service levels of the different customer classes, we propose a family of routing controls called FixedQueueRatio (FQR) rules. A newly available agent next serves the customer from the head of the queue of the class (from among those he is eligible to serve) whose queue length most exceeds a specified proportion of the total queue length. We show that the proportions can be set to achieve desired servicelevel targets for all classes; these targets are achieved asymptotically as the total arrival rate increases. The FQR rule is a special case of the QueueandIdlenessRatio (QIR) family of controls which in a previous paper where shown to produce an important statespace collapse (SSC) as the total arrival rate increases. This SSC facilitates establishing asymptotic results. In simplified settings, SSC allows us to solve a combined designstaffingandrouting problem in a nearly optimal way. Our analysis also establishes a diminishingreturns property of flexibility: Under FQR, very moderate crosstraining is sufficient to make the call center as efficient as a singlepool system, again in the limit as the total arrival rate increases.
Staffing of timevarying queues to achieve timestable performance
, 2005
"... Continuing research by Jennings, Mandelbaum, Massey and Whitt (1996), we investigate methods to perform timedependent staffing for manyserver queues. Our aim is to achieve timestable performance in face of general timevarying arrival rates. It turns out that it suffices to target a stable probab ..."
Abstract

Cited by 28 (19 self)
 Add to MetaCart
Continuing research by Jennings, Mandelbaum, Massey and Whitt (1996), we investigate methods to perform timedependent staffing for manyserver queues. Our aim is to achieve timestable performance in face of general timevarying arrival rates. It turns out that it suffices to target a stable probability of delay. That procedure tends to produce timestable performance for several other operational measures. Motivated by telephone call centers, we focus on manyserver models with customer abandonment, especially the Markovian Mt/M/st + M model, having an exponential timetoabandon distribution (the +M), an exponential servicetime distribution and a nonhomogeneous Poisson arrival process. We develop three different methods for staffing, with decreasing generality and decreasing complexity: First, we develop a simulationbased iterativestaffing algorithm (ISA), and conduct experiments showing that it is effective. The ISA is appealing because it applies to very general models and is automatically validating: we directly see how well it works. Second, we extend the squarerootstaffing rule, proposed by Jennings et al., which is based on the associated infiniteserver model. The rule dictates that the staff level at time t be st = mt + β √ mt, where mt is the offered load (mean number of busy servers in the infiniteserver model) and the constant β reflects the service grade. We show that the service grade β in the staffing formula can be represented as a function of the target delay probability α by
Engineering solution of a basic callcenter model
 Management Science
, 2005
"... An algorithm is developed to rapidly compute approximations for all the standard steadystate performance measures in the basic callcenter queueing model M/GI/s/r+GI, which has a Poisson arrival process, IID service times with a general distribution, s servers, r extra waiting spaces and IID custom ..."
Abstract

Cited by 27 (21 self)
 Add to MetaCart
An algorithm is developed to rapidly compute approximations for all the standard steadystate performance measures in the basic callcenter queueing model M/GI/s/r+GI, which has a Poisson arrival process, IID service times with a general distribution, s servers, r extra waiting spaces and IID customer abandonment times with a general distribution. Empirical studies of call centers indicate that the servicetime and abandontime distributions often are not nearly exponential, so that it is important to go beyond the Markovian M/M/s/r + M special case, but the general servicetime and abandontime distributions make the realistic model very difficult to analyze directly. The proposed algorithm is based on an approximation by an appropriate Markovian M/M/s/r + M(n) queueing model, where M(n) denotes statedependent abandonment rates. After making an additional approximation, steadystate waitingtime distributions are characterized via their Laplace transforms. Then the approximate distributions are computed by numerically inverting the transforms. Simulation experiments show that the approximation is quite accurate. The overall algorithm can be applied to determine desired staffing levels, e.g., the minimum number of servers needed to guarantee that, first, the abandonment rate is below any specified target value and, second, that the conditional probability that an arriving customer will be served within a specified deadline, given that the customer eventually will be served, is at least a specified target value.
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 26 (8 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.)
A diffusion approximation for the G/GI/n/m queue
 Operations Research
"... informs ® doi 10.1287/opre.1040.0136 © 2004 INFORMS We develop a diffusion approximation for the queuelength stochastic process in the G/GI/n/m queueing model (having a general arrival process, independent and identically distributed service times with a general distribution, n servers, and m extra ..."
Abstract

Cited by 26 (7 self)
 Add to MetaCart
informs ® doi 10.1287/opre.1040.0136 © 2004 INFORMS We develop a diffusion approximation for the queuelength stochastic process in the G/GI/n/m queueing model (having a general arrival process, independent and identically distributed service times with a general distribution, n servers, and m extra waiting spaces). We use the steadystate distribution of that diffusion process to obtain approximations for steadystate performance measures of the queueing model, focusing especially upon the steadystate delay probability. The approximations are based on heavytraffic limits in which n tends to infinity as the traffic intensity increases. Thus, the approximations are intended for large n. For the GI/M/n/ � special case, Halfin and Whitt (1981) showed that scaled versions of the queuelength process converge to a diffusion process when the traffic intensity �n approaches 1 with �1 − �n � √ n → � for 0 <�<�. A companion paper, Whitt (2005), extends that limit to a special class of G/GI/n/mn models in which the number of waiting places depends on n and the servicetime distribution is a mixture of an exponential distribution with probability p and a unit point mass at 0 with probability 1 − p. Finite waiting rooms are treated by incorporating the additional limit mn / √ n → � for 0 <� � �. The approximation for the more general G/GI/n/m model developed here is consistent