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Fair dynamic routing in largescale heterogeneousserver systems
, 2008
"... In a call center, there is a natural tradeoff between minimizing customer wait time and fairly dividing the workload amongst agents of different skill levels. The relevant control is the routing policy; that is, the decision concerning which agent should handle an arriving call when more than one a ..."
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Cited by 24 (5 self)
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In a call center, there is a natural tradeoff between minimizing customer wait time and fairly dividing the workload amongst agents of different skill levels. The relevant control is the routing policy; that is, the decision concerning which agent should handle an arriving call when more than one agent is available. We formulate an optimization problem for a call center with two heterogeneous agent pools, one that handles calls at a faster speed than the other, and a single customer class. The objective is to minimize steadystate expected customer wait time subject to a “fairness” constraint on the workload division. The optimization problem we formulate is difficult to solve exactly. Therefore, we solve the diffusion control problem that arises in the manyserver heavytraffic QED limiting regime. The resulting routing policy is a threshold policy that prioritizes faster agents when the number of customers in the system exceeds some threshold level and otherwise prioritizes slower agents. We prove our proposed threshold routing policy is nearoptimal as the number of agents increases, and the system’s load approaches its maximum processing capacity. We further show simulation results that evidence that our proposed threshold routing policy outperforms a common routing policy used in call centers (that routes to the agent that has been idle the longest) in terms of the steadystate expected customer waiting time for identical desired workload divisions.
Manyserver diffusion limits for G/Ph/n+GI queues
, 2009
"... This paper studies manyserver limits for multiserver queues that have a phasetype service time distribution and allow for customer abandonment. The first set of limit theorems is for critically loaded G/Ph/n + GI queues, where the patience times are independent, identically distributed following ..."
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Cited by 19 (9 self)
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This paper studies manyserver limits for multiserver queues that have a phasetype service time distribution and allow for customer abandonment. The first set of limit theorems is for critically loaded G/Ph/n + GI queues, where the patience times are independent, identically distributed following a general distribution. The next limit theorem is for overloaded G/Ph/n + M queues, where the patience time distribution is restricted to be exponential. We prove that a pair of diffusionscaled totalcustomercount and serverallocation processes, properly centered, converges in distribution to a continuous Markov process as the number of servers n goes to infinity. In the overloaded case, the limit is a multidimensional diffusion process, and in the critically loaded case, the limit is a simple transformation of a diffusion process. When the queues are critically loaded, our diffusion limit generalizes the result by Puhalskii and Reiman (2000) for GI/Ph/n queues without customer abandonment. When the queues are overloaded, the diffusion limit provides a refinement to a fluid limit and it generalizes a result by Whitt (2004) for M/M/n / + M queues with an exponential service time distribution. The proof techniques employed in this paper are innovative. First, a perturbed system is shown to be equivalent to the original system. Next, two maps are employed in both fluid and diffusion scalings. These maps allow one to
Staffing Call Centers with Uncertain Demand Forecasts: A ChanceConstrained Optimization Approach
, 2010
"... We consider the problem of staffing call centers with multiple customer classes and agent types operating under qualityofservice (QoS) constraints and demand rate uncertainty. We introduce a formulation of the staffing problem that requires that the QoS constraints are met with high probability wi ..."
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Cited by 8 (1 self)
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We consider the problem of staffing call centers with multiple customer classes and agent types operating under qualityofservice (QoS) constraints and demand rate uncertainty. We introduce a formulation of the staffing problem that requires that the QoS constraints are met with high probability with respect to the uncertainty in the demand rate. We contrast this chanceconstrained formulation with the averageperformance constraints that have been used so far in the literature. We then propose a twostep solution for the staffing problem under chance constraints. In the first step, we introduce a random static planning problem (RSPP) and discuss how it can be solved using two different methods. The RSPP provides us with a firstorder (or fluid) approximation for the true optimal staffing levels and a staffing frontier. In the second step, we solve a finite number of staffing problems with known arrival rates—the arrival rates on the optimal staffing frontier. Hence, our formulation and solution approach has the important property that it translates the problem with uncertain demand rates to one with known arrival rates. The output of our procedure is a solution that is feasible with respect to the chance constraint and nearly optimal for large call centers.
Scheduling parallel servers in the nondegenerate slowdown diffusion regime: Asymptotic optimality results
, 2011
"... We consider the problem of minimizing queuelength costs in a system with heterogenous parallel servers, operating in a manyserver heavytraffic regime with nondegenerate slowdown. This regime is distinct from the wellstudied heavy traffic diffusion regimes, namely the (single server) conventiona ..."
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We consider the problem of minimizing queuelength costs in a system with heterogenous parallel servers, operating in a manyserver heavytraffic regime with nondegenerate slowdown. This regime is distinct from the wellstudied heavy traffic diffusion regimes, namely the (single server) conventional regime and the (manyserver) HalfinWhitt regime. It has the distinguishing property that waiting times and service times are of comparable magnitudes. We establish an asymptotic lower bound on the cost and devise a sequence of policies that asymptotically attain this bound. As in the conventional regime, the asymptotics can be described by means of a Brownian control problem, the solution of which exhibits a state space collapse.