CALL CENTERS (CENTRES) - Faculty of Industrial Engineering and ...

Keywords: Operations research, Call centers, Service level agreements, Equilibrium, Mathematical
models, Routing, Optimization, Real time
130. Atar, R., A. Mandelbaum and M.I. Reiman. Scheduling a multi-class queue with many exponential
servers: Asymptotic optimality in heavy-traffic, Annals of Appl. Prob., 14 (3), 2004,
1084–1134. Downloadable from: .
Abstract. We consider the problem of scheduling a queueing system in which many i.i.d.
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 heavy-traffic 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.)
We first consider a formal weak limit, through which our queueing scheduling problem gives rise
to a diffusion control problem. We show that the latter has an optimal Markov control policy,
and that the corresponding Hamilton-Jacobi-Bellman (HJB) equation has a unique classical solution.
The Markov control policy and the HJB equation are then used to define scheduling
control policies which we prove are asymptotically optimal for our original queueing system.
The analysis yields both qualitative and quantitative insights, in particular on staffing levels,
the roles of non-preemption and work-conservation, and the tradeoff between service quality and
servers’ efficiency.
131. Atar, R., A. Mandelbaum and M.I. Reiman. A Brownian control problem for a simple queueing
system in the Halfin-Whitt regime, Systems and Control Letters, 51 (3–4), 2004, 269–275.
Abstract. We consider a formal diffusion limit for a control problem of a multi-type multiserver
queueing system, in the regime proposed by Halfin and Whitt, in the form of a control
problem where the dynamics are driven by a Brownian motion. In one dimension, a pathwise
minimum is obtained and is characterized as the solution to a SDE. The pathwise solution to a
special multi-dimensional problem (corresponding to a multi-type system) follows.
Keywords: Queueing networks, Stochastic control, Heavy traffic asymptotics
132. Atlason, Julius, Marina A. Epelman and Shane G. Henderson. Call center staffing with simulation
and cutting plane methods, Annals of Operations Research, 127 (1–4), March 2004, 333–358.
Available at: http://critical.orie.cornell.edu/∼shane/pubs.html.
Abstract. We present an iterative cutting plane method for minimizing staffing costs in a
service system subject to satisfying acceptable service level requirements over multiple time periods.
We assume that the service level cannot be easily computed, and instead, is evaluated
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