Title:
Many-server queues with customer abandonment

dc.contributor.advisor Dai, Jiangang
dc.contributor.author He, Shuangchi en_US
dc.contributor.committeeMember Ayhan, Hayriye
dc.contributor.committeeMember Foley, Robert D.
dc.contributor.committeeMember Kleywegt, Anton J.
dc.contributor.committeeMember Tezcan, Tolga
dc.contributor.department Industrial and Systems Engineering en_US
dc.date.accessioned 2011-09-22T17:50:45Z
dc.date.available 2011-09-22T17:50:45Z
dc.date.issued 2011-07-05 en_US
dc.description.abstract Customer call centers with hundreds of agents working in parallel are ubiquitous in many industries. These systems have a large amount of daily traffic that is stochastic in nature. It becomes more and more difficult to manage a call center because of its increasingly large scale and the stochastic variability in arrival and service processes. In call center operations, customer abandonment is a key factor and may significantly impact the system performance. It must be modeled explicitly in order for an operational model to be relevant for decision making. In this thesis, a large-scale call center is modeled as a queue with many parallel servers. To model the customer abandonment, each customer is assigned a patience time. When his waiting time for service exceeds his patience time, a customer abandons the system without service. We develop analytical and numerical tools for analyzing such a queue. We first study a sequence of G/G/n+GI queues, where the customer patience times are independent and identically distributed (iid) following a general distribution. The focus is the abandonment and the queue length processes. We prove that under certain conditions, a deterministic relationship holds asymptotically in diffusion scaling between these two stochastic processes, as the number of servers goes to infinity. Next, we restrict the service time distribution to be a phase-type distribution with d phases. Using the aforementioned asymptotic relationship, we prove limit theorems for G/Ph/n+GI queues in the quality- and efficiency-driven (QED) regime. In particular, the limit process for the customer number in each phase is a d-dimensional piecewise Ornstein-Uhlenbeck (OU) process. Motivated by the diffusion limit process, we propose two approximate models for a GI/Ph/n+GI queue. In each model, a d-dimensional diffusion process is used to approximate the dynamics of the queue. These two models differ in how the patience time distribution is built into them. The first diffusion model uses the patience time density at zero and the second one uses the entire patience time distribution. We also develop a numerical algorithm to analyze these diffusion models. The algorithm solves the stationary distribution of each model. The computed stationary distribution is used to estimate the queue's performance. A crucial part of this algorithm is to choose an appropriate reference density that controls the convergence of the algorithm. We develop a systematic approach to constructing a reference density. With the proposed reference density, the algorithm is shown to converge quickly in numerical experiments. These experiments also show that the diffusion models are good approximations of queues with a moderate to large number of servers. en_US
dc.description.degree Ph.D. en_US
dc.identifier.uri http://hdl.handle.net/1853/41185
dc.publisher Georgia Institute of Technology en_US
dc.subject Finite element method en_US
dc.subject Heavy-traffic limit en_US
dc.subject Diffusion approximation en_US
dc.subject Customer abandonment en_US
dc.subject Quality- and efficiency-regime en_US
dc.subject Many-server queue en_US
dc.subject.lcsh Call centers
dc.subject.lcsh Queuing theory
dc.subject.lcsh Approximation theory
dc.subject.lcsh Algorithms
dc.title Many-server queues with customer abandonment en_US
dc.type Text
dc.type.genre Dissertation
dspace.entity.type Publication
local.contributor.corporatename H. Milton Stewart School of Industrial and Systems Engineering
local.contributor.corporatename College of Engineering
relation.isOrgUnitOfPublication 29ad75f0-242d-49a7-9b3d-0ac88893323c
relation.isOrgUnitOfPublication 7c022d60-21d5-497c-b552-95e489a06569
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