THESIS
2013
xiv, 132 pages : illustrations ; 30 cm
Abstract
As well-developed methodologies and tools, stochastic modeling and simulation techniques are
widely used in many areas in operations research and management science. In this thesis, we
investigate three issues in stochastic modeling and simulation.
The first one is to study instant-massaging (IM) contact centers, a new type of customer
service centers built by many companies, as a many-server queueing model. In an IM center,
agents communicate with customers via instant massaging over the Internet rather than phone
calls in a traditional call center. A distinctive feature of the service centers based on IM is that
one agent can serve multiple customers in parallel, which has been modeled as a server pool
consisting of many limited processor sharing (LPS) servers. In this thesis,...[
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As well-developed methodologies and tools, stochastic modeling and simulation techniques are
widely used in many areas in operations research and management science. In this thesis, we
investigate three issues in stochastic modeling and simulation.
The first one is to study instant-massaging (IM) contact centers, a new type of customer
service centers built by many companies, as a many-server queueing model. In an IM center,
agents communicate with customers via instant massaging over the Internet rather than phone
calls in a traditional call center. A distinctive feature of the service centers based on IM is that
one agent can serve multiple customers in parallel, which has been modeled as a server pool
consisting of many limited processor sharing (LPS) servers. In this thesis, we characterize the
underlying stochastic processes by establishing a fluid approximation in the many-server heavy-traffic
regime. The limiting behavior of the stochastic processes is shown to involve a stochastic
averaging principle, and the fluid approximation provides insights into the optimal staffing and
control for such service centers.
Stochastic modeling plays a key role in the first part while the simulation contributes mainly
as a tool to demonstrate the established theoretical results. However, in the second part, we
focus on a purely simulation problem in which the research difficulties arisen can be illustrated
by a queueing analogy. The simulation problem considered in the second topic is to design sequential
selection procedures that can be implemented in a parallel computing environment to
select the best from a finite set of alternatives, which is known as ranking-and-selection (R&S)
problems in the simulation literature. Existing sequential R&S procedures are often designed
for a single-processor simulation environment. However, with fast development of computing
technologies, parallel computing environments, such as multi-core personal computers and many-core servers, are becoming ubiquitous and easily accessible for ordinary users. To design
sequential procedures that can be used in parallel computing environments, a critical question
that needs to be answered is “what makes sequential procedures on multiple processors different
from the ones on a single processor?” In this thesis, we develop a multi-server queueing
analogy to answer this question and show that simply plugging existing sequential procedures
in a parallel scheme may be neither statistically valid nor efficient. To address these issues, we
propose two general approaches: vector filling (VF) procedures and asymptotic parallel sequential
(APS) procedures. Roughly speaking, a distinguished difference between these two types of
procedures is that VF procedures conduct elimination decisions according to the input sequence
(i.e., simulation observations sorted according to the time points at which they start simulation)
while APS procedures make elimination decisions based on the output sequence (i.e., simulation
observations sorted according to the time points at which they finish simulation). To
implement the two proposed procedures, we design a parallel computing environment using a
multi-processor simulator on a single processor. Extensive numerical experiments show that
the proposed procedures can take advantage of parallel computing schemes to solve large-scale
R&S problems.
The R&S problems in the second part consider only one performance measure as the objective
to be compared with each other. There exists, however, another type of selection problems
that intend to select the best solution with the largest or smallest mean of a primary performance
measure from finite solutions while requiring secondary performance measures to satisfy certain
constraints, which is called constrained selection of the best (CSB) in the simulation R&S
literature. In this thesis, we consider CSB problems whose secondary performance measures
must satisfy probabilistic constraints, and we call such problems chance constrained selection
of the best (CCSB).We design procedures that first check the feasibility of all solutions and then
select the best among all of the sample feasible solutions; and we prove the statistical validity of
these procedures for variations of the CCSB problem under the indifference-zone formulation.
Numerical results show that the proposed procedures can efficiently handle different CCSB problems.
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