THESIS
2018
xi, 82 pages : illustrations ; 30 cm
Abstract
In this thesis, we consider two applications of queueing theory. In the first part, we
study a two-stage security-check system which is motivated by the border-crossing stations
between United States and Canada. The main tradeoff in such a system is good
customer service (short waiting time) and high security level. We establish a two-stage
queueing model and derive the diffusion approximations under nondegenerate slowdown
regime for the system. Some numerical results are demonstrated to show the good
performance of our approximation formulas. We also consider the staffing problem under
guaranteed security and service levels based on the diffusion approximations, with
the decision variables being the proportion of travelers from stage 1 to stage 2 and the
number of staff membe...[
Read more ]
In this thesis, we consider two applications of queueing theory. In the first part, we
study a two-stage security-check system which is motivated by the border-crossing stations
between United States and Canada. The main tradeoff in such a system is good
customer service (short waiting time) and high security level. We establish a two-stage
queueing model and derive the diffusion approximations under nondegenerate slowdown
regime for the system. Some numerical results are demonstrated to show the good
performance of our approximation formulas. We also consider the staffing problem under
guaranteed security and service levels based on the diffusion approximations, with
the decision variables being the proportion of travelers from stage 1 to stage 2 and the
number of staff members in each stage. An efficient algorithm is proposed to solve the
staffing problem.
In the second part, we consider the problem of server scheduling in an overloaded multi-class queueing system with multiple homogeneous servers and general customer
abandonment. In the case of exponential reneging, an indexed priority policy, called the
cμ/θ rule, is known to be asymptotically optimal in the many-server heavy traffic regime,
where the arrival rates and number of servers increase proportionally. For general patience
distributions, we aim to find an asymptotically optimal control policy among the
class of fixed priority rules. We first describe a fluid model, which is known to be the limit
of the stochastic system under priority rules, and show its convergence to an equilibrium
state in the case of exponential service. We then formulate an optimization problem in
terms of these equilibrium states and derive a closed from expression for the optimal solution
when the hazard rate function of patience distribution is increasing and the cost
function is concave.
Post a Comment