Maximizing Patient Satisfaction in Systems with Time-Varying Arrival Rates
Date
2023-04-24
Authors
Rabiei Fard, Leila
Journal Title
Journal ISSN
Volume Title
Publisher
ORCID
0009-0009-6534-3243
Type
Thesis
Degree Level
Masters
Abstract
Time-Varying Little’s Law (TVLL) can be regarded as part of the theory of Infinite Servers (IS)
models, for the abstract system can be considered as a general IS model if waiting time is considered as service time. Moreover, the time-varying arrival rate does not affect the waiting time
distribution, when there are adequate time-varying servers in the system. In this study, we estimate
the average number of entities in the system over a sub-interval and the arrival rate function, and
apply TVLL combined with time-varying staffing to estimate the unknown mean wait times. When
the arrival rate function is approximated by a linear (quadratic) function, the average waiting time
satisfies a quadratic (cubic) equation. The estimation of average waiting time based on TVLL is a
positive real root of the average waiting time equation.
If, the arrival rate function is neither approximately linear nor approximately quadratic, it must
be approximated by a polynomial function of higher degree. In this study, we investigate systems
with arrival rate function of degree 3, and find the estimation of average waiting time which is the
root of a polynomial of degree 4.
Also, we study queues with time-varying arrival rate to obtain optimal visit time leading to
maximum satisfaction of patients in walk-in clinics. If there is adequate time-varying staffing,
then customers receive service upon arrival and waiting times tend to be approximately as equal as
the service times though the arrival rates are time-varying. However, in the systems with limited
servers, some customers must wait in the waiting room and when there is no room in the area,
the new arriving customers are refused. Rejection of customers may lead to their dissatisfaction.
If we decrease the average service time, less customers will be refused, but shorter service time
decreases happiness of admitted customers.
Another issue is the revenue of walk-in clinics. Walk-in clinics work on a fee-for-service
model, so they benefit from the number of patients they serve. As the number of patients increases,
more revenue is gained. Hence, it may be in interest of some walk-in clinics to reduce visit times to increase profit. As mentioned, short visit time sacrifices the quality of service and leads to the
dissatisfaction of patients. Patients want to be heard carefully and be asked directly why they have
come to the clinic. The problem gets worse in rush hours when the number of arrivals increases
but the number of servers could not be increased due to limitation in the number of doctors.
We obtain optimal value for visit time considering satisfaction of customers and revenue of
walk-in clinics simultaneously.
Description
Keywords
Queueing System, Markov Chain, Queueing Theory, Little’s law (LL), Time-Varying Little’s Law (TVLL), Time-Varying Arrival rate
Citation
Degree
Master of Science (M.Sc.)
Department
Mathematics and Statistics
Program
Mathematics