Maximizing Patient Satisfaction in Systems with Time-Varying Arrival Rates
| dc.contributor.advisor | Samei, Ebrahim | |
| dc.contributor.advisor | Samarghandi, Hamed | |
| dc.contributor.committeeMember | Liu, Juxin | |
| dc.contributor.committeeMember | Xing, Li | |
| dc.contributor.committeeMember | Rayan, Steven | |
| dc.creator | Rabiei Fard, Leila | |
| dc.creator.orcid | 0009-0009-6534-3243 | |
| dc.date.accessioned | 2023-04-26T17:00:38Z | |
| dc.date.available | 2023-04-26T17:00:38Z | |
| dc.date.copyright | 2023 | |
| dc.date.created | 2023-04 | |
| dc.date.issued | 2023-04-24 | |
| dc.date.submitted | April 2023 | |
| dc.date.updated | 2023-04-26T17:00:38Z | |
| dc.description.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. | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | https://hdl.handle.net/10388/14626 | |
| dc.language.iso | en | |
| dc.subject | Queueing System, Markov Chain, Queueing Theory, Little’s law (LL), Time-Varying Little’s Law (TVLL), Time-Varying Arrival rate | |
| dc.title | Maximizing Patient Satisfaction in Systems with Time-Varying Arrival Rates | |
| dc.type | Thesis | |
| dc.type.material | text | |
| thesis.degree.department | Mathematics and Statistics | |
| thesis.degree.discipline | Mathematics | |
| thesis.degree.grantor | University of Saskatchewan | |
| thesis.degree.level | Masters | |
| thesis.degree.name | Master of Science (M.Sc.) |