טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentGalit Yom-Tov
SubjectQueues in Hospitals: Stochastic Networks with ReEntering
Customers in the QED Regime (QED - Quality and
Efficiency Driven)
DepartmentDepartment of Industrial Engineering and Management
Supervisor Full Professor Mandelbaum Avishai
Full Thesis textFull thesis text - English Version


Abstract

We study queues in healthcare. We start by developing and analyzing a queueing model, which we call Erlang-R, where the ``R" stands for ReEntrant customers. The Erlang-R model accommodates customers who return to service several times during their sojourn within the system. It is most significant in time-varying environments. Indeed, it was motivated by healthcare systems, in which workloads are time-inhomogeneous and patients often go through a discontinuous service process. For example, in Emergency Wards, physicians are revisited by patients whose service process consists of cycles: examination by a physician, lab tests, treatment by a physician and so forth .


The main question we address is: how many servers (doctors/nurses) are required (staffing) in order to achieve predetermined service levels stably over time . Based on our theory, we propose a staffing policy that attains pre-specified service levels in the Halfin-Whitt (QED) regime. This policy applies the Modified Offered Load (MOL) approximation. We validate our policy, via simulation, both for large and small systems, and we use an EW simulator to validate its usefulness in realistic scenarios. We thus show how to stabilize, via proper staffing, both service levels and servers' utilizations, in time-varying healthcare environments .


In the second part, we concentrate on analyzing semi-open queuing networks with ReEntrant customers. These networks are used to model a Medical Unit with s nurses that cater to n beds, which are partly/fully occupied by patients. Here the questions we addressed here are: How many servers (nurses) are required (staffing), and how many fixed resources (beds) are needed (allocation) in order to minimize costs while sustaining a certain service level? We answer this by developing QED regime policies that are asymptotically optimal at the limit, as the number of patients entering the system (λ), the number of beds (n) and the number of servers (s) grows jointly. Our steady-state approximations turn out accurate for parameter values that are realistic in a hospital setting.

We then use these approximations to develop MOL approximation to the closed-version of the Erlang-R model in a time-varying environment.


Our research was done in collaboration with one of the largest hospitals in Israel. This partnership provided us with the opportunity to analyze real data of patient-flow throughout the hospital, and validate our research in realistic situations. The last part of the research consists of this data analysis, concentrating mainly on hospitalization data in internal wards.