טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentTseytlin Yulia
SubjectQueueing Systems with Heterogeneous Serves: On Fair Routing
of Patients in Emergency Departments
DepartmentDepartment of Industrial Engineering and Management
Supervisor Professor Avishai Mandelbaum
Full Thesis textFull thesis text - English Version


Abstract

We consider the process of patients' routing from an Emergency Department (ED) to Internal Wards (IWs) in Anonymous Hospital. We recognize two main problems in the process: patients' waiting times in the ED for a transfer to the IWs are long, and patients' allocation to the wards does not appear to be fair. This motivates us to model the ``ED-to-IW process" as a queueing system with heterogeneous server pools, where the pools represent the wards and servers are beds. We analyze this system under various queue-architectures and routing policies, in search for fairness and good operational performance.

Our queueing system, with a single centralized queue and several server pools, forms an Inverted-V model. We introduce the Randomized Most-Idle routing policy (RMI): each arriving customer joins one of the available pools, with a probability that equals the proportion of idle servers in this pool out of the overall number of idle servers in the system. The Inverted-V system under RMI gives rise to a reversible Markov process which can be analyzed, in steady-state, in closed form. Its analysis yields interesting operational insights, for example comparison of faster pools to slower pools.

We supplement the closed-form analysis by an asymptotic analysis in the QED (Quality and Efficiency Driven) regime, where efficiency is carefully balanced against service quality. The asymptotic analysis provides simplified expressions for some operational measures, e.g., the probability of delay in the system; it also yields insights on how idleness is shared among the pools, which adds more favorable ``points" to the fairness of RMI routing. A disadvantage of RMI is its being randomized, which motivates us to study alternatives: a class of non-randomized policies - WMI (Weighted Most-Idle). We compare those policies in the QED regime, according to various fairness and performance criteria; our analysis is tested against computer simulations.

Another queue-architecture considered is Distributed Finite Queues (DFQ). We propose the RMI equivalent for such a system, which also gives rise to a reversible Markov process and is analyzed in steady-state. In order to achieve additional practical insights, by accommodating some analytically intractable features and testing various routing policies, we model the ED-to-IW process by a computer simulation. With the simulation, we compare various routing policies, according to some fairness and performance criteria, while also accounting for the availability of information in the system. Finally, we comment on the ED-to-IW process from a game-theoretic view point.