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Modeling the surge beds in the emergency department in a hospital by Markov decision process and queueing theory Tirdad, Ali


In this thesis, we apply Markov decision theory to the problem involving M(t)/M/c/c queue to conduct a case study at Kelowna General Hospital (KGH) in British Columbia, Canada. Health-care systems have been challenged in recent years to deliver high quality care with limited resources. Emergency departments (ED) are perhaps the most sensitive components of the health-care system due to their nature. KGH has extra beds in its ED in a unit called the surge section. They use this section in case the ED is overcrowded. There is no systematic approach to when this section should be in use, and managerial decisions are made based on the what seems necessary at the time. Obviously, these decisions are usually costly and not based on a careful analysis. Therefore, they want to have a policy to know when to use the surge section. In this thesis, first we adapt the fourth order Runge-Kutta method (RK4) to obtain more accurate transient solutions for M(t)/M/c/c queues. We show numerically that our method works better than RK4 for our specific queue. Then we provide the Markov decision process (MDP) model for solving the problem. In this model, the arrival rate is time-dependent, and there are two levels for the number of servers. We prove that decisions for an MDP with periodic and time-dependent Poisson arrivals are periodic as well. Consequently, the contour control policies which are obtained based on the optimal decision show periodic behavior as well. Numerical results presented support this claim. Moreover, we model the seasonal flu epidemics and define a combined arrival rate for the ED. The results of this model support the claim about the periodicity of the policies as well. In addition, we show that a type of linear extrapolation is a reliable way to obtain control polices for large-scale problems.

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