Statistical analysis of queueing problems using real data

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2020-01-01
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Dai, Dong
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Arka P Ghosh
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Mathematics
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There are three topics in the thesis. In the first topic, the problem is a staffing problem for queues: we need to decide the number of representatives in a bank call center to optimize different performance measures. We compare the stability of the performance of two common staffing methods, square root staffing formula (SQSF) and iterative staffing algorithm (ISA), using the actual call center data from an Israeli bank. We also show the proof of the convergence of the ISA iterative method under the assumption of M(t)/M/s(t). In the second topic, we investigate the patients flow in the emergency department in the Rambam Medical Center, an Israeli hospital. We study the arrival process, the length of stay and the departure process. We show using simulations that the arrival process can be approximate by non-homogeneous Poisson process and the length of stay is a time-varying process in a day of week view. Based on our model, we can predict the number of beds needed each day in the hospital. In the third topic, we apply the actual data from Mercy Hospital in Des Moines. The problem is to compare the cost of add pharmacy technicians in the hospital to help correct patients' previous medications comparing to the benefit of reducing the errors made by patients. We build models to predict the number of errors corrected and the time needed by the pharmacy technicians. Using the salary of pharmacy technicians and known costs for correcting errors, our cost benefit analysis shows that additional help was financially beneficial to Mercy Hospital.

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Sat Feb 01 00:00:00 UTC 2020