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Essays on Stochastic Models of Service Systems Open Access


Other title
Stochastic Models
Service Systems
Healthcare - Emergency Departments
Queueing Systems
Case Managers
Type of item
Degree grantor
University of Alberta
Author or creator
Campello de Souza, Fernanda M
Supervisor and department
Armann Ingolfsson (Faculty of Business)
Examining committee member and department
Janelle Harms (Department of Computing Science, University of Alberta)
Robert A Shumsky (Tuck School of Business at Dartmouth)
Bora Kolfal (Faculty of Business, University of Alberta)
Noah Gans (The Wharton School of the University of Pennsylvania)
Yonghua Ji (Faculty of Business, University of Alberta)
Raymond Paterson (Faculty of Business, University of Alberta)
Faculty of Business
Operations and Information Systems
Date accepted
Graduation date
Doctor of Philosophy
Degree level
We propose methods to plan capacity for two types of service systems: traditional multiserver systems, where customers wait in a single queue to be served by the first available service provider, in a single processing step (e.g., bank tellers); and case manager systems, where customers wait in a single queue to be assigned to a case manager who will handle all (multiple) processing steps required to complete service to that customer (e.g, emergency departments physicians). Many researchers have addressed the problem of determining staffing requirements for traditional multiserver service systems. These requirements are often determined by segmenting time into periods and using a sequence of steady-state queueing models. The resulting requirements are approximate because nonstationary and transient effects are not considered. We propose using a non-stationary infinite-server model to determine staffing requirements for a finite-server model with the same arrival process. We prove that the resulting staffing requirements are necessary in the sense that the number of servers in a period must be greater than or equal to that period's staffing requirement in order to achieve the desired quality of service, regardless of how the system was staffed in previous periods. The requirements are exact in the sense that no steady-state approximation is used. We demonstrate the effectiveness of the requirements with numerical examples. Comparatively few researchers have studied case manager systems, despite its ubiquity in real-world service systems. We propose a baseline stochastic model for this type of system, along with three stochastic models to aid in performance evaluation and capacity planning: a model that provides lower bounds on performance measures and approximates stability conditions for the baseline system, a model that provides upper bounds on performance measures for the baseline system, and a model that approximates performance measures for the baseline system. We also examine how waiting times in case manager systems are affected by the imposition of an upper limit on the number of customers simultaneously handled by each case manager, and propose heuristic methods for choosing such a limit effectively.
Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. Where the thesis is converted to, or otherwise made available in digital form, the University of Alberta will advise potential users of the thesis of these terms. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.
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