Essays on Stochastic Models of Service Systems

• Author / Creator

  Campello de Souza, Fernanda M

• 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.

• Subjects / Keywords

  • Service Systems
  • Stochastic Models
  • Healthcare - Emergency Departments
  • Case Managers
  • Queueing Systems

• Graduation date

  Fall 2013

• Type of Item

  Thesis

• Degree

  Doctor of Philosophy

• DOI

  https://doi.org/10.7939/R3J966

• License

  This thesis is made available by the University of Alberta Libraries with permission of the copyright owner solely for non-commercial purposes. This thesis, or any portion thereof, may not otherwise be copied or reproduced without the written consent of the copyright owner, except to the extent permitted by Canadian copyright law.