Queueing network approximations for mass dispensing and vaccination clinics

Abstract

To respond to bioterrorism events or to curb outbreaks of contagious diseases, county health departments must set up and operate clinics to dispense medications or vaccines. Planning these clinics before such an event occurs requires determining clinic capacity and estimating queueing performance.

Due to the nature of these facilities, we model a clinic as an open queueing network and estimate the time that county residents will spend at each workstation in such facilities. County residents are the customers, and the servers are the clinic staffs, who are the critical resource. Residents arrive according to an external (not necessarily Poisson) arrival process. When a resident arrives, he goes to the first workstation. Based on his information the resident moves from one workstation to another in the clinic.

We decompose the queueing network by estimating the performance of each workstation using a combination of exact and approximate models. There is a network of nodes and directed arcs. The nodes represent service facilities (workstations) and the arcs represent residents' flows through the clinic. We characterize each workstation by the first two moments of the interarrival time and service time distributions and consider it as a G/G/m queueing system. Congestion measures for the entire network are obtained by assuming as an approximation that the nodes are stochastically independent given the approximate flow parameters.

A key contribution of this thesis is to introduce approximations for workstations with batch arrivals and multiple parallel servers, for workstations with batch service processes and multiple parallel servers, and for self service workstations.

We validated the models for likely scenarios using data collected from emergency preparedness exercises and from simulation experiments. Although this research was motivated by this specific application, it should be applicable also to the design and analysis of manufacturing systems with batch service processes.