Abstract
Deployment or distribution of valuable medical resources has emerged as an increasing challenge to hospital administrators and health policy makers. The hospital emergency department (HED) census and workload can be highly variable. Improvement of emergency services is an important stage in the development of the healthcare system and research on the optimal deployment of medical resources appears to be an important issue for HED long-term management. HED performance, in terms of patient flow and available resources, can be studied using the queue-based approach. The kernel point of this research is to approach the optimal cost on logistics using queuing theory. To model the proposed approach for a qualitative profile, a generic HED system is mapped into the M/M/R/N queue-based model, which assumes an R-server queuing system with Poisson arrivals, exponentially distributed service times and a system capacity of N. A comprehensive quantitative mathematical analysis on the cost pattern was done, while relevant simulations were also conducted to validate the proposed optimization model. The design illustration is presented in this paper to demonstrate the application scenario in a HED platform. Hence, the proposed approach provides a feasibly cost-oriented decision support framework to adapt a HED management requirement.
Highlights
To formulate the cost function, some cost parameters are defined in the following vector form as follows: CCqq ==ccoossttppeerruunnititttimimeewwhheennoonneeccuussttoommeerriisswwaaiittiinnggffoorrsseerrvviiccee, CCss ==ccoossttppeerruunnititttimimeewwhheennoonneeccuussttoommeerrjojoiinnsstthheessyysstteemmaannddiisssseerrvveedd, ((CCBB,CCI)I)==cocsotstppereruunnitittitmimeewwhhenenoonneesesrevrvererisis(b(buusysy,ididlele).)
Using the definitions of each cost element with its corresponding feature, the cost function F(R, N) can be developed in association with the system metrics Ls, PB, Lq, E[I], and E[B], which are given in Equations (10)–(12), (7) and (8), respectively
It is noted that the steady-state probabilities for two segments are given in Equations (2) and (3)
Summary
Hospitals play an important role in the healthcare system of society. They have changed rapidly in parallel with improvements in medical instruments and medicine. One of the most demanding departments in terms of economic resource consumption and programming is the hospital emergency department (HED) To this extent its operational profile should be monitored and optimized in order to provide the optimal quality of medical service subject to the budget constraint. An M/M/R/N queuing model was adopted to explore the cost profile from analyzing the relationships among relevant performance parameters in a HED, such as the number of staffing providers (i.e., servers) needed during each staffing interval. This model assumes a single queue with a limited system capacity of N that feeds into R identical medical servers (i.e., staffing providers). One advantage of adopting the M/M/R/N model is that given an arrival rate, an average service duration, and the number of servers, formulae for performance measures such as the cost profile, the average number of patients, or the average waiting time can be obtained
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