M/C₂/c/K queuing model and optimization for a geriatric care center

Abstract

Queuing systems with finite buffers are reasonable models for many manufacturing, telecommunication, and healthcare systems. Although some approximations exist, the exact analysis of multi‐server and finite‐buffer queues with general service time distribution is unknown. However, the phase‐type assumption for service time is a frequently used approach. Because the Cox distribution, a kind of phase‐type distribution, provides a good representation of data with great variability, it has a vast area of application in modeling service times. The research focus is twofold. First, a theoretical structure of a multi‐server and finite‐buffer queuing system in which the service time is modeled by the two‐phase Cox distribution is studied. It is focused on finding an efficient solution to the stationary probabilities using the matrix‐geometric method. It is shown that the stationary probability vector can be obtained with the matrix‐geometric method by using level‐dependent rate matrices, and the mean queue length is computed. Second, an empirical analysis of the model is presented. The proposed methodology is applied in a case study concerning the geriatric patients. Some numerical calculations and optimizations are performed by using geriatric data. Copyright © 2015 John Wiley & Sons, Ltd.

A hybrid genetic algorithm-queuing multi-compartment model for optimizing inpatient bed occupancy and associated costs

“…Finite-capacity queuing systems are often used in healthcare. In [3], the authors study a queuing system with finitecapacity buffer and a two-phase Cox distribution for service. The proposed methodology is applied to optimize a geriatric care unit by using an empirical analysis of the model and numerical calculations.…”

A Data-Driven Hybrid Three-Stage Framework for Hospital Bed Allocation: A Case Study in a Large Tertiary Hospital in China

“…A range of operational research (OR) methods have been developed and applied to problems of healthcare resource allocation [15], especially bed resources. These methods include queuing theory [16, 17], simulation [18, 19], goal programming [20, 21], and mathematical programming [22–24]. Most of the current research uses a single method for each study.…”