Healthcare queueing models.

Healthcare systems differ intrinsically from manufacturing systems. As such, they require a distinct modeling approach. In this article, we show how to construct a queueing model of a general class of healthcare systems. We develop new expressions to assess the impact of service outages and use the resulting model to approximate patient flow times and to evaluate a number of practical applications. We illustrate the devastating impact of service interruptions on patient flow times and show the potential gains obtained by pooling hospital resources. In addition, we present an optimization model to determine the optimal number of patients to be treated during a service session.Operations research; Health care evaluation mechanisms; Organizational efficiency; Management decision support systems; Time management; Queueing theory;

Analysis of the finite-source multiclass priority queue with an unreliable server and setup time

In this article, we study a queueing system serving multiple classes of customers. Each class has a finite-calling population. The customers are served according to the preemptive-resume priority policy. We assume general distributions for the service times. For each priority class, we derive the steady-state system size distributions at departure/arrival and arbitrary time epochs. We introduce the residual augmented process completion times conditioned on the number of customers in the system to obtain the system time distribution. We then extend the model by assuming that the server is subject to operation-independent failures upon which a repair process with random duration starts immediately. We also demonstrate how setup times, which may be required before resuming interrupted service or picking up a new customer, can be incorporated in the model

Modeling a healthcare system as a queueing network:The case of a Belgian hospital.

The performance of health care systems in terms of patient flow times and utilization of critical resources can be assessed through queueing and simulation models. We model the orthopaedic department of the Middelheim hospital (Antwerpen, Belgium) focusing on the impact of outages (preemptive and nonpreemptive outages) on the effective utilization of resources and on the flowtime of patients. Several queueing network solution procedures are developed such as the decomposition and Brownian motion approaches. Simulation is used as a validation tool. We present new approaches to model outages. The model offers a valuable tool to study the trade-off between the capacity structure, sources of variability and patient flow times.Belgium; Brownian motion; Capacity management; Decomposition; Health care; Healthcare; Impact; Model; Models; Performance; Performance measurement; Queueing; Queueing theory; Simulation; Stochastic processes; Structure; Studies; Systems; Time; Tool; Validation; Variability;

Simple bounds for queueing systems with breakdowns

Computationally attractive and intuitively obvious simple bounds are proposed for finite service systems which are subject to random breakdowns. The services are assumed to be exponential. The up and down periods are allowed to be generally distributed. The bounds are based on product-form modifications and depend only on means. A formal proof is presented. This proof is of interest in itself. Numerical support indicates a potential usefulness for quick engineering and performance evaluation purposes

The impact of disruption characteristics on the performance of a server

In this paper, we study a queueing system serving N customers with an unreliable server subject to disruptions even when idle. Times between server interruptions, service times, and times between customer arrivals are assumed to follow exponential distributions. The main contribution of the paper is to use general distributions for the length of server interruption periods/down times. Our numerical analysis reveals the importance of incorporating the down time distribution into the model, since their impact on customer service levels could be counterintuitive. For instance, while higher down time variability increases the mean queue length, for other service levels, can prove to be improving system performance. We also show how the process completion time approach from the literature can be extended to analyze the queueing system if the unreliable server fails only when it is serving a customer

The Impact of Processing Time Knowledge on Dynamic Job-Shop Scheduling

The goal of this paper is to determine if the results for dynamic job-shop scheduling problems are affected by the assumptions made with regard to the processing time distributions and the scheduler's knowledge of the processing times. Three dynamic jobshop scheduling problems (including a two station version of Conway et al.'s [2] nine station symmetric shop) are tested under seven different scenarios, one deterministic and six stochastic, using computer simulation. The deterministic scenario, where the processing times are exponential and observed by the scheduler, has been considered in many simulation studies, including Conway et al's. The six stochastic scenarios include the case where the processing times are exponential and only the mean is known to the scheduler, and five different cases where the machines are subject to unpredictable failures. Two policies were tested, the shortest expected processing time (SEPT) rule, and a rule derived from a Brownian analysis of the corresponding queueing network scheduling problem. Although the SEPT rule performed well in the deterministic scenario, it was easily outperformed by the Brownian policies in the six stochastic scenarios for all three problems. Thus, the results from simulation studies of dynamic, deterministic job-shop scheduling problems do not necessarily carry over to the more realistic setting where there is unpredictable variability present