This paper evaluates the practice of determining staffing requirements in service systems with random cyclic demands by using a series of stationary queueing models. We consider Markovian models with sinusoidal arrival rates and use numerical methods to show that the commonly used "stationary independent period by period" (SIPP) approach to setting staffing requirements is inaccurate for parameter values corresponding to many real situations. Specifically, using the SIPP approach can result in staffing levels that do not meet specified period by period probability of delay targets during a significant fraction of the cycle. We determine the manner in which the various system parameters affect SIPP reliability and identify domains for which SIPP will be accurate. After exploring several alternatives, we propose two simple modifications of SIPP that will produce reliable staffing levels in models whose parameters span a broad range of practical situations. Our conclusions from the sinusoidal model are tested against some empirical data.
We investigate the properties of a new merit function which allows us to reduce a nonlinear complementarity problem to an unconstrained global minimization one. Assuming that the complementarity problem is de ned by a P 0-function we prove that every stationary point of the unconstrained problem is a global solution; furthermore, if the complementarity problem is de ned by a uniform P-function, the level sets of the merit function are bounded. The properties of the new merit function are compared with those of the Mangasarian-Solodov's implicit Lagrangian and Fukushima's regularized gap function. We also introduce a new, simple, active-set local method for the solution of complementarity problems and show how this local algorithm can be made globally convergent by using the new merit function.
Timely access to a provider is a critical dimension of ED quality performance. In an environment in which EDs are often understaffed, analyses of arrival patterns and the use of queueing models can be extremely useful in identifying the most effective allocation of staff.
Objectives: Significant variation in emergency department (ED) patient arrival rates necessitates the adjustment of staffing patterns to optimize the timely care of patients. This study evaluated the effectiveness of a queueing model in identifying provider staffing patterns to reduce the fraction of patients who leave without being seen.
Methods:The authors collected detailed ED arrival data from an urban hospital and used a Lag SIPP queueing analysis to gain insights on how to change provider staffing to decrease the proportion of patients who leave without being seen. The authors then compared this proportion for the same 39-week period before and after the resulting changes.Results: Despite an increase in arrival volume of 1,078 patients (6.3%), an average increase in provider hours of 12 hours per week (3.1%) resulted in 258 fewer patients who left without being seen. This represents a decrease in the proportion of patients who left without being seen by 22.9%. Restricting attention to a four-day subset of the week during which there was no increase in total provider hours, a reallocation of providers based on the queueing model resulted in 161 fewer patients who left without being seen (21.7%), despite an additional 548 patients (5.5%) arriving in the second half of the study.Conclusions: Timely access to a provider is a critical dimension of ED quality performance. In an environment in which EDs are often understaffed, analyses of arrival patterns and the use of queueing models can be extremely useful in identifying the most effective allocation of staff.ACADEMIC EMERGENCY MEDICINE 2006; 13:61-68 ª
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