Using Poisson Modeling and Queuing Theory to Optimize Staffing and Decrease Patient Wait Time in the Emergency Department

Introduction: Studies have shown Emergency Department (ED) crowding contributes to reduced quality of patient care, delays in starting treatments, and increased number of patients leaving without being seen. This analysis shows how to theoretically and optimally align staffing to demand. Methods: The ED value stream was identified and mapped. Patients were stratified into three resource-driven care flow cells based on the severity indices. Time observations were conducted for each of the key care team members and the manual cycle times and service rate were calculated and stratified by severity indices. Using X32 Healthcare’s Online Staffing Optimization (OSO) tool, staffing inefficiencies were identified and an optimal schedule was created for each provider group. Results: Lower Severity Indices (higher acuity patient) led to longer times for providers, nurses, patient care assistants, and clerks. The patient length of stay varied from under one hour to over five hours. The flow of patients varied considerably over the 24 hours’ period but was similar by day of the week. Using flow data, we showed that we needed more nurses, more care team members during peak times of patient flow. Eight hour shifts would allow better flexibility. We showed that the additional salary hours added to the budget would be made up for by increased revenue recognized by decreasing the number of patients who leave without being seen. Conclusion: If implemented, these changes will improve ED flow by using lean tools and principles, ultimately leading to timeliness of care, reduced waits, and improved patient experience.

Modeling and analysis of multiservice queuing system for WiMAX network

An analytical queuing model is proposed for the classified services of WiMAX network. Simulation model is also developed that corresponds to the Markovian analytical model using Java modeling tool （JMT）. This is a new and efficient discrete event tool for queuing network modeling and workload analysis. QoS metrics have been evaluated for the multi-rate traffic in multiple scenari- os. Results obtained from simulation are compared for validation and analysis. Outcomes show that the proposed model is more efficient than the conventional method by improving residence time, re- sponse time, increasing system throughput and efficiency at queuing level with a slight degradation in call acceptance factor.

Modeling Rainfall Intensity-Duration-Frequency (IDF) and Establishing Climate Change Existence in Uyo-Nigeria Using Non-Stationary Approach

This study aims at establishing if climate change exists in the Niger Delta environment using non-stationary rainfall Intensity-Duration-Frequency (IDF) modelling incorporating time-variant parameters. To compute the intensity levels, the open-access R-studio software was used based on the General Extreme Value (GEV) distribution function. Among the four linear parameter models adopted for integrating time as a covariate, the fourth linear model incorporating scale and location with the shape function constant produced the least corrected Akaike Information Criteria (AICc), varying between 306.191 to 101.497 for 15 and 1440 minutes, respectively, selected for calibration of the GEV distribution equation. The non-stationary intensities yielded higher values above those of stationary models, proving that the assumption of stationary IDF models underestimated extreme events. The difference of 13.71 mm/hr (22.71%) to 14.26 mm/hr (17.0%) intensities implies an underestimation of the peak flood from a stationary IDF curve. The statistical difference at a 95% confidence level between stationary and non-stationary models was significant, confirming evidence of climatic change influenced by time-variant parameters. Consequently, emphasis should be on applying shorter-duration storms for design purposes occurring with higher intensities to help reduce the flood risk and resultant infrastructural failures.

基于Queuing Theory的收费服务系统模型优化及仿真

针对目前诸多形态的收费服务系统运行效率不高的现状,通过对收费服务系统排队规定和措施的研究分析,基于排队论对收费服务系统数学模型进行优化,并以超市为实证对象,对优化模型进行仿真。根据仿真结果,所提出的收费服务系统优化模型能在一定程度上减少排队时间或者是在排队时间既定的情况下,减少收费资源的投入。

Modeling and Parameter Optimization of Statistical Priority-Based Multiple Access Protocol

The Statistical Priority-based Multiple Access Protocol(SPMA)is the de facto standard for Tactical Target Network Technology(TTNT)and has also been implemented in ad hoc networks.In this paper,we present a non-preemptive M/M/1/K queuing model to analyze the performance of different priorities in SPMA in terms of average packet loss rate and delay.And based on this queuing model,we designed a percentile scoring system combined with Q-learning algorithm to optimize the protocol parameters.The simulation results show that our theoretical model is closely matched with the reality,and the proposed algorithm improves the efficiency and accuracy in finding the optimal parameter set of SPMA protocol.

A Novel 3D Non-Stationary UAV-MIMO Channel Model and Its Statistical Properties

The wireless communication systems based on Unmanned Aerial Vehicles(UAVs) have found a wide range of applications recently. In this paper, we propose a new three-dimensional(3 D) non-stationary multiple-input multiple-output(MIMO) channel model for the communication links between the UAV and mobile terminal(MT). The new model originates the traditional geometry-based stochastic models(GBSMs) but considers the non-stationary propagation environment due to the rapid movements of the UAV, MT, and clusters. Meanwhile, the upgrade time evolving algorithms of time-variant channel parameters, i.e., the path number based on birth-death processes of clusters, path delays, path powers, and angles of arrival and departure, are developed and optimized. In addition, the statistical properties of proposed GBSM including autocorrelation function(ACF), cross-correlation function(CCF), and Doppler power spectrum density(DPSD) are investigated and analyzed. Simulation results demonstrate that our proposed model provides a good agreement on the statistical properties with the corresponding derived theoretical ones, which indicates its usefulness for the performance evaluation and validation of the UAV based communication systems.

Application of the Queuing Theory in Characterizing and Optimizing the Passenger Flow at the Airport Security

This paper presents mathematics models that describe and optimize the passenger flow at the airport security checkpoints by applying the queuing theory. Firstly, a Poisson process is used to estimate the flow of passengers waiting for going through the security. Then, the Poisson distribution is combined with a multiple M/M/s model. Following that, an arrival model (passengers’ arriving at the checkpoints preparing for security examination and departure) with Gumbel extreme value estimation is described that predicts the busiest time in the busiest airport. Real case data collected from several major airports worldwide is used for creating a hybrid Poisson model to generate the simulation of passenger volume. At last, Markov Chain theory is applied to the analysis to randomly simulate the flow of enplaned passengers again, and the results of these two simulations are compared and discussed, revealing that the hybrid Poisson model is the more accurate one. After successfully characterizing the passenger flow mathematically, two methods for optimizing the passenger flow are then provided in two different respects: one is bypassing passengers and creating an express pass;while the other one promotes Pre-Check service application.

A Geometry-Based Non-Stationary MIMO Channel Model for Vehicular Communications

This paper derives a non-stationary multiple-input multiple-output(MIMO) from the one-ring scattering model. The proposed channel model characterizes vehicular radio propagation channels with considerations of moving base and mobile stations, which makes the angle of arrivals(AOAs) along with the angle of departures(AODs) time-variant. We introduce the methodology of including the time-variant impacts when characterizing non-stationary radio propagation channels through the geometrical channel modelling approach. We analyze the statistical properties of the proposed channel model including the local time-variant autocorrelation function(ACF) and the space cross-correlation functions(CCFs). We show that the model developed in this paper for non-stationary scenarios includes the existing one-ring wide-sense stationary channel model as its special case.

An Overview of Non.Stationary Property for Massive MIMO Channel Modeling

Massive multiple-input multiple-output(MIMO)emerges as one of the most promising technologies for 5G mobile communication systems.Compared to the conventional MIMO channel models,channel researches and measurements show that significant nonstationary properties rise in massive MIMO channels.Therefore,an accurate channel model is indispensable for the sake of massive MIMO system design and performance evaluation.This article presents an overview of methods of modeling non-stationary properties on both the array and time axes,which are mainly divided into two major categories:birth-death(BD)process and cluster visibility region(VR)method.The main concepts and theories are described,together with useful implementation guidelines.In conclusion,a comparison between these two methods is made.

A Realistic 3D Non-Stationary Channel Model for UAV-to-Vehicle Communications Incorporating Fuselage Posture

Considering the unmanned aerial vehicle(UAV) three-dimensional(3D) posture, a novel 3D non-stationary geometry-based stochastic model(GBSM) is proposed for multiple-input multipleoutput(MIMO) UAV-to-vehicle(U2V) channels. It consists of a line-of-sight(Lo S) and non-line-of-sight(NLo S) components. The factor of fuselage posture is considered by introducing a time-variant 3D posture matrix. Some important statistical properties, i.e.the temporal autocorrelation function(ACF) and spatial cross correlation function(CCF), are derived and investigated. Simulation results show that the fuselage posture has significant impact on the U2V channel characteristic and aggravate the non-stationarity. The agreements between analytical, simulated, and measured results verify the correctness of proposed model and derivations. Moreover, it is demonstrated that the proposed model is also compatible to the existing GBSM without considering fuselage posture.

Empirical-Statistical Methodology and Methods for Modeling and Forecasting of Climate Variability of Different Temporal Scales

Main problem of modern climatology is to assess the present as well as future climate change, For this aim two approaches are used: physic-mathematic modeling on the basis of GCMs and palaeoclimatic analogues. The third approach is based on the empirical-statistical methodology and is developed in this paper. This approach allows to decide two main problems: to give a real assessment of climate changes by observed data for climate monitoring and extrapolation of obtained climate tendencies to the nearest future (10-15 years) and give the empirical basis for further development of physic-mathematical models. The basic theory and methodology of empirical-statistic approach have been developed as well as a common model for description of space-time climate variations taking into account the processes of different time scales. The way of decreasing of the present and future uncertainty is suggested as the extraction of long-term climate changes components in the particular time series and spatial generalization of the same climate tendencies in the obtained homogeneous regions. Algorithm and methods for realization of empirical-statistic methodology have been developed along with methods for generalization of intraannual fluctuations, methods for extraction of homogeneous components of different time scales (interannual, decadal, century), methodology and methods for spatial generalization and modeling, methods for extrapolation on the basis of two main kinds of time models: stochastic and deterministic-stochastic. Some applications of developed methodology and methods are given for the longest time series of temperature and precipitation over the world and for spatial generalization over the European area.

On-Line Structural Breaks Estimation for Non-stationary Time Series Models

Non-stationary time series could be divided into piecewise stationary stochastic signal. However, the number and locations of breakpoints, as well as the approximation function of the respective segment signal are unknown. To solve this problem, a novel on-line structural breaks estimation algorithm based on piecewise autoregressive processes is proposed. In order to find the "best" combination of the number, lengths, and orders of the piecewise autoregressive (AR) processes, the Akaikes Information Criterion (AIC) and Yule-Walker equations are applied to estimate an AR model fit to the data. Numerical results demonstrate that the proposed estimation algorithm is suitable for different data series. Furthermore, the algorithm is used in a clinical study of electroencephalogram (EEG) with satisfactory results, and the ability to deal with real-time data is the most outstanding characteristic of on-line structural breaks estimation algorithm proposed.

End-to-End Performance Evaluation of TCP Traffic under Multi-Queuing Networks

While Internet traffic is currently dominated by elastic data transfers, it is anticipated that streaming applications will rapidly develop and contribute a significant amount of traffic in the near future. Therefore, it is essential to understand and capture the relation between streaming and elastic traffic behavior. In this paper, we focus on developing simple yet effective approximations to capture this relationship. We study, then, an analytical model to evaluate the end-to-end performance of elastic traffic under multi-queuing system. This model is based on the fluid flow approximation. We assume that network architecture gives the head of priority to real time traffic and shares the remaining capacity between the elastic ongoing flows according to a specific weight.

Optimization of the CBSMAP Queueing Model

The present paper is devoted to the research of controlled queueing models at control of CBSMAP （Controlled Batch Semi-Markov Arrival Process）. The control is based on the theory of controlled semi-markov processes for system optimization. The control is carried out using a type of the next batch and moments of batch arrivals.

Data Processing Model of Coalmine Gas Early-Warning System

The data processing mode is vital to the performance of an entire coalmine gas early-warning system, especially in real-time performance. Our objective was to present the structural features of coalmine gas data, so that the data could be processed at different priority levels in C language. Two different data processing models, one with priority and the other without priority, were built based on queuing theory. Their theoretical formulas were determined via a M/M/I model in order to calculate average occupation time of each measuring point in an early-warning program. We validated the model with the gas early-warning system of the Huaibei Coalmine Group Corp. The results indicate that the average occupation time for gas data processing by using the queuing system model with priority is nearly 1/30 of that of the model without priority.

Advanced User-Based Interaction Model in Cloud

With the increasing popularity of cloud computing, there is an increased de mand for cloud resources in cloud. It has be come even more urgent to find solutions to improve resource utilization. From the per spective of a cloud consumer, a cloud applica tion processes a large information flow in volving user actions that access resources, but little work has so far been devoted to research from the perspective of the interaction be tween the user and the cloud application. In this paper, we analyze the interaction in detail, and propose a general mathematical interac tion model to formulate the challenge pertain ing to storage resource allocation as an opti mization problem, focusing on minimizing both the user＇s cost and server＇s consumption. A potential response mechanism is then de signed based on the interaction model. Fur thermore, the proposed model is used to ex plore strategies when multiple users access the same file simultaneously. Additionally, an improved queuing system, namely M/ G~ oo queue with standby, is introduced. Finally, an evaluation is presented to verify the interac- tion model.

Analysis models and methods on the network storage system I/O performance

Network storage provides high scalability, availability and flexibility for storage systems, and is widely applied to many fields. Particularly, I/O performance is of great significance. Its application is wide and expanding rapidly. I/O performance has already become the bottleneck of the whole performance of computer systems for a long time, and under the condition of the present computer technology, I/O performance optimization method looks especially important. In the paper, I/O performance model was analyzed based on the combination of quasi birth, death process and queuing model, and then solved the model. A number of important related performance indicators and the relationship between them were given. By the way of example, this method can show the I/O performance more accurately. Finally, we got some useful conclusions, which may be used to evaluate network storage performance, and are the basis of confirming I/O scheduling strategy.

FogQSYM: An Industry 4.0 Analytical Model for Fog Applications

Industry 4.0 refers to the fourth evolution of technology development,which strives to connect people to various industries in terms of achieving their expected outcomes efficiently.However,resource management in an Industry 4.0 network is very complex and challenging.To manage and provide suitable resources to each service,we propose a FogQSYM(Fog—Queuing system)model;it is an analytical model for Fog Applications that helps divide the application into several layers,then enables the sharing of the resources in an effective way according to the availability of memory,bandwidth,and network services.It follows theMarkovian queuing model that helps identify the service rates of the devices,the availability of the system,and the number of jobs in the Industry 4.0 systems,which helps applications process data with a reasonable response time.An experiment is conducted using a Cloud Analyst simulator with multiple segments of datacenters in a fog application,which shows that the model helps efficiently provide the arrival resources to the appropriate services with a low response time.After implementing the proposed model with different sizes of fog services in Industry 4.0 applications,FogQSYM provides a lower response time than the existing optimized response time model.It should also be noted that the average response time increases when the arrival rate increases.

Quasi-Negative Binomial: Properties, Parametric Estimation, Regression Model and Application to RNA-SEQ Data

Background: The Poisson and the Negative Binomial distributions are commonly used to model count data. The Poisson is characterized by the equality of mean and variance whereas the Negative Binomial has a variance larger than the mean and therefore both models are appropriate to model over-dispersed count data. Objectives: A new two-parameter probability distribution called the Quasi-Negative Binomial Distribution (QNBD) is being studied in this paper, generalizing the well-known negative binomial distribution. This model turns out to be quite flexible for analyzing count data. Our main objectives are to estimate the parameters of the proposed distribution and to discuss its applicability to genetics data. As an application, we demonstrate that the QNBD regression representation is utilized to model genomics data sets. Results: The new distribution is shown to provide a good fit with respect to the “Akaike Information Criterion”, AIC, considered a measure of model goodness of fit. The proposed distribution may serve as a viable alternative to other distributions available in the literature for modeling count data exhibiting overdispersion, arising in various fields of scientific investigation such as genomics and biomedicine.