scholarly journals Providing a Model for the Optimal Allocation of Hospital Beds Based on Markov Chain Approach (Case Study: Shiraz-Shahid-Faghihi Hospital)

2021 ◽  
Author(s):  
Mehdi Kabiri Naeini ◽  
Zeynab Elahi ◽  
Abolfazl Moghimi Esfandabadi
Keyword(s):  
Markov Chain ◽  
Waiting Time ◽  
Queuing Theory ◽  
Optimal Allocation ◽  
Referral Rate ◽  
Service Rate ◽  
Model Parameters ◽  
Markov Chain Approach ◽  
Proposed Model ◽  
Hospital Beds

Background: As was observed in the corona crisis, in situations, such as war or natural disasters or epidemic diseases, the intensity of the applicants for medical services causes congestion problems. In this situation, due to the limited capacity of the system, queuing phenomenon for service applicants and in some cases, rejection of clients occur. Reducing the length of hospital stays by improving performance productivity can compensate for the shortage of hospital beds. In order to increase the productivity of personnel and equipment, it is necessary to eliminate unemployment and improve service scheduling. One of the ways to achieve these goals is to optimize the distribution of beds between wards. In the present study, in the form of Markov chain approach, according to the referral rate and service rate, the existing beds were allocated to different wards of the hospital to maximize service and minimize rejection of patients. Methods: The present study is an applied study conducted in 2019 for the optimal distribution of beds between the 3 wards of Shahid Faghihi Hospital in Shiraz. The research problem was modeled in the form of Markov chain approach and assuming the referral of clients according to the continuous-time Markov chain, the model parameters value was identified. The obtained mathematical model was solved by GAMS 24.1.3 software. Results: The proposed model led to an improvement in ward performance in terms of reducing patient waiting time and increasing the number of admitted patients. The proposed model reduced patient rejection by 8.6 %. According to the patients' referral rate to the wards and the service rate of each ward, based on sensitivity analysis, the number of beds allocated to each of the 3 wards was determined. Conclusion: Queuing theory can be applied as a tool to analyze the phenomena of the treatment system and determine the features of the waiting time, queue length, and capacity of the system. Appropriate allocation of hospital beds results in improving the efficiency and decreasing the patient rejection. Therefore, it could be useful in crisis, congestion in patients, and when increasing facilities is required.

Application of Queuing Theory to Address Traffic Problems at a Highway Toll Plaza

2014 ◽  
Vol 592-594 ◽  
pp. 2583-2587 ◽  
Author(s):  
Dheeraj Duhan ◽  
Nishant Arya ◽  
Prateek Dhanda ◽  
Lalit Upadhayay ◽  
K. Mathiyazhagan
Keyword(s):  
Data Analysis ◽  
Waiting Time ◽  
Traffic Congestion ◽  
Queuing Theory ◽  
Arrival Rate ◽  
North India ◽  
Service Rate ◽  
Operational Effectiveness ◽  
Toll Plazas ◽  
Toll Plaza

In India, due to the escalating traffic issues, a large number of highways have been built in the recent past, which are maintained by tax collection at toll plazas, by various operating agencies. Due to smooth and hassle free driving on highways, the arrival rate of vehicles at Toll Plazas increases. The arrival rate goes beyond control if the traffic on the highway increases in an uncontrolled manner, with the passage of time. Thus, one of the irrefutable drawbacks of putting up Toll Plazas, is the traffic congestion. The waiting time, in the service lanes, due to such a congestion becomes high and excruciating for the commuters on the route. The objective of this study is to analyze the current situation, of traffic congestion, at a highway toll plaza using queuing theory and suggest possible solutions to encourage greater efficiency, thus reducing waiting time of the customers and money wasted because of that. This study has been carried out in various phases, i.e. problem identification, data collection, data analysis and results at a selected Toll Plaza in North India. The data analysis in the study helps to find out the current operational effectiveness of the Toll Plaza through parameters like, Arrival Rate, Service Rate and Number of toll booths. Finally, possible solutions have been put forward which can be recommended and implemented on various Toll Plazas in the country.

scholarly journals Capacity and Delay Estimation for Roundabouts Using Conflict Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Zhaowei Qu ◽  
Yuzhou Duan ◽  
Hongyu Hu ◽  
Xianmin Song
Keyword(s):  
Queuing Theory ◽  
High Volume ◽  
Conflict Theory ◽  
Model Parameters ◽  
Delay Model ◽  
Highway Capacity ◽  
Highway Capacity Manual ◽  
Traffic Characteristics ◽  
Capacity Model ◽  
Proposed Model

To estimate the capacity of roundabouts more accurately, the priority rank of each stream is determined through the classification technique given in the Highway Capacity Manual 2010 (HCM2010), which is based on macroscopical analysis of the relationship between entry flow and circulating flow. Then a conflict matrix is established using the additive conflict flow method and by considering the impacts of traffic characteristics and limited priority with high volume. Correspondingly, the conflict relationships of streams are built using probability theory. Furthermore, the entry capacity model of roundabouts is built, and sensitivity analysis is conducted on the model parameters. Finally, the entrance delay model is derived using queuing theory, and the proposed capacity model is compared with the model proposed by Wu and that in the HCM2010. The results show that the capacity calculated by the proposed model is lower than the others for an A-type roundabout, while it is basically consistent with the estimated values from HCM2010 for a B-type roundabout.

A BAYESIAN APPROACH TO FIND RANDOM-TIME PROBABILITIES FROM EMBEDDED MARKOV CHAIN PROBABILITIES

2007 ◽  
Vol 21 (4) ◽  
pp. 551-556 ◽  
Author(s):  
Winfried K. Grassmann ◽  
Javad Tavakoli
Keyword(s):  
Markov Chain ◽  
Bayesian Approach ◽  
Queuing Theory ◽  
Classical Method ◽  
Renewal Theory ◽  
Random Time ◽  
Embedded Markov Chain ◽  
Markov Chain Approach ◽  
Complex Approach ◽  
Markov Renewal Theory

The embedded Markov chain approach is widely used in queuing theory, in particular in M/G/1 and GI/M/c queues. In these cases, one has to relate the embedded equilibrium probablities to the corresponding random-time probabilities. The classical method to do this is based on Markov renewal theory, a rather complex approach, especially if the population is finite or if there is balking. In this article we present a much simpler method to derive the random-time probabilities from the embedded Markov chain probabilities. The method is based on conditional probability. Our approach might also be applicable in such situations.

FUZZY HIDDEN MARKOV CHAIN FOR WEB APPLICATIONS

2013 ◽  
Vol 12 (04) ◽  
pp. 813-835 ◽  
Author(s):  
R. SUJATHA ◽  
T. M. RAJALAXMI ◽  
B. PRABA
Keyword(s):  
Markov Chain ◽  
Web Applications ◽  
Hidden Markov ◽  
Model Parameters ◽  
Hidden Markov Chain ◽  
Web Navigation ◽  
Ambiguous Situation ◽  
Proposed Model ◽  
Observation Sequence ◽  
Browsing Behavior

Hidden Markov model (HMM) has become increasingly popular in the last several years. Real-world problems such as prediction of web navigation are uncertain in nature; in this case, HMM is less appropriate i.e., we cannot assign certain probability values while in fuzzy set theory everything has elasticity. In addition to that, a theory of possibility on fuzzy sets has been developed to handle uncertainity. Thus, we propose a fuzzy hidden Markov chain (FHMC) on possibility space and solve three basic problems of classical HMM in our proposed model to overcome the ambiguous situation. Client's browsing behavior is an interesting aspect in web access. Analysis of this issue can be of great benefit in discovering user's behavior in this way we have applied our proposed model to our institution's website ( www.ssn.edu.in ) to identify how well a given model matches a given observation sequence, next to find the corresponding state sequence which is the best to explain the given observation sequence and then to attempt to optimize the model parameters so as to describe best how a given observation sequence comes about. The solution of these problems help us to know the authenticity of the website.

scholarly journals A Study of Service in Restaurant by Using Queuing Model

2013 ◽  
Vol 5 ◽  
pp. 14-18
Author(s):  
G.D. Mishra ◽  
Vijiya Singh Chauhan ◽  
Nikita Chandra
Keyword(s):  
Numerical Model ◽  
Waiting Time ◽  
Queuing Theory ◽  
Arrival Rate ◽  
Utilization Rate ◽  
Service Rate ◽  
Case Scenario ◽  
Queuing Model ◽  
Restaurant Management ◽  
Potential Customers

The restaurants want to avoid losing their customers due to a long wait on the line. This shows a need of a numerical model for the restaurant management to understand the situation better. This paper aims to show that queuing theory satisfies the model when tested with a real-case scenario. We obtained the data from a restaurant. We then derive the arrival rate, service rate, utilization rate, waiting time in queue and the probability of potential customers to balk based on the data using Little’s Theorem and M/M/1 queuing model. We conclude the paper by discussing the benefits of performing queuing analysis to a busy restaurant.

scholarly journals Simulation Model for Blockchain Systems Using Queuing Theory

Electronics ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 234 ◽  
Author(s):  
Raheel Memon ◽  
Jian Li ◽  
Junaid Ahmed
Keyword(s):  
Internet Of Things ◽  
Performance Measures ◽  
Waiting Time ◽  
Queuing Theory ◽  
Smart Home ◽  
System Throughput ◽  
Block System ◽  
Proposed Model ◽  
Wide Range ◽  
Good Agreement

In recent years, blockchains have obtained so much attention from researchers, engineers, and institutions; and the implementation of blockchains has started to revive a large number of applications ranging from e-finance, e-healthcare, smart home, Internet of Things, social security, logistics and so forth. In the literature on blockchains, it is found that most articles focused on their engineering implementation, while little attention has been devoted to the exploration of theoretical aspects of the system; however, the existing work is limited to model the mining process only. In this paper, a queuing theory-based model is proposed for understanding the working and theoretical aspects of the blockchain. We validate our proposed model using the actual statistics of two popular cryptocurrencies, Bitcoin and Ethereum, by running simulations for two months of transactions. The obtained performance measures parameters such as the Number of Transactions per block, Mining Time of Each Block, System Throughput, Memorypool count, Waiting Time in Memorypool, Number of Unconfirmed Transactions in the Whole System, Total Number of Transactions, and Number of Generated Blocks; these values are compared with actual statistics. It was found that the results gained from our proposed model are in good agreement with actual statistics. Although the simulation in this paper presents the modeling of blockchain-based cryptocurrencies only, the proposed model can be used to represent a wide range of blockchain-based systems.

scholarly journals Application of queuing theory to a fast food outfit: a study of blue meadows restaurant

2017 ◽  
Vol 8 (2) ◽  
pp. 441 ◽  
Author(s):  
Seigha Gumus ◽  
Gordon Monday Bubou ◽  
Mobolaji Humphrey Oladeinde
Keyword(s):  
Waiting Time ◽  
Fast Food ◽  
Queuing Theory ◽  
Goodness Of Fit ◽  
Arrival Rate ◽  
Time Frame ◽  
Utilization Rate ◽  
Service Rate ◽  
Operating Characteristics ◽  
Number Of Customers

The study evaluated the queuing system in Blue Meadows restaurant with a view to determining its operating characteristics and to improve customers’ satisfaction during waiting time using the lens of queuing theory. Data was obtained from a fast food restaurant in the University of Benin. The data collected was tested to show if it follows a Poisson and exponential distribution of arrival and service rate using chi square goodness of fit. A 95% confidence interval level was used to show the range of customers that come into the system at an hour time frame and the range of customers served at an hour time frame. Using the M/M/s model, the arrival rate, service rate, utilization rate, waiting time in the queue and the probability of customers likely balking from the restaurant was derived. The arrival rate (λ) at Blue Meadows restaurant was about 40 customers per hour, while the service rate was about 22 customers per hour per server. The number of servers present in the system was two. The average number of customers in the system in an hour window was 40 customers with a utilization rate of 0.909. The paper concludes with a discussion on the benefits of performing queuing analysis to a restaurant.

AN IMPROVED MARKOV CHAIN APPROXIMATION METHODOLOGY: DERIVATIVES PRICING AND MODEL CALIBRATION

2014 ◽  
Vol 17 (07) ◽  
pp. 1450047 ◽  
Author(s):  
CHIA CHUN LO ◽  
KONSTANTINOS SKINDILIAS
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Empirical Studies ◽  
Jump Diffusion ◽  
Model Parameters ◽  
Underlying Distribution ◽  
Markov Chain Approximation ◽  
Proposed Model ◽  
Jump Diffusion Model ◽  
Chain Approximation

This paper presents an improved continuous-time Markov chain approximation (MCA) methodology for pricing derivatives and for calibrating model parameters. We propose a generalized nonequidistant grid model for a general stochastic differential equation, and extend the proposed model to accommodate a jump component. Because the prices of derivatives generated by the MCA models are sensitive to the setting of the chain's state space, we suggest a heuristic determination of the grid spacing such that the Kolmogorov–Smirnov distance between the underlying distribution and the MCA distribution is minimized. The continuous time setting allows us to introduce semi-analytical formulas for pricing European and American style options. The numerical examples demonstrate that the proposed model with a nonequidistant grid setting provides superior results over the equidistant grid setting. Finally, we present the MCA maximum likelihood estimator for a jump-diffusion process. The encouraging results from the simulation and empirical studies provide insight into calibration problems in finance where the density function of a jump-diffusion model is unknown.

In-Plane Flexible Ring Tire Model—Part 1: Modeling and Parameter Identification

2018 ◽  
Vol 46 (3) ◽  
pp. 174-219 ◽  
Author(s):  
Bin Li ◽  
Xiaobo Yang ◽  
James Yang ◽  
Yunqing Zhang ◽  
Zeyu Ma
Keyword(s):  
Static Load ◽  
Model Parameters ◽  
Tire Model ◽  
Test Results ◽  
Lumped Mass ◽  
Virtual Test ◽  
Proposed Model ◽  
Particle Swarm Method ◽  
Vehicle Dynamic Simulation ◽  
Flexible Ring

ABSTRACT The tire model is essential for accurate and efficient vehicle dynamic simulation. In this article, an in-plane flexible ring tire model is proposed, in which the tire is composed of a rigid rim, a number of discretized lumped mass belt points, and numerous massless tread blocks attached on the belt. One set of tire model parameters is identified by approaching the predicted results with ADAMS® FTire virtual test results for one particular cleat test through the particle swarm method using MATLAB®. Based on the identified parameters, the tire model is further validated by comparing the predicted results with FTire for the static load-deflection tests and other cleat tests. Finally, several important aspects regarding the proposed model are discussed.

EXPONENTIATED HALF-LOGISTIC LOMAX DISTRIBUTION WITH PROPERTIES AND APPLICATION

2019 ◽  
Vol XVI (2) ◽  
pp. 1-11
Author(s):  
Farrukh Jamal ◽  
Hesham Mohammed Reyad ◽  
Soha Othman Ahmed ◽  
Muhammad Akbar Ali Shah ◽  
Emrah Altun
Keyword(s):  
Real Data ◽  
Continuous Model ◽  
Model Parameters ◽  
Data Set ◽  
Lomax Distribution ◽  
Mathematical Properties ◽  
Proposed Model ◽  
Probability Weighted Moment ◽  
Record Statistics ◽  
Maximum Likelihood Criterion

A new three-parameter continuous model called the exponentiated half-logistic Lomax distribution is introduced in this paper. Basic mathematical properties for the proposed model were investigated which include raw and incomplete moments, skewness, kurtosis, generating functions, Rényi entropy, Lorenz, Bonferroni and Zenga curves, probability weighted moment, stress strength model, order statistics, and record statistics. The model parameters were estimated by using the maximum likelihood criterion and the behaviours of these estimates were examined by conducting a simulation study. The applicability of the new model is illustrated by applying it on a real data set.

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