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.

Markov renewal theory

1969 ◽  
Vol 1 (02) ◽  
pp. 123-187 ◽  
Author(s):  
Erhan Çinlar
Keyword(s):  
Stochastic Process ◽  
Markov Chain ◽  
State Space ◽  
Renewal Theory ◽  
The State ◽  
Countable State Space ◽  
Countable State ◽  
Markov Renewal Theory ◽  
Random Amount

Consider a stochastic process X(t) (t ≧ 0) taking values in a countable state space, say, {1, 2,3, …}. To be picturesque we think of X(t) as the state which a particle is in at epoch t. Suppose the particle moves from state to state in such a way that the successive states visited form a Markov chain, and that the particle stays in a given state a random amount of time depending on the state it is in as well as on the state to be visited next. Below is a possible realization of such a process.

An embedded Markov chain approach to stock rationing

2010 ◽  
Vol 38 (6) ◽  
pp. 510-515 ◽  
Author(s):  
Mehmet Murat Fadıloğlu ◽  
Önder Bulut
Keyword(s):  
Markov Chain ◽  
Embedded Markov Chain ◽  
Markov Chain Approach

An embedded Markov chain approach to stock rationing under batch orders

2019 ◽  
Vol 47 (2) ◽  
pp. 92-98 ◽  
Author(s):  
Mehmet Murat Fadıloğlu ◽  
Önder Bulut
Keyword(s):  
Markov Chain ◽  
Embedded Markov Chain ◽  
Markov Chain Approach

Cost Analysis of Movement-Based Location Management in PCS Networks: An Embedded Markov Chain Approach

2014 ◽  
Vol 63 (4) ◽  
pp. 1886-1902 ◽  
Author(s):  
Xian Wang ◽  
Xianfu Lei ◽  
Pingzhi Fan ◽  
Rose Qingyang Hu ◽  
Shi-Jinn Horng
Keyword(s):  
Markov Chain ◽  
Cost Analysis ◽  
Location Management ◽  
Embedded Markov Chain ◽  
Markov Chain Approach ◽  
Pcs Networks

Markov renewal theory

1969 ◽  
Vol 1 (2) ◽  
pp. 123-187 ◽  
Author(s):  
Erhan Çinlar
Keyword(s):  
Stochastic Process ◽  
Markov Chain ◽  
State Space ◽  
Renewal Theory ◽  
The State ◽  
Countable State Space ◽  
Countable State ◽  
Markov Renewal Theory ◽  
Random Amount

Consider a stochastic process X(t) (t ≧ 0) taking values in a countable state space, say, {1, 2,3, …}. To be picturesque we think of X(t) as the state which a particle is in at epoch t. Suppose the particle moves from state to state in such a way that the successive states visited form a Markov chain, and that the particle stays in a given state a random amount of time depending on the state it is in as well as on the state to be visited next. Below is a possible realization of such a process.

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.

scholarly journals Study on the Calculation Models of Bus Delay at Bays Using Queueing Theory and Markov Chain

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Feng Sun ◽  
Li Sun ◽  
Shao-wei Sun ◽  
Dian-hai Wang
Keyword(s):  
Markov Chain ◽  
Queueing Theory ◽  
Traffic Congestion ◽  
Queuing Theory ◽  
Distribution Functions ◽  
Embedded Markov Chain ◽  
Service Efficiency ◽  
Bus Delay ◽  
Gap Acceptance Theory ◽  
Calculation Models

Traffic congestion at bus bays has decreased the service efficiency of public transit seriously in China, so it is crucial to systematically study its theory and methods. However, the existing studies lack theoretical model on computing efficiency. Therefore, the calculation models of bus delay at bays are studied. Firstly, the process that buses are delayed at bays is analyzed, and it was found that the delay can be divided into entering delay and exiting delay. Secondly, the queueing models of bus bays are formed, and the equilibrium distribution functions are proposed by applying the embedded Markov chain to the traditional model of queuing theory in the steady state; then the calculation models of entering delay are derived at bays. Thirdly, the exiting delay is studied by using the queueing theory and the gap acceptance theory. Finally, the proposed models are validated using field-measured data, and then the influencing factors are discussed. With these models the delay is easily assessed knowing the characteristics of the dwell time distribution and traffic volume at the curb lane in different locations and different periods. It can provide basis for the efficiency evaluation of bus bays.

scholarly journals Labour Market Dynamics in Greek Regions: a Bayesian Markov Chain Approach Using Proportions Data

2010 ◽  
Vol 2 (1) ◽  
pp. 32-45
Author(s):  
George A. Christodoulakis ◽  
Emmanuel C. Mamatzakis
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Labour Market ◽  
Bayesian Approach ◽  
Transition Probabilities ◽  
Full Employment ◽  
Monte Carlo Integration ◽  
Market Dynamics ◽  
Markov Chain Approach ◽  
First Time

This paper focuses on Greek labour market dynamics at a regional base, which comprises of 16 provinces, as defined by NUTS levels 1 and 2 (Eurostat, 2008), using Markov Chains for proportions data for the first time in the literature. We apply a Bayesian approach, which employs a Monte Carlo Integration procedure that uncovers the entire empirical posterior distribution of transition probabilities from full employment to part employment, unemployment and economically unregistered unemployment and vice a versa. Our results show that there are disparities in the transition probabilities across regions, implying that the convergence of the Greek labour market at a regional base is far from being considered as completed. However, some common patterns are observed as regions in the south of the country exhibit similar transition probabilities between different states of the labour market.

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