scholarly journals SOLUTION TO FLEET SIZE OF DOCKLESS BIKE-SHARING STATION BASED ON MATRIX ANALYSIS

2018 ◽  
Vol IV-4 ◽  
pp. 255-262
Author(s):  
Y. Zhai ◽  
J. Liu ◽  
J. Du ◽  
J. Chen
Keyword(s):  
Markov Chain ◽  
Steady State ◽  
Sparse Matrix ◽  
Transition Probability ◽  
Limit State ◽  
Matrix Analysis ◽  
Steady State Probability ◽  
Probability Limit ◽  
Fleet Size ◽  
Bike Sharing

<p><strong>Abstract.</strong> Aiming at the problems of the lack of reasonable judgment of fleet size and non-optimization of rebalancing for dockless bike-sharing station, based on the usage characteristics of dockless bike-sharing, this paper demonstrates that the Markov chain is suitable for the analysis of the fleet size of station. It is concluded that dockless bike-sharing Markov chain probability limit state (steady-state) only exists and is independent of the initial probability distribution. On that basis, this paper analyses the difficulty of the transition probability matrix parameter statistics and the power method of the bike-sharing Markov chain, and constructs the transition probability sparse matrix in order to reduce computational complexity. Since the sparse matrices may be reducible, the rank-one updating method is used to construct the transition probability random prime matrix to meet the requirements of steady-state size calculation. An iterative method for solving the steady-state probability is therefore given and the convergence speed of the method is analysed. In order to improve the practicability of the algorithm, the paper further analyses the construction methods of the initial values of the dockless bike-sharing and the transition probability matrices at different time periods in a day. Finally, the algorithm is verified with practical and simulation data. The results of the algorithm can be used as a baseline reference data to dynamically optimize the fleet size of dockless bike-sharing station operated by bike-sharing companies for strengthening standardized management.</p>

scholarly journals Fleet Size and Rebalancing Analysis of Dockless Bike-Sharing Stations Based on Markov Chain

2019 ◽  
Vol 8 (8) ◽  
pp. 334 ◽  
Author(s):  
Zhai ◽  
Liu ◽  
Du ◽  
Wu
Keyword(s):  
Linear Programming ◽  
Markov Chain ◽  
Steady State ◽  
Transition Probability ◽  
Programming Method ◽  
Linear Programming Method ◽  
Steady State Probability ◽  
Fleet Size ◽  
Analysis Experiment ◽  
Bike Sharing

In order to improve the dynamic optimization of fleet size and standardized management of dockless bike-sharing, this paper focuses on using the Markov stochastic process and linear programming method to solve the problem of bike-sharing fleet size and rebalancing. Based on the analysis of characters of bike-sharing, which are irreducible, aperiodic and positive-recurrence, we prove that the probability limits the state (steady-state) of bike-sharing Markov chain only exists and is independent of the initial probability distribution. Then a new “Markov chain dockless bike-sharing fleet size solution” algorithm is proposed. The process includes three parts. Firstly, the irreducibility of the bike-sharing transition probability matrix is analyzed. Secondly, the rank-one updating method is used to construct the transition probability random prime matrix. Finally, an iterative method for solving the steady-state probability vector is therefore given and the convergence speed of the method is analyzed. Furthermore, we discuss the dynamic solution of the bike-sharing steady-state fleet size according to the time period, so as improving the practicality of the algorithm. To verify the efficiency of this algorithm, we adopt the linear programming method for bicycle rebalancing analysis. Experiment results show that the algorithm could be used to solve the disordered deployment of dockless bike-sharing.

scholarly journals MATHEMATICAL ANALYSIS OF VEHICLE DELIVERY SCALE OF BIKE-SHARING RENTAL NODES

2018 ◽  
Vol XLII-3 ◽  
pp. 2229-2235
Author(s):  
Y. Zhai ◽  
J. Liu ◽  
L. Liu
Keyword(s):  
Markov Chain ◽  
Steady State ◽  
Transition Probability ◽  
Limit State ◽  
Linear Equations ◽  
Transition Probability Matrix ◽  
State Probability ◽  
Steady State Probability ◽  
Bike Sharing ◽  
State Scale

Aiming at the lack of scientific and reasonable judgment of vehicles delivery scale and insufficient optimization of scheduling decision, based on features of the bike-sharing usage, this paper analyses the applicability of the discrete time and state of the Markov chain, and proves its properties to be irreducible, aperiodic and positive recurrent. Based on above analysis, the paper has reached to the conclusion that limit state (steady state) probability of the bike-sharing Markov chain only exists and is independent of the initial probability distribution. Then this paper analyses the difficulty of the transition probability matrix parameter statistics and the linear equations group solution in the traditional solving algorithm of the bike-sharing Markov chain. In order to improve the feasibility, this paper proposes a "virtual two-node vehicle scale solution" algorithm which considered the all the nodes beside the node to be solved as a virtual node, offered the transition probability matrix, steady state linear equations group and the computational methods related to the steady state scale, steady state arrival time and scheduling decision of the node to be solved. Finally, the paper evaluates the rationality and accuracy of the steady state probability of the proposed algorithm by comparing with the traditional algorithm. By solving the steady state scale of the nodes one by one, the proposed algorithm is proved to have strong feasibility because it lowers the level of computational difficulty and reduces the number of statistic, which will help the bike-sharing companies to optimize the scale and scheduling of nodes.

scholarly journals Estimation of extreme inter-day changes to peak electricity demand using Markov chain analysis: A comparative analysis with extreme value theory

2017 ◽  
Vol 28 (4) ◽  
Author(s):  
Caston Sigauke ◽  
Delson Chikobvu
Keyword(s):  
Markov Chain ◽  
Steady State ◽  
Return Period ◽  
Electricity Demand ◽  
State Probability ◽  
Markov Chain Analysis ◽  
State Problem ◽  
Steady State Probability ◽  
Chain Analysis ◽  
Steady State Probabilities

Uncertainty in electricity demand is caused by many factors. Large changes are usually attributed to extreme weather conditions and the general random usage of electricity by consumers. More understanding requires a detailed analysis using a stochastic process approach. This paper presents a Markov chain analysis to determine stationary distributions (steady state probabilities) of large daily changes in peak electricity demand. Such large changes pose challenges to system operators in the scheduling and dispatching of electrical energy to consumers. The analysis used on South African daily peak electricity demand data from 2000 to 2011 and on a simple two-state discrete-time Markov chain modelling framework was adopted to estimate steady-state probabilities of two states: positive inter-day changes (increases) and negative inter-day changes (decreases). This was extended to a three-state Markov chain by distinguishing small positive changes and extreme large positive changes. For the negative changes, a decrease state was defined. Empirical results showed that the steady state probability for an increase was 0.4022 for the two-state problem, giving a return period of 2.5 days. For the three state problem, the steady state probability of an extreme increase was 0.0234 with a return period of 43 days, giving approximately nine days in a year that experience extreme inter-day increases in electricity demand. Such an analysis was found to be important for planning, load shifting, load flow analysis and scheduling of electricity, particularly during peak periods.

A kind of dual form for coupling from the past algorithm, to sample from Markov chain steady-state probability

2019 ◽  
Vol 25 (4) ◽  
pp. 317-327
Author(s):  
Abdelaziz Nasroallah ◽  
Mohamed Yasser Bounnite
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Steady State ◽  
Performance Comparison ◽  
State Probability ◽  
Steady State Probability ◽  
Dual Form ◽  
The Past ◽  
Coupling From The Past ◽  
History Of

Abstract The standard coupling from the past (CFTP) algorithm is an interesting tool to sample from exact Markov chain steady-state probability. The CFTP detects, with probability one, the end of the transient phase (called burn-in period) of the chain and consequently the beginning of its stationary phase. For large and/or stiff Markov chains, the burn-in period is expensive in time consumption. In this work, we propose a kind of dual form for CFTP called D-CFTP that, in many situations, reduces the Monte Carlo simulation time and does not need to store the history of the used random numbers from one iteration to another. A performance comparison of CFTP and D-CFTP will be discussed, and some numerical Monte Carlo simulations are carried out to show the smooth running of the proposed D-CFTP.

A formula for singular perturbations of Markov chains

1994 ◽  
Vol 31 (03) ◽  
pp. 829-833 ◽  
Author(s):  
Jean B. Lasserre
Keyword(s):  
Markov Chain ◽  
Steady State ◽  
Probability Distribution ◽  
Markov Chains ◽  
Singular Perturbations ◽  
Singularly Perturbed ◽  
State Probability ◽  
Regular Perturbation ◽  
Steady State Probability ◽  
Fundamental Matrices

We give formulas for updating both the steady-state probability distribution and the fundamental matrices of a singularly perturbed Markov chain. This formula generalizes Schweitzer's regular perturbation formulas to the case of singular perturbations.

A formula for singular perturbations of Markov chains

1994 ◽  
Vol 31 (3) ◽  
pp. 829-833 ◽  
Author(s):  
Jean B. Lasserre
Keyword(s):  
Markov Chain ◽  
Steady State ◽  
Probability Distribution ◽  
Markov Chains ◽  
Singular Perturbations ◽  
Singularly Perturbed ◽  
State Probability ◽  
Regular Perturbation ◽  
Steady State Probability ◽  
Fundamental Matrices

We give formulas for updating both the steady-state probability distribution and the fundamental matrices of a singularly perturbed Markov chain. This formula generalizes Schweitzer's regular perturbation formulas to the case of singular perturbations.

scholarly journals Container Terminal Berth-Quay Crane Capacity Planning Based on Markov Chain

2021 ◽  
Vol 33 (2) ◽  
pp. 267-281
Author(s):  
Meixian Jiang ◽  
Guoxing Wu ◽  
Jianpeng Zheng ◽  
Guanghua Wu
Keyword(s):  
Markov Chain ◽  
Capacity Planning ◽  
Queuing Theory ◽  
Container Terminal ◽  
Transition Probability ◽  
Transfer Model ◽  
Planning Model ◽  
Steady State Probability ◽  
Quay Cranes ◽  
Time Operation

This paper constructs a berth-quay crane capacity planning model with the lowest average daily cost in the container terminal, and analyzes the influence of the number of berths and quay cranes on the terminal operation. The object of berth-quay crane capacity planning is to optimize the number of berths and quay cranes to maximize the benefits of the container terminal. A steady state probability transfer model based on Markov chain for container terminal is constructed by the historical time series of the queuing process. The current minimum time operation principle (MTOP) strategy is proposed to correct the state transition probability of the Markov chain due to the characteristics of the quay crane movement to change the service capacity of a single berth. The solution error is reduced from 7.03% to 0.65% compared to the queuing theory without considering the quay crane movement, which provides a basis for the accurate solution of the berth-quay crane capacity planning model. The proposed berth-quay crane capacity planning model is validated by two container terminal examples, and the results show that the model can greatly guide the container terminal berth-quay crane planning.

Runway Utilization Analysis Based on the Stochastic Petri Net Model

2013 ◽  
Vol 411-414 ◽  
pp. 1750-1756
Author(s):  
Gao Yang Jiang ◽  
Jie Ning Wang ◽  
Chun Feng Zhang ◽  
Mei Dong
Keyword(s):  
Markov Chain ◽  
Steady State ◽  
Petri Net ◽  
Simulation Method ◽  
State Probability ◽  
Homogeneous Markov Chain ◽  
Steady State Probability ◽  
Stochastic Petri Net ◽  
Markov Chain Method ◽  
Key Indicators

Runway utilization is one of the key indicators of airport operational efficiency. Firstly, stochastic Petri net was introduced to built runway system operational model, and then we analyzed the reachability graph of this model, which not only prove the reachability and boundedness of this model, but also can be used to transform to homogeneous Markov chain. Secondly, The system steady-state probability expressions in various states were established based on the homogeneous Markov chain. Thirdly, runway utilization was calculated based on the steady-state probability expressions. During simulation, runway utilizations in various conditions were analyzed by changing some transitions fire rate. Both Markov chain method and petri net simulation method are useful for runway utilization improvement.

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