A DEMAND PREDICTION MODEL FOR REPLACEMENT PARTS USING A MARKOV RENEWAL PROCESS WITH TERMINATION

2010 ◽  
Vol 41 (4) ◽  
pp. 287-306 ◽  
Author(s):  
Yasushi Endow ◽  
Shin Tanimoto
Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 55
Author(s):  
P.-C.G. Vassiliou

For a G-inhomogeneous semi-Markov chain and G-inhomogeneous Markov renewal processes, we study the change from real probability measure into a forward probability measure. We find the values of risky bonds using the forward probabilities that the bond will not default up to maturity time for both processes. It is established in the form of a theorem that the forward probability measure does not alter the semi Markov structure. In addition, foundation of a G-inhohomogeneous Markov renewal process is done and a theorem is provided where it is proved that the Markov renewal process is maintained under the forward probability measure. We show that for an inhomogeneous semi-Markov there are martingales that characterize it. We show that the same is true for a Markov renewal processes. We discuss in depth the calibration of the G-inhomogeneous semi-Markov chain model and propose an algorithm for it. We conclude with an application for risky bonds.


PLoS ONE ◽  
2021 ◽  
Vol 16 (3) ◽  
pp. e0248064
Author(s):  
Pengshun Li ◽  
Jiarui Chang ◽  
Yi Zhang ◽  
Yi Zhang

Taxi order demand prediction is of tremendous importance for continuous upgrading of an intelligent transportation system to realise city-scale and personalised services. An accurate short-term taxi demand prediction model in both spatial and temporal relations can assist a city pre-allocate its resources and facilitate city-scale taxi operation management in a megacity. To address problems similar to the above, in this study, we proposed a multi-zone order demand prediction model to predict short-term taxi order demand in different zones at city-scale. A two-step methodology was developed, including order zone division and multi-zone order prediction. For the zone division step, the K-means++ spatial clustering algorithm was used, and its parameter k was estimated by the between–within proportion index. For the prediction step, six methods (backpropagation neural network, support vector regression, random forest, average fusion-based method, weighted fusion-based method, and k-nearest neighbour fusion-based method) were used for comparison. To demonstrate the performance, three multi-zone weighted accuracy indictors were proposed to evaluate the order prediction ability at city-scale. These models were implemented and validated on real-world taxi order demand data from a three-month consecutive collection in Shenzhen, China. Experiment on the city-scale taxi demand data demonstrated the superior prediction performance of the multi-zone order demand prediction model with the k-nearest neighbour fusion-based method based on the proposed accuracy indicator.


2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Dongbo Liu ◽  
Jian Lu ◽  
Wanjing Ma

One-way carsharing system has been widely adopted in the carsharing field due to its flexible services. However, as one of the main limitations of the one-way carsharing system, the imbalance between supply and demand needs to be solved. Predicting pick-up demand has been studied to achieve the goal, but using returned vehicles to reduce unnecessary relocation is also one of the important methods. Nowadays, trajectory data and other data are available for real-time prediction for return demand. Based on the return demand prediction, the relocation response can be more reasonable. Thus, the balance of demand and supply can be largely improved. The multisource data include trajectory data, user application log data, order data, station data, and user characteristic data. Based on these data, a return demand prediction model was used to predict whether the user will return the vehicle in 15 min in real time, and a destination station prediction model was applied to forecast which station the user will park at. Finally, a case study using ten stations’ one-week field data was conducted to test the benefit of the dynamic return demand prediction. The results showed that the return demand prediction improves the efficiency of the relocations by mitigating the condition that the station parking space is full or empty. The potential application of this study would effectively reduce unnecessary relocation and further formulate an active operation optimization strategy to reduce the system’s operational cost and improve the service quality of the system.


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