This paper attempts to study the optimal stopping time for semi- Markov processes (SMPs) under the discount optimization criteria with unbounded cost rates. In our work, we introduce an explicit construction of the eq...This paper attempts to study the optimal stopping time for semi- Markov processes (SMPs) under the discount optimization criteria with unbounded cost rates. In our work, we introduce an explicit construction of the equivalent semi-Markov decision processes (SMDPs). The equivalence is embodied in the expected discounted cost functions of SMPs and SMDPs, that is, every stopping time of SMPs can induce a policy of SMDPs such that the value functions are equal, and vice versa. The existence of the optimal stopping time of SMPs is proved by this equivalence relation. Next, we give the optimality equation of the value function and develop an effective iterative algorithm for computing it. Moreover, we show that the optimal and ε-optimal stopping time can be characterized by the hitting time of the special sets. Finally, to illustrate the validity of our results, an example of a maintenance system is presented in the end.展开更多
Several factors influence bus transit reliability which includes bus stop conditions along the route, traffic conditions, route of travel and time of day. The overall transit bus reli- ability is generally affected by...Several factors influence bus transit reliability which includes bus stop conditions along the route, traffic conditions, route of travel and time of day. The overall transit bus reli- ability is generally affected by dwell time （DT）, the fare payment method, the bus stop location, and the number of passengers alighting or boarding. A new variable is defined in this study, total bus stop time （TBST）, which is the summation of DT and the time it takes a bus to effectively park at a bus stop and the re-entering the traffic stream. It is suggested that the overall bus transit reliability along routes could be improved if the TBST is mini- mized at bus stops. In this study, TBST models for bus stops located at mid-blocks and near intersections were developed based on multivariate regression analysis using ordinary least squares method. Data collection was conducted at 60 bus stops, 30 of which were near intersections and 30 at mid-blocks, in Washington DC during morning, mid-day and evening peak hours. The variables observed at each bus stop are as follows： number of passengers alighting or boarding, DT, TBST, bus stop type, bus pad, length number of lanes on approach to the bus stop, and permitted parking. Statistical inferences were based on 5% level of significance. From the results, it was inferred that the new variable, TBST, could potentially be used to improve scheduling and transit bus systems planning in a dense urban area.展开更多
Among a variety of adaptive designs, stage-wise design, especially, two-stage design is an important one because patient responses are not available immediately but are available in batches or intermittently in some s...Among a variety of adaptive designs, stage-wise design, especially, two-stage design is an important one because patient responses are not available immediately but are available in batches or intermittently in some situations. In this paper, by Bayesian method, the general formula of asymptotical optimal worth is given, meanwhile the length of some optimal designs at first stage concerning two-stage trials in several important cases has been obtained.展开更多
基金This work was supported in part by the National Natural Science Foundation of China(Grant Nos.11931018,61773411,11701588,11961005)the Guangdong Basic and Applied Basic Research Foundation(Grant No.2020B1515310021).
文摘This paper attempts to study the optimal stopping time for semi- Markov processes (SMPs) under the discount optimization criteria with unbounded cost rates. In our work, we introduce an explicit construction of the equivalent semi-Markov decision processes (SMDPs). The equivalence is embodied in the expected discounted cost functions of SMPs and SMDPs, that is, every stopping time of SMPs can induce a policy of SMDPs such that the value functions are equal, and vice versa. The existence of the optimal stopping time of SMPs is proved by this equivalence relation. Next, we give the optimality equation of the value function and develop an effective iterative algorithm for computing it. Moreover, we show that the optimal and ε-optimal stopping time can be characterized by the hitting time of the special sets. Finally, to illustrate the validity of our results, an example of a maintenance system is presented in the end.
文摘Several factors influence bus transit reliability which includes bus stop conditions along the route, traffic conditions, route of travel and time of day. The overall transit bus reli- ability is generally affected by dwell time （DT）, the fare payment method, the bus stop location, and the number of passengers alighting or boarding. A new variable is defined in this study, total bus stop time （TBST）, which is the summation of DT and the time it takes a bus to effectively park at a bus stop and the re-entering the traffic stream. It is suggested that the overall bus transit reliability along routes could be improved if the TBST is mini- mized at bus stops. In this study, TBST models for bus stops located at mid-blocks and near intersections were developed based on multivariate regression analysis using ordinary least squares method. Data collection was conducted at 60 bus stops, 30 of which were near intersections and 30 at mid-blocks, in Washington DC during morning, mid-day and evening peak hours. The variables observed at each bus stop are as follows： number of passengers alighting or boarding, DT, TBST, bus stop type, bus pad, length number of lanes on approach to the bus stop, and permitted parking. Statistical inferences were based on 5% level of significance. From the results, it was inferred that the new variable, TBST, could potentially be used to improve scheduling and transit bus systems planning in a dense urban area.
基金the National Natural Science Foundation of China (Grant No.10271001).
文摘Among a variety of adaptive designs, stage-wise design, especially, two-stage design is an important one because patient responses are not available immediately but are available in batches or intermittently in some situations. In this paper, by Bayesian method, the general formula of asymptotical optimal worth is given, meanwhile the length of some optimal designs at first stage concerning two-stage trials in several important cases has been obtained.
