In renewal theory, the Inspection Paradox refers to the fact that an interarrival period in a renewal process which contains a fixed inspection time tends to be longer than one for the corresponding uninspected proces...In renewal theory, the Inspection Paradox refers to the fact that an interarrival period in a renewal process which contains a fixed inspection time tends to be longer than one for the corresponding uninspected process. We focus on the paradox for Bernoulli trials. Probability distributions and moments for the lengths of the interarrival periods are derived for the inspected process, and we compare them to those for the uninspected case.展开更多
The Inspection Paradox refers to the fact that in a Renewal Process, the length of the interarrival period which contains a fixed time is stochastically larger than the length of a typical interarrival period. To prov...The Inspection Paradox refers to the fact that in a Renewal Process, the length of the interarrival period which contains a fixed time is stochastically larger than the length of a typical interarrival period. To provide a more complete understanding of this phenomenon, conditioning arguments are used to obtain the distributions and moments of the lengths of the interarrival periods other than the one containing this fixed time for the case of the time-homogeneous Poisson Process. Distributions of the waiting times for events that occur both before and after this fixed time are derived. This provides a fairly complete probabilistic analysis of the Inspection Paradox.展开更多
Energy efficiency plays vital roles in wireless communication system due to the “energy limited battery service” of a mobile station (MS). To ensure longer battery life in WiMAX, a new protocol has been introduced i...Energy efficiency plays vital roles in wireless communication system due to the “energy limited battery service” of a mobile station (MS). To ensure longer battery life in WiMAX, a new protocol has been introduced in its IEEE802.16m version. This new sleep mode has extended listening window and adjustable sleep cycle length. In this paper, we analyze the probability of attaining at three states: serving state, state of timer inactivity and silent state in a simplified statistical model using traffic parameters of arrival rate, pdf (probability density function) of interarrival time and its threshold value. Finally we developed a new state transition chain of the above three states of a MS of IEEE802.16m and solved the chain in closed form.展开更多
The distribution probability of the photon interarrival time （PIT） without signal initial phases is derived based on the Poisson model of X-ray pulsar signals, and a pulsar signal detection algorithm employing the P...The distribution probability of the photon interarrival time （PIT） without signal initial phases is derived based on the Poisson model of X-ray pulsar signals, and a pulsar signal detection algorithm employing the PIT sequence is put forward. The joint probability of the PIT sequence is regarded as a function of the distribution probability and used to compare a constant radiation intensity model with the nonhomogeneous Poisson model for the signal detection. The relationship between the number of detected photons and the probabilities of false negative and positive is studied, and the success rate and mean detection time are estimated based on the number of the given photons. For the spacecraft velocity data detection, the changes of time of photon arrival （TOPA） and PIT caused by spacecraft motion are presented first, then the influences on detection are analyzed respectively. By using the analytical pulse profile of PSR B0531＋21, the simulation of the Xray pulsar signal detection is implemented. The simulation results verify the effectiveness of the proposed method, and the contrast tests show that the proposed method is suitable for the spacecraft velocity data detection.展开更多
文摘In renewal theory, the Inspection Paradox refers to the fact that an interarrival period in a renewal process which contains a fixed inspection time tends to be longer than one for the corresponding uninspected process. We focus on the paradox for Bernoulli trials. Probability distributions and moments for the lengths of the interarrival periods are derived for the inspected process, and we compare them to those for the uninspected case.
文摘The Inspection Paradox refers to the fact that in a Renewal Process, the length of the interarrival period which contains a fixed time is stochastically larger than the length of a typical interarrival period. To provide a more complete understanding of this phenomenon, conditioning arguments are used to obtain the distributions and moments of the lengths of the interarrival periods other than the one containing this fixed time for the case of the time-homogeneous Poisson Process. Distributions of the waiting times for events that occur both before and after this fixed time are derived. This provides a fairly complete probabilistic analysis of the Inspection Paradox.
文摘Energy efficiency plays vital roles in wireless communication system due to the “energy limited battery service” of a mobile station (MS). To ensure longer battery life in WiMAX, a new protocol has been introduced in its IEEE802.16m version. This new sleep mode has extended listening window and adjustable sleep cycle length. In this paper, we analyze the probability of attaining at three states: serving state, state of timer inactivity and silent state in a simplified statistical model using traffic parameters of arrival rate, pdf (probability density function) of interarrival time and its threshold value. Finally we developed a new state transition chain of the above three states of a MS of IEEE802.16m and solved the chain in closed form.
基金supported by the National Natural Science Foundation of China (61172138)the Open Fund of Key Laboratory of Precision Navigation and Technology,National Time Service Center,CAS (2012PNTT02)
文摘The distribution probability of the photon interarrival time （PIT） without signal initial phases is derived based on the Poisson model of X-ray pulsar signals, and a pulsar signal detection algorithm employing the PIT sequence is put forward. The joint probability of the PIT sequence is regarded as a function of the distribution probability and used to compare a constant radiation intensity model with the nonhomogeneous Poisson model for the signal detection. The relationship between the number of detected photons and the probabilities of false negative and positive is studied, and the success rate and mean detection time are estimated based on the number of the given photons. For the spacecraft velocity data detection, the changes of time of photon arrival （TOPA） and PIT caused by spacecraft motion are presented first, then the influences on detection are analyzed respectively. By using the analytical pulse profile of PSR B0531＋21, the simulation of the Xray pulsar signal detection is implemented. The simulation results verify the effectiveness of the proposed method, and the contrast tests show that the proposed method is suitable for the spacecraft velocity data detection.
