Studying the propagation of cascading failures through the transmission network is key to asses and mitigate the risk faced the energy system. As complex systems the power grid failure is often studied using some prob...Studying the propagation of cascading failures through the transmission network is key to asses and mitigate the risk faced the energy system. As complex systems the power grid failure is often studied using some probability distributions. We apply 4 well-known probabilistic models, Poisson model, Power Law model, Generalized Poisson Branching process model and Borel-Tanner Branching process model, to a 14-year utility historical outage data from a regional power grid in China, computing probabilities of cascading line outages. For this data, the empirical distribution of the total number of line outages is well approximated by the initial line outages propagating according to a Borel-Tanner branching process. Also for this data, Power law model overestimates, while Generalized Possion branching process and Possion model underestimate, the probability of larger outages. Especially, the probability distribution generated by the Poisson model deviates heavily from the observed data, underestimating the probability of large events (total no. of outages over 5) by roughly a factor of 10-2 to 10-5. The observation is confirmed by a statistical test of model fitness. The results of this work indicate that further testing of Borel-Tanner branching process models of cascading failure is appropriate, and should be further discussed as it outperforms other more traditional models.展开更多
In this paper we consider the arrival process of a multiserver queue governed by a discrete autoregressive process of order 1 [DAR(1)] with Quasi-Negative Binomial Distribution-II as the marginal distribution. This di...In this paper we consider the arrival process of a multiserver queue governed by a discrete autoregressive process of order 1 [DAR(1)] with Quasi-Negative Binomial Distribution-II as the marginal distribution. This discrete time multiserver queueing system with autoregressive arrivals is more suitable for modeling the Asynchronous Transfer Mode(ATM) multiplexer queue with Variable Bit Rate (VBR) coded teleconference traffic. DAR(1) is described by a few parameters and it is easy to match the probability distribution and the decay rate of the autocorrelation function with those of measured real traffic. For this queueing system we obtained the stationary distribution of the system size and the waiting time distribution of an arbitrary packet with the help of matrix analytic methods and the theory of Markov regenerative processes. Also we consider negative binomial distribution, generalized Poisson distribution, Borel-Tanner distribution defined by Frank and Melvin(1960) and zero truncated generalized Poisson distribution as the special cases of Quasi-Negative Binomial Distribution-II. Finally, we developed computer programmes for the simulation and empirical study of the effect of autocorrelation function of input traffic on the stationary distribution of the system size as well as waiting time of an arbitrary packet. The model is applied to a real data of number of customers waiting for checkout in an airport and it is established that the model well suits this data.展开更多
文摘Studying the propagation of cascading failures through the transmission network is key to asses and mitigate the risk faced the energy system. As complex systems the power grid failure is often studied using some probability distributions. We apply 4 well-known probabilistic models, Poisson model, Power Law model, Generalized Poisson Branching process model and Borel-Tanner Branching process model, to a 14-year utility historical outage data from a regional power grid in China, computing probabilities of cascading line outages. For this data, the empirical distribution of the total number of line outages is well approximated by the initial line outages propagating according to a Borel-Tanner branching process. Also for this data, Power law model overestimates, while Generalized Possion branching process and Possion model underestimate, the probability of larger outages. Especially, the probability distribution generated by the Poisson model deviates heavily from the observed data, underestimating the probability of large events (total no. of outages over 5) by roughly a factor of 10-2 to 10-5. The observation is confirmed by a statistical test of model fitness. The results of this work indicate that further testing of Borel-Tanner branching process models of cascading failure is appropriate, and should be further discussed as it outperforms other more traditional models.
文摘In this paper we consider the arrival process of a multiserver queue governed by a discrete autoregressive process of order 1 [DAR(1)] with Quasi-Negative Binomial Distribution-II as the marginal distribution. This discrete time multiserver queueing system with autoregressive arrivals is more suitable for modeling the Asynchronous Transfer Mode(ATM) multiplexer queue with Variable Bit Rate (VBR) coded teleconference traffic. DAR(1) is described by a few parameters and it is easy to match the probability distribution and the decay rate of the autocorrelation function with those of measured real traffic. For this queueing system we obtained the stationary distribution of the system size and the waiting time distribution of an arbitrary packet with the help of matrix analytic methods and the theory of Markov regenerative processes. Also we consider negative binomial distribution, generalized Poisson distribution, Borel-Tanner distribution defined by Frank and Melvin(1960) and zero truncated generalized Poisson distribution as the special cases of Quasi-Negative Binomial Distribution-II. Finally, we developed computer programmes for the simulation and empirical study of the effect of autocorrelation function of input traffic on the stationary distribution of the system size as well as waiting time of an arbitrary packet. The model is applied to a real data of number of customers waiting for checkout in an airport and it is established that the model well suits this data.
