This paper considers a single server queue in which the service time is exponentially distributed and the service station may breakdown according to a Poisson process with the rates γ and γ' in busy period and idle period respectively. Repair will be performed immediately following a breakdown. The repair time is assumed to have an exponential distribution. Let g(t) and G(t) be the probability density function and the cumulative distribution function of the interarrival time respectively. When t tends to infinity, the rate of g(t)/[1 -G(t)] will tend to a constant. A set of equations will be derived for the probabilities of the queue length and the states of the arrival, repair and service processes when the queue is in a stationary state. By solving these equations, numerical results for the stationary queue length distribution can be obtained.
This project focuses on the clustering of genome sequences from different chromosomes of different organisms, back to the group of organism itself. The clustering is performed based on the ratio of the palindromic occurrence in the genomes to the statistically computed expected occurrence of the palindrome. The individual phylogenetic nodal distance is calculated based on the clustering results, at which sequences from different organism could be distinguished clearly.
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