The Geometry of M D Queues and Large Deviation
نویسنده
چکیده
Since an M D queue is represented by a Markov chain we can consider the set of all the M D queues as a subset of Markov chains A geometric structures is induced from the geometric structure of the set of Markov chains which forms an exponential family In this paper we show that in the large deviation of the tail probability of the queue length of an M D the rate function and a twisted Markov chain etc are represented in terms of the geometry Moreover in the importance sampling IS simulation for the M D queue we elucidate the geometric relation between the underlying distribution and a simulation distribution and evaluate the variance of an IS estimate by geometric quantities Kew words M D queue large deviation importance sampling information geom etry
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