Stationary Ergodic
نویسنده
چکیده
This paper gives a survey of recent results on generalized Jackson networks , where classical exponential or i.i.d. assumptions on services and routings are replaced by stationary and ergodic assumptions. We rst show that the most basic features of the network may exhibit unexpected behavior. Several probabilistic properties are then discussed, including a strong law of large numbers for the number of events in the stations, the existence, uniqueness and representation of stationary regimes for queue size and workload.
منابع مشابه
Records from Stationary Observations Subject to a Random Trend
We prove strong convergence and asymptotic normality for the record and the weak record rate of observations of the form Yn = Xn + Tn, n ≥ 1, where (Xn)n∈Z is a stationary ergodic sequence of random variables and (Tn)n≥1 is a stochastic trend process, with stationary ergodic increments. The strong convergence result follows from the Dubins-Freedman law of large numbers and Birkhoff’s ergodic th...
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We construct a stationary ergodic process {X1, X2, X3 . . .} such that each Xt, 1 ≤ t <∞, has the uniform distribution on the unit square and the length Ln of the shortest path through {X1, X2, . . . , Xn} is not asymptotic to a constant times the square root of n. In other words, we show that the Beardwood, Halton and Hammersley theorem does not extend from the case of independent uniformly di...
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We construct a stationary ergodic process X1,X2, . . . such that each Xt has the uniform distribution on the unit square and the length Ln of the shortest path through the points X1,X2, . . . ,Xn is not asymptotic to a constant times the square root of n. In other words, we show that the Beardwood, Halton, and Hammersley [Proc. Cambridge Philos. Soc. 55 (1959) 299–327] theorem does not extend f...
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