-
作者：Joseph, Adrien
作者单位：Sorbonne Universite; Universite Paris Cite
摘要：Consider a critical random multigraph G(n) with n vertices constructed by the configuration model such that its vertex degrees are independent random variables with the same distribution v (criticality means that the second moment of v is finite and equals twice its first moment). We specify the scaling limits of the ordered sequence of component sizes of G(n) as n tends to infinity in different cases. When v has finite third moment, the components sizes rescaled by n(-2/3) converge to the exc...
-
作者：Liu, Jingchen; Xu, Gongjun
作者单位：Columbia University; University of Minnesota System; University of Minnesota Twin Cities
摘要：In this paper, we consider the extreme behavior of a Gaussian random field f(t) living on a compact set T. In particular, we are interested in tail events associated with the integral integral(T) e(f(t)) dt. We construct a (non-Gaussian) random field whose distribution can be explicitly stated. This field approximates the conditional Gaussian random field f (given that integral(T) e(f(t)) dt exceeds a large value) in total variation. Based on this approximation, we show that the tail event of ...
-
作者：Liu, Yunan; Whitt, Ward
作者单位：North Carolina State University; Columbia University
摘要：A many-server heavy-traffic FCLT is proved for the Gt/M/st + GI queueing model, having time-varying arrival rate and staffing, a general arrival process satisfying a FCLT, exponential service times and customer abandonment according to a general probability distribution. The FCLT provides theoretical support for the approximating deterministic fluid model the authors analyzed in a previous paper and a refined Gaussian process approximation, using variance formulas given here. The model is assu...
-
作者：Shah, D.; Tsitsiklis, J. N.; Zhong, Y.
作者单位：Massachusetts Institute of Technology (MIT); University of California System; University of California Berkeley
摘要：We consider a flow-level model of a network operating under an a-fair bandwidth sharing policy (with alpha > 0) proposed by Roberts and Massoulie [Telecomunication Systems 15 (2000) 185-201]. This is a probabilistic model that captures the long-term aspects of bandwidth sharing between users or flows in a communication network. We study the transient properties as well as the steady-state distribution of the model. In particular, for alpha >= 1, we obtain bounds on the maximum number of flows ...
