Large deviations of the steady-state distribution of reflected processes with applications to queueing systems期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Large deviations of the steady-state distribution of reflected processes with applications to queueing systems

Authors:	Majewski Kurt

Affiliation:	(1) Siemens Corp. Research and Development, 81730 Munich, Germany E-mail:

Abstract:	We consider a Skorohod map which takes paths in $mathbb{R}^n$ to paths which stay in the positive orthant $mathbb{R}_{^ + }^n$ . We let be the domain of definition of . A convex and lower semi-continuous function $lambda {text{:}}mathbb{R}^n to left[ {0,infty } right]$ and a set $A subset mathbb{R}_{^ + }^n$ are given. We are concerned with the calculation of the infimum of the value $int_0^t lambda left( {{dot omega }left( {mathcal{S}} right)} right){d}mathcal{S}$ for t ⩾ 0 and absolutely continuous subject to the conditions and . We show that such minimization problems characterize large deviation asymptotics of tail probabilities of the steady-state distribution of certain reflected processes. We approximate the infimum by a sequence of finite-dimensional minimization problems. This approximation allows to formulate an algorithm for the calculation of the infimum and to derive analytical bounds for its value. Several applications are discussed including large deviations of generalized processor sharing and large deviations of heavily loaded queueing networks. This revised version was published online in June 2006 with corrections to the Cover Date.

Keywords:	large deviations Skorohod map path space minimization problem generalized processor sharing heavy traffic approximation minimizing path
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