Single Class Queueing Networks with Discrete and Fluid Customers on the Time Interval R
Queueing Systems: Theory and Applications
Pathwise comparison results for stochastic fluid networks
Queueing Systems: Theory and Applications
Heavy traffic approximation for the stationary distribution of stochastic fluid networks
Queueing Systems: Theory and Applications
Mathematics of Operations Research
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We consider the deterministic Skorokhod problem in an orthant of the formZw( t) =w( t) + ?b( u,Yw( u),Zw( u))du + ?R( u,Yw( u--);Zw( u--)) dYw( u) with ( Yw) i(脗·) nondecreasing, and ( Yw) i(脗·) not increasing while ( Zw) i(脗·)0. This can be viewed as a subsidy-surplus model in an interdependent economy. Existence of a unique solution is established under fairly general conditions (viz. with R(脗·, 脗·, 脗·) satisfying a uniform spectral radius condition). Comparison result for (SP) vis-a-vis the usual partial order on the orthant is studied; we show that the more "inward looking" the reflection vectors and the drift, the larger the values ofYw will be but the values ofZw will be smaller. In addition to showing that the Leontief-type output is a feasible subsidy, connection between (SP) and "minimality" of feasible subsidies is discussed (consequently it is suggested that (SP) may be taken as a continuous time feedback-form analogue of open Leontief model).In the stochastic case, ( Y( t),Z( t)) turns out to be a strong Markov process ifw(脗·) arises from aLevy process. Relevance of the comparison result to recurrence/positive recurrence ofZ(脗·) process is pointed out.