Synchronous constrained uid systems
نویسندگان
چکیده
This paper introduces the framework of synchronous constrained uid systems (SCFS) to model queueing networks driven synchronously by general uid virtual departure processes, and explores structural properties of queueing networks that t this model. The synchronous timing mechanism used in this paper allows us to model sources and servers with time-varying capacity as in communication systems with cross traac or manufacturing systems with time-dependent machine failures. The SCFS framework allows a variety of traac models (modulated Pois-son//uid, (;) ows, etc.) as well as network topologies (tandems, cycles, fork-join networks, generalized Jackson networks, etc.). Given any such network with m stations, we translate its primitives (topology, connguration of buuers, initial uid levels, and the pathwise routing) into a constraint set T IR m + , the m-dimensional non-negative orthant. Associated with i-th server of the network, is a non-decreasing, right-continuous virtual departure process D i , which describes the time-varying service capacity of that server. We obtain the actual departure process D = (D 1 ; : : :; D m) through the synchronous map (D ; T) s ! D, and prove that D is a non-decreasing and concave function of (D ; T). Finally, we use these properties to study optimal buuer allocation and traac smoothing for a best-eeort multicast connection with hop-by-hop credit-based ow control.
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