702 research outputs found
Validity of heavy traffic steady-state approximations in generalized Jackson Networks
We consider a single class open queueing network, also known as a generalized
Jackson network (GJN). A classical result in heavy-traffic theory asserts that
the sequence of normalized queue length processes of the GJN converge weakly to
a reflected Brownian motion (RBM) in the orthant, as the traffic intensity
approaches unity. However, barring simple instances, it is still not known
whether the stationary distribution of RBM provides a valid approximation for
the steady-state of the original network. In this paper we resolve this open
problem by proving that the re-scaled stationary distribution of the GJN
converges to the stationary distribution of the RBM, thus validating a
so-called ``interchange-of-limits'' for this class of networks. Our method of
proof involves a combination of Lyapunov function techniques, strong
approximations and tail probability bounds that yield tightness of the sequence
of stationary distributions of the GJN.Comment: Published at http://dx.doi.org/10.1214/105051605000000638 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Lattice path counting and the theory of queues
In this paper we will show how recent advances in the combinatorics of lattice paths can be applied to solve interesting and nontrivial problems in the theory of queues. The problems we discuss range from classical ones like M^a/M^b/1 systems to open tandem systems with and without global blocking and to queueing models that are related to random walks in a quarter plane like the Flatto-Hahn model or systems with preemptive priorities. (author´s abstract)Series: Research Report Series / Department of Statistics and Mathematic
A development of logistics management models for the Space Transportation System
A new analytic queueing approach was described which relates stockage levels, repair level decisions, and the project network schedule of prelaunch operations directly to the probability distribution of the space transportation system launch delay. Finite source population and limited repair capability were additional factors included in this logistics management model developed specifically for STS maintenance requirements. Data presently available to support logistics decisions were based on a comparability study of heavy aircraft components. A two-phase program is recommended by which NASA would implement an integrated data collection system, assemble logistics data from previous STS flights, revise extant logistics planning and resource requirement parameters using Bayes-Lin techniques, and adjust for uncertainty surrounding logistics systems performance parameters. The implementation of these recommendations can be expected to deliver more cost-effective logistics support
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