30,984 research outputs found
Stochastic Network Calculus with Localized Application of Martingales
Stochastic Network Calculus is a probabilistic method to compute performance
bounds in networks, such as end-to-end delays. It relies on the analysis of
stochastic processes using formalism of (Deterministic) Network Calculus.
However, unlike the deterministic theory, the computed bounds are usually very
loose compared to the simulation. This is mainly due to the intensive use of
the Boole's inequality. On the other hand, analyses based on martingales can
achieve tight bounds, but until now, they have not been applied to sequences of
servers. In this paper, we improve the accuracy of Stochastic Network Calculus
by combining this martingale analysis with a recent Stochastic Network Calculus
results based on the Pay-Multiplexing-Only-Once property, well-known from the
Deterministic Network calculus. We exhibit a non-trivial class of networks that
can benefit from this analysis and compare our bounds with simulation.Comment: 29 pages, 9 figure
Model checking probabilistic and stochastic extensions of the pi-calculus
We present an implementation of model checking for probabilistic and stochastic extensions of the pi-calculus, a process algebra which supports modelling of concurrency and mobility. Formal verification techniques for such extensions have clear applications in several domains, including mobile ad-hoc network protocols, probabilistic security protocols and biological pathways. Despite this, no implementation of automated verification exists. Building upon the pi-calculus model checker MMC, we first show an automated procedure for constructing the underlying semantic model of a probabilistic or stochastic pi-calculus process. This can then be verified using existing probabilistic model checkers such as PRISM. Secondly, we demonstrate how for processes of a specific structure a more efficient, compositional approach is applicable, which uses our extension of MMC on each parallel component of the system and then translates the results into a high-level modular description for the PRISM tool. The feasibility of our techniques is demonstrated through a number of case studies from the pi-calculus literature
An End-to-End Stochastic Network Calculus with Effective Bandwidth and Effective Capacity
Network calculus is an elegant theory which uses envelopes to determine the
worst-case performance bounds in a network. Statistical network calculus is the
probabilistic version of network calculus, which strives to retain the
simplicity of envelope approach from network calculus and use the arguments of
statistical multiplexing to determine probabilistic performance bounds in a
network. The tightness of the determined probabilistic bounds depends on the
efficiency of modelling stochastic properties of the arrival traffic and the
service available to the traffic at a network node. The notion of effective
bandwidth from large deviations theory is a well known statistical descriptor
of arrival traffic. Similarly, the notion of effective capacity summarizes the
time varying resource availability to the arrival traffic at a network node.
The main contribution of this paper is to establish an end-to-end stochastic
network calculus with the notions of effective bandwidth and effective capacity
which provides efficient end-to-end delay and backlog bounds that grows
linearly in the number of nodes () traversed by the arrival traffic, under
the assumption of independence.Comment: 17 page
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