Abstract — Significant research has been dedicated to methods that estimate the available bandwidth in a network from traffic measurements. While estimation methods abound, less progress has been made on achieving a foundational understanding of the bandwidth estimation problem. In this paper, we develop a min-plus system theoretic formulation of bandwidth estimation. We show that the problem as well as previously proposed solutions can be concisely described and derived using min-plus system theory, thus establishing the existence of a strong link between network calculus and network probing methods. We relate difficulties in network probing to potential non-linearities of the underlying systems, and provide a justification for the distinctive treatment of FIFO scheduling in network probing. I.

Abstract—We provide an analytical proof that the departure rate of a CBR flow at an overloaded link with FIFO buffers is proportional to the flow’s share of the total offered load at the link. This property of FIFO scheduling was recently validated in [1] in a series of traffic measurement experiments. An extension of the analysis to a multi-node scenario shows that the output rate of a flow in a network with many overloaded FIFO switches approaches the pessimistic values given by blind multiplexing. I.

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It is shown that bandwidth estimation in packet networks can be viewed in terms of min-plus linear system theory. The available bandwidth of a link or complete path is expressed in terms of a service curve, which is a function that appears in the network calculus to express the service available to a traffic flow. The service curve is estimated based on measurements of a sequence of probing packets or passive measurements of a sample path of arrivals. It is shown that existing bandwidth estimation methods can be derived in the min-plus algebra of the network calculus, thus providing further mathematical justification for these methods. Principal difficulties of estimating available bandwidth from measurement of network probes are related to potential non-linearities of the underlying network. When networks are viewed as systems that operate either in a linear or in a non-linear regime, it is argued that probing schemes extract the most information at a point when the network crosses from a linear to a non-linear regime. Experiments on the Emulab testbed at the University of Utah evaluate the robustness of the system theoretic interpretation of networks in practice. Multi-node experiments evaluate how well the convolution operation of the min-plus algebra provides estimates for the available bandwidth of a path from estimates of individual links.

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