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Abstract-The Internet has recently been evolving from homogeneous congestion control to heterogeneous congestion control. Several years ago, Internet traffic was mainly controlled by the traditional RENO, whereas it is now controlled by multiple different TCP algorithms, such as RENO, CUBIC, and Compound TCP (CTCP). However, there is very little work on the performance and stability study of the Internet with heterogeneous congestion control. One fundamental reason is the lack of the deployment information of different TCP algorithms. In this paper, we first propose a tool called TCP Congestion Avoidance Algorithm Identification (CAAI) for actively identifying the TCP algorithm of a remote Web server. CAAI can identify all default TCP algorithms (e.g., RENO, CUBIC, and CTCP) and most non-default TCP algorithms of major operating system families. We then present the CAAI measurement result of about 30 000 Web servers. We found that only of the Web servers still use RENO, 46.92% of the Web servers use BIC or CUBIC, and of the Web servers use CTCP. Our measurement results show a strong sign that the majority of TCP flows are not controlled by RENO anymore, and a strong sign that the Internet congestion control has changed from homogeneous to heterogeneous.

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Clifford algebra is introduced as a theoretical foundation for network topology expression and algorithm construction. Network nodes are coded with basis vectors in a vector space double-struckRn, and the edges and k‐walk routes can be expressed by 2‐blades and k‐blades, respectively, in the Clifford algebra Cl(n,0). The topologies among nodes, edges, and routes of networks can be directly calculated, and the network routes can be extended and traversed with oriented join products. The network algorithm construction processes based on Clifford algebra are instantiated by the single source shortest path algorithm. The experimental results on different scale random networks suggest that Clifford algebra is suited for network expression and relation computation. The Clifford algebra‐based shortest path algorithm is vivid and clear in geometric meaning and has great advantage on temporal and spatial complexity. Copyright © 2013 John Wiley & Sons, Ltd.

Introducing Clifford algebra as the mathematical foundation, a unified spatiotemporal data model and hierarchical spatio-temporal index are constructed by linking basic data objects, like pointclouds and Spatio-Temporal Hyper Cubes of different dimensions, within the multivector structure of Clifford algebra. The transformation from geographic space into homogeneous and conformal space means that geometric, metric and many other kinds of operators of Clifford algebra can be implemented and we then design the shortest path, high-dimensional Voronoi and unified spatial-temporal process analyses with spacetime algebra. Tests with real world data suggest these traditional GIS analysis algorithms can be extended and constructed under Clifford Algebra framework, which can accommodate multiple dimensions. The prototype software system CAUSTA (Clifford Algebra based Unified Spatial-Temporal Analysis) provides a useful tool for investigating and modeling the distribution characteristics and dynamic process of complex geographical phenomena under the unified spatio-temporal structure.