(In chronological order, grouped by topic)

A strong Tauberian theorem for characteristic functions
R. Ried and P.Gonçalves
Appl. Comput. Harmon. Anal.
Letter to the Editor, no 39, p 552-557, 2015

Cascades Infiniment Divisibles
R. Riedi
Gazette des Mathématiciens (Soc. Math. France)
numéro spécial "Benoît Mandelbrot, Père de la géométrie fractale" 2013, no 136, p 119-128

Brownian Motion
R. H. Riedi
in Encyclopedia of Environmetrics, A.-H. El-Shaarawi and W. Piegorsch (eds), John Wiley & Sons Ltd: Chichester, UK.
Published online 1/15/2013 at the home page of the Encyclopedia at Wiley Online Library

Multifractal Analysis of Infinite Products of Stationary Jump Processes
P. Mannersalo, I. Norros and R. Riedi
Journal of Probability and Statistics vol. 2010, Article ID 807491, 26 pages, (2010).
version with a higher level of details available as
Technical Report TR2009-02, Department of Statistics, Rice University, (June 2009)

Infinitely Divisible Shot-Noise: Modeling Fluctuations in Networking, Finance and Turbulence
R. Riedi and D. Gershman, ICNF 07, Proc.\ International Conference on Noise and Fluctuations, Tokyo, Japan, September 2007

Shot-Noise Cascades R. Riedi, Fractal Geometry & Stochastics 4, Greifswald, Germany, September 2008.

Infinitely Divisible Shot-Noise: Cascades of Non-Compact Pulses R. Riedi Technical Report TR2010-02, Department of Statistics, Rice University, (March 2009)


Measurement-Based Analysis, Modeling, and Synthesis of the Internet Delay Space
Bo Zhang, T. S. Eugene Ng, Animesh Nandi, Rudolf Riedi, Peter Druschel, Guohui Wang
Transactions on Networking 18(1), 229-242, 2010
presented at Internet Measurement Conference IMC2006, Rio de Janeiro, Brazil, October 2006.

A Cloud Data Center Optimization Approach Using Dynamic Data Interchanges
Rappos Efstratios, Robert Stephan , Riedi Rudolf
IEEE 2nd International Conference on Cloud Networking (CloudNet),
San Francisco, CA, November 2013, p 175-179.

Opportunities and Limits of Remote Timing Attacks
S. Crosby, R. Riedi and D. Wallach
ACM Transactions on Information and Systems Security (TISSEC)
12(3), 485--507, (January 2009).

Safari: A Self-Organizing, Hierarchical Architecture for Scalable Ad Hoc Networking.
S. Du, A. Khan, S. PalChaudhuri, A. Post, A. Saha, P. Druschel, D. Johnson and R. Riedi
Ad Hoc Networks 6(4), 485--507, (2008).

On the Impact of Realism of Mobility Models for Wireless Networks
H. Flores, R. Riedi, S. Eidenbenz and N. Hengartner
IEEE Globecom 2008, Global Communications Conference,
New Orleans, LA, December 2008.

Bounds on the Benefit of Network Coding: Throughput and Energy Saving in Wireless Networks
A. Keshavarz-Haddad, R. Riedi
IEEE INFOCOM 2008, 27th Ann. Conf. Computer Communications,
Phoenix, Arizona, April 2008.

Bounds on the Benefit of Network Coding for Wireless Multicast and Unicast
A. Keshavarz-Haddad and R. Riedi
IEEE Transactions on Mobile Computing
vol 13(1), 102-115, Jan 2014.

Multicast Capacity of Large Homogeneous Multihop Wireless Networks
A. Keshavarz-Haddad, R. Riedi
6th Intern. Symp. on Modeling and Optimization in Wireless Networks,
WiOPT’08, Berlin, Germany, April 2008.

Arena Function: A Framework for Computing Capacity Bounds in Wireless Networks
A. Keshavarz-Haddad and R. Riedi
IEEE Transactions on Wireless Communications
no 17, issue 2, p 1134-1146, 2018
Bounds for the Capacity of Wireless Multihop Networks Imposed by Topology and Demand
A. Keshavarz-Haddad and R. Riedi
MobiHoc 07, 8th ACM International Symposium on Mobile Ad Hoc Networking and Computing, September 2007

Broadcast Flooding Revisited: Survivability and Latency
P. Mannersalo, A. Keshavarz-Haddad, and R. Riedi
IEEE INFOCOM 2007, Anchorage, Alaska, USA, May 2007. 

Broadcast Capacity in Multihop Wireless Networks
A. Keshavarz-Haddad, V. Ribeiro, R. Riedi, MobiCom’06, Los Angeles, CA, September 2006
On the Broadcast Capacity of Multihop Wireless Networks: Interplay of Power, Density and Interference
A. Keshavarz-Haddad and R. Riedi, SECON 2007, San Diego, CA, June 2007.


DRB and DCCB: Efficient and Robust Dynamic Broadcast for Ad Hoc and Sensor Networks
A. Keshavarz-Haddad, V. Ribeiro and R. Riedi
SECON 2007, San Diego, CA, June 2007.


Describing MANETS: Principal Component Analysis of Sparse Mobility Traces
N. Hengartner, H. Flores, S. Eidenbenz and R. Riedi
Intern. Workshop on Performance Evaluation of Wireless Ubiquitous Networks, Malaga, Spain, October 2006.


Color-Based Broadcasting for Ad Hoc Networks
4th Intern. Symp. on Modeling and Optimization in WirelessNetworks,
WiOPT’06, Boston, MA, April 2006.

A. Keshavarz-Haddad, V. Ribeiro, R. Riedi


 
On Non-Scale-Invariant Infinitely Divisible Cascades
IEEE Trans IT, 51 (3), pp 1063--1083, (March 2005)
[Short versions:
Warped infinitely divisible cascades: beyond power laws
(Traitement du Signal 22(1), 2005)
Compound Poisson Cascades
(Proc. Colloque "Autosimilarite et Applications" Clermont-Ferrant, France, May 2002;
appeared in Annales Mathematiques Blaise Pascal.)
Scale invariant Infinitely Divisible Cascades [PS]<>
(Proceedings of PSIP'2003 - 2nd Internat. Symp. on
Physics in Signal and Image Processing, Grenoble, France, January 2003)
On non scale invariant Infinitely Divisible Cascades (in pdf)
(19th GRETSI Symposium on Signal and Image Processing Paris, France, September 2003) ]

P. Chainais, R. Riedi and P. Abry,

Diverging moments and parameter estimation
Paulo Goncalves and R. H. Riedi
J. American Statistical Association, 100 (472), 1382-1393, (December 2005). [PS]

A strong Tauberian theorem for characteristic functions
R. Riedi and P.Gonçalves
Appl. Comput. Harmon. Anal.
Letter to the Editor, no 39, p 552-557, 2015




Spatio-Temporal Available Bandwidth Estimation with STAB
V. J. Ribeiro, R. H. Riedi and R. G. Baraniuk
IEEE Internet Computing Magazine, 8 (5), pp 34-41.

Spatio-Temporal Available Bandwidth Estimation with STAB
V. J. Ribeiro, R. H. Riedi and R. G. Baraniuk
Proceedings SIGMETRICS/Performance'04, New York, NY, June 2004.

STAB stands for Spatio-temporal Available bandwidth and is a new
edge-based probing tool to locate tight links on an end-to-end
network path in space and over time. Tight links are those links
with less available bandwidth than all links preceding them on the
path. STAB uses special chirp probing trains that allow accurate
estimation of available bandwidth using few packets. Tight link
localization helps network operations and troubleshooting,
provides insight into the causes of network congestion, as well as
aids network-aware applications. We review the current
state-of-the-art available bandwidth tools, describe the working
of STAB,  and validate it through Internet experiments and
simulations.

Multiscale Queuing Analysis
V. J. Ribeiro, R. H. Riedi and R. G. Baraniuk
IEEE Trans. on Networking, scheduled to appear October 2006.


This paper introduces a new multiscale framework for estimating the
tail probability of a queue fed by an arbitrary traffic process.
Using traffic statistics at a small number of time scales, our
analysis extends the theoretical concept of the critical time scale
and provides practical approximations for the tail queue probability.
These approximations are non-asymptotic; that is they apply to any
finite queue threshold.  While our approach applies to any traffic
process, it is particularly apt for long-range-dependent (LRD)
traffic.  For LRD fractional Brownian motion, we
prove that a sparse exponential spacing of time scales yields optimal
performance.  Simulations with LRD traffic models and real Internet
traces demonstrate the accuracy of the approach.  Finally, simulations
reveal that the marginals of traffic at multiple time scales have a
strong influence on queuing that is not captured well by its global
second-order correlation in non-Gaussian scenarios.

Fractals in Networking: Modeling and Inference
R. Riedi, A. Keshavarz-Haddad, Shriram Sarvotham and Richard G. Baraniuk
Proceedings of Fractals 2004, Conference on ``Fractals and Complexity in Nature'', Vancouver, Canada, April~2004


Network and User Driven On-Off Source Model for Network Traffic
Shriram Sarvotham, Rudolf H. Riedi, and Richard G. Baraniuk
Special Issue of the Computer Network Journal on "Long-range
Dependent Traffic", Computer Networks, 
48 (2005), p 335-350

Optimal sampling strategies for multiscale stochastic processes
IMS Lecture Notes–Monograph Series, 2nd Lehmann Symposium – Optimality 49, 266–290, (2006)
Sampling Strategies for Multiscale Models with Application to Network Traffic Estimation
Proceedings Workshop on Statistical Signal Processing SSP03, St. Louis, MO, Sept 2003
Optimal Sampling Strategies for Tree-based Time Series
TR2004-05, Rice University, Dept. of Statistics, August 2004
to be submitted to Proceedings Lehmann Symposium on Optimality

Vinay J. Ribeiro, Rudolf H. Riedi and Richard G. Baraniuk

pathChirp: Efficient Available Bandwidth Estimation for Network Paths
Vinay J. Ribeiro, Rudolf H. Riedi, Jiri Navratil, Les Cottrell, and Richard G. Baraniuk
Proceedings Workshop on Passive and Active Measurement PAM2003
Best Student Paper Award

The Multiscale Nature of Network Traffic: Discovery, Analysis, and Modelling
Patrice Abry, Richard Baraniuk, Patrick Flandrin, Rudolf Riedi, Darryl Veitch
IEEE Signal Processing Magazine vol 19, no 3, pp 28--46 (May 2002).

Long-Range Dependence: Now you see it now you don't! [PDF]
T. Karagiannis, M. Faloutsos and R. H. Riedi
Proceedings Global Internet, Taiwan, November 2002


Network Traffic Modeling using Connection-Level Information
Xin Wang, Shriram Sarvotham, Rudolf H. Riedi, and Richard G. Baraniuk
Proceedings SPIE ITCom, Boston, MA, August 2002
Network Traffic Analysis and Modeling at the Connection Level
S. Sarvotham, R. Riedi, and R. Baraniuk
Proceedings IEEE/ACM SIGCOMM Internet Measurement Workshop 2001, San Francisco, CA.
Related conference papers:
Additive and Multiplicative Mixture trees for Network Traffic Modeling
S. Sarvotham, X. Wang, R. Riedi, and R. Baraniuk
Proceedings ICASSP Orlando, FL, (May 2002).
Connection-Level Modeling of Network Traffic
X. Wang, S. Sarvotham, R. Riedi, and R. Baraniuk
Proceedings DIMACS Workshop on Internet and WWW Measurement, Mapping and Modeling, 2002, Rutgers, NJ, (February 2002).
Technical Report:
Technical Report, ECE Dept., Rice University, June 30, 2001


Multifractal products of stochastic processes: construction and some basic properties
[Preliminary results (COST 257 (1999) p31)]
P. Mannersalo, I. Norros and R. Riedi
Advances in Applied Probability, 34 (4), Dec 2002, pp 888-903.
 

In various fields, such as teletraffic and economics, measured times series have been reported to adhere to multifractal scaling. Classical cascading measures possess multifractal scaling, but their increments form a non-stationary process. To overcome this problem we introduce a construction of random multifractal measures based on iterative multiplication of stationary stochastic processes, a special form of T-martingales. We study L2-convergence, non-degeneracy and continuity of the limit process. Establishing a power law for its moments we obtain a formula for the multifractal spectrum and hint at how to prove the full formalism.

Zooming Statistics: Inference across scales
J. Hannig, J. S. Marron and R. H. Riedi
J. Korean Statistical Society 30(2) (June 2001), pp. 327--345

Wavelets and Multifractals for network traffic modeling and inference
V. J. Ribeiro, R. H. Riedi and R. G. Baraniuk
Proceedings ICASSP Salt Lake City, Utah, (May 2001).

Analyzing Robot Behavior in E-Business Sites
Virgílio Almeida, Daniel Menascé, Rudolf Riedi, Flávia Ribeiro, Rodrigo Fonseca, Wagner Meira Jr.,
IEEE Internet Computing submitted February 2001
Conference paper:
Analyzing Robot Behavior and their Impact on Caching Virgílio Almeida, Daniel Menascé, Rudolf Riedi, Flávia Ribeiro, Rodrigo Fonseca, Wagner Meira Jr.,
Workshop on Web Caching and Content Delivery June 2001
Analyzing Robot Behavior in E-Business Sites
Daniel Menascé, Virgílio Almeida, Rudolf Riedi, Flávia Ribeiro, Rodrigo Fonseca, Wagner Meira Jr.,
Proc. ACM SigMetrics'01 (June 2001)

A Hierarchical and Multiscale Analysis of E-Business Workloads
Daniel Menascé, Virgílio Almeida, Rudolf Riedi, Flávia Ribeiro, Rodrigo Fonseca, Wagner Meira Jr.,
Performance Evaluation 54(1), Sept 2003, pp 33--57.

On the multiplicative structure of network traffic
Rudolf H. Riedi
Proceedings IMA Conference on Mathematics in Signal Processing, Warwick, (December 2000)

Multifractal Cross-Traffic Estimation
V. Ribeiro, M. Coates, R. Riedi, S. Sarvotham, B. Hendricks and R. Baraniuk,
Proceedings ITC Specialist Seminar on IP Traffic Measurement, Modeling and Management, September 2000, Monterey, CA

In Search of Invariants for E-Business Workloads
Daniel Menascé, Flávia Ribeiro, Virgílio Almeida, Rodrigo Fonseca, Rudolf Riedi, Wagner Meira Jr.,
Proceedings EC'00, Inst. Math. Appl., October 2000, Minneapolis, MN.

Multiplicative Multiscale Image Decompositions: Analysis and Modeling
Justin K. Romberg, Rolf H. Riedi, Hyeokho Choi, and Richard G. Baraniuk
Proceedings of the SPIE's 45th Annual Meeting, Internat. Symp. on Optical Science and Technology, August 2000, San Diego, CA.

Multiscale Image Segmentation using Joint Texture and Shape analysis
Ramesh Neelamani, Justin Romberg, Hyeokho Choi, Rudolf Riedi, and Richard Baraniuk
Proceedings of the SPIE's 45th Annual Meeting, Internat. Symp. on Optical Science and Technology, August 2000, San Diego, CA.

Multifractal Processes
R. H. Riedi,
in Long range dependence : theory and applications,
eds. Doukhan, Oppenheim and Taqqu, (Birkh\"auser 2002) ISBN: 0817641688, pp 625-715.
12 page summary


Long-Range Dependence and Data Network Traffic
W. Willinger, V. Paxson, R. H. Riedi and M. S. Taqqu,
in Long range dependence : theory and applications,
eds. Doukhan, Oppenheim and Taqqu (Birkh\"auser 2002) ISBN: 0817641688.
 

This is an overview of a relatively recent application of long-range dependence (LRD) to the area of communication networks, in particular to problems concerned with the dynamic nature of packet flows in high-speed data networks such as the Internet. We demonstrate that this new application area offers unique opportunities for significantly advancing our understanding of LRD and related phenomena. These advances are made possible by moving beyond the conventional approaches associated with the wide-spread ``black-box'' perspective of traditional time series analysis and exploiting instead the physical mechanisms that exist in the networking context and that are intimately tied to the observed characteristics of measured network traffic. In order to describe this complexity we provide a basic understanding of the design, architecture and operations of data networks, including a description of the TCP/IP protocols used in today's Internet. LRD is observed in the large scale behavior of the data traffic and we provide a physical explanation for its presence. LRD tends to be caused by user and application characteristics and has little to do with the network itself. The network affects mostly small time scales, and this is why a rudimentary understanding of the main protocols is important. We illustrate why multifractals may be relevant for describing some aspects of the highly irregular traffic behavior over small time scales. We distinguish between a time-domain and wavelet-domain approach to analyzing the small time scale dynamics and discuss why the time-domain appears to be better suited for studying the performance (e.g., a queueing analysis) while the wavelet-domain approach appears to be better suited for identifying particular features in measured traffic with a dominant influence on particular time scales (e.g., relatively regular traffic patterns over certain time scales which have a direct networking interpretation in terms of ``round trip'' time behavior).
Keywords: Long-range dependence, network traffic, self-similar processes, fractional Brownian motion, multifractal analysis, cascades.

Network Traffic Modeling Using a Multifractal Wavelet Model
R. H. Riedi, V. J. Ribeiro, M. S. Crouse and R. G. Baraniuk
Proceedings European Congress of Mathematics, Barcelona 2000.


Multiscale Queuing Analysis of Long-Range-Dependent Network Traffic
V. J. Ribeiro, R. H. Riedi, M. S. Crouse and R. G. Baraniuk
IEEE Trans. on Networking, submitted
see also: Technical Report 99-08, ECE Dept., Rice University;
as well as: Proceedings of IEEE INFOCOM 2000, Tel Aviv, Israel, March 2000.
 

This paper develops a novel approach to queuing analysis tailor-made for multiscale long-range-dependent (LRD) traffic models. We review two such traffic models, the wavelet-domain independent Gaussian model (WIG) and the multifractal wavelet model (MWM). The WIG model is a recent generalization of the ubiquitous fractional Brownian motion process. Both models are based on a multiscale binary tree structure that captures the correlation structure of traffic and hence its LRD. Due to its additive nature, the WIG is inherently Gaussian, while the multiplicative MWM is non-Gaussian. The MWM is set within the framework of multifractals, which provide natural tools to measure the multiscale statistical properties of traffic loads, in particular their burstiness.
Our queuing analysis leverages the tree structure of the models and provides a simple closed-form approximation to the tail queue probability for any given queue size. This makes the WIG and MWM suitable for numerous practical applications, including congestion control, admission control, and cross-traffic estimation. The queuing analysis reveals that the marginal distribution and, in particular, the large values of traffic at different time scales strongly affect queuing. This implies that merely modeling the traffic variance at multiple time scales, or equivalently, the second-order correlation structure, can be insufficient for capturing the queuing behavior of real traffic. We confirm these analytical findings by comparing the queuing behavior of WIG and MWM traffic through simulations.

Toward an Improved Understanding of Network Traffic Dynamics [PDF]
R. H. Riedi and W. Willinger
in: Self-similar Network Traffic and Performance Evaluation
eds. Park and Willinger, (Wiley 2000), chapter 20 , pp 507-530.

Attracteurs, orbites et ergodicité
C. Tricot and R. Riedi Ann. Math. Blaise Pascal 6 (1999), 55-72.

Wavelet Analysis of Fractional Brownian Motion in Multifractal Time
P. Gonçalvès and R. H. Riedi
Proceedings of the 17th Colloquium GRETSI, Vannes, France, Sept 1999.

Simulation of Non-Gaussian Long-Range-Dependent Traffic using Wavelets
V. J. Ribeiro, R. H. Riedi, M. S. Crouse and R. G. Baraniuk
Proc. ACM SigMetrics'99 (May 1999), 1-12

A Multifractal Wavelet Model with Application to Network Traffic
R. H. Riedi, M. S. Crouse, V. J. Ribeiro, and R. G. Baraniuk
IEEE Special Issue on Information Theory, 45. (April 1999), 992-1018. Simple Statistical Analysis of Wavelet-based Multifractal Spectrum Estimation,
P. Gonçalvès, R. H. Riedi and R. G. Baraniuk
Proceedings of the 32nd Conference on `Signals, Systems and Computers', Asilomar, Nov 1998 Multifractal Properties of TCP Traffic: a Numerical Study,
R. H. Riedi and J. Lévy Véhel.
INRIA research report 3129, March 1997. Fractional Brownian motion and data traffic modeling: The other end of the spectrum,
J. Lévy Véhel and R. H. Riedi
in: Fractals in Engineering 97 , Springer 1997. Exceptions to the Multifractal Formalism for Discontinuous Measures,
R. H. Riedi and B. B Mandelbrot,
Math. Proc. Cambr. Phil. Soc.123 (1998), 133--157. Inversion formula for Continuous Multifractals,
R. H. Riedi and B. B Mandelbrot,
Adv. Appl. Math.19 (1997), 332--354. Inverse Measures, the Inversion formula and Discontinuous Multifractals,
B. B. Mandelbrot and R. H. Riedi,
Adv. Appl. Math. 18 (1997), 50--58. Multifractals and Wavelets: A potential tool in Geophysics
R. H. Riedi,
SEG, New Orleans 1998 Conditional and Relative Multifractal Spectra.
R. H. Riedi and I. Scheuring,
Fractals. An Interdisciplinary Journal.5 (1997), 153--168. Numerical Estimates of Generalized Dimensions D_q for Negative q
R. Pastor-Satorras and R. H. Riedi,
J. Phys. A29 (1996) L391-L398. Multifractal Formalism for Infinite Multinomial Measures
R. H. Riedi and B. B Mandelbrot, Adv. Appl. Math. 16 (1995) 132--150. An Improved Multifractal Formalism and Self-Similar Measures
R. H. Riedi,
J. Math. Anal. Appl. 189 (1995) 462-490. Explicit Lower Bounds of the Hausdorff Dimension of Certain Self-Affine Sets [pdf]
R. H. Riedi,
Fractals in the Natural and Applied Sciences pp 313--324,
IFIP Transactions, M. Novak ed., North-Holland, Amsterdam 1994. An Improved Multifractal Formalism and Self-affine Measures
R. H. Riedi,
Summary of Ph.D. thesis ETH Zurich, Switzerland, 1993 An introduction to multifractals
R. H. Riedi,
Rice University, (Version Oct 26, 1999)