End-to-end routing behavior in the Internet
Conference proceedings on Applications, technologies, architectures, and protocols for computer communications
End-to-end internet packet dynamics
IEEE/ACM Transactions on Networking (TON)
On the constancy of internet path properties
IMW '01 Proceedings of the 1st ACM SIGCOMM Workshop on Internet Measurement
Bridging router performance and queuing theory
Proceedings of the joint international conference on Measurement and modeling of computer systems
Improving accuracy in end-to-end packet loss measurement
Proceedings of the 2005 conference on Applications, technologies, architectures, and protocols for computer communications
The role of PASTA in network measurement
Proceedings of the 2006 conference on Applications, technologies, architectures, and protocols for computer communications
Adding definition to active probing
ACM SIGCOMM Computer Communication Review
Poisson versus periodic path probing (or, does PASTA matter?)
IMC '05 Proceedings of the 5th ACM SIGCOMM conference on Internet Measurement
A Comparison of Poisson and Uniform Sampling for Active Measurements
IEEE Journal on Selected Areas in Communications
Packet doppler: network monitoring using packet shift detection
CoNEXT '08 Proceedings of the 2008 ACM CoNEXT Conference
The role of PASTA in network measurement
IEEE/ACM Transactions on Networking (TON)
Towards multihop available bandwidth estimation
ACM SIGMETRICS Performance Evaluation Review
Inverse problems in queueing theory and Internet probing
Queueing Systems: Theory and Applications
Accuracy improvement of CoMPACT monitor by using new probing method
APNOMS'09 Proceedings of the 12th Asia-Pacific network operations and management conference on Management enabling the future internet for changing business and new computing services
Measurement of loss pairs in network paths
IMC '10 Proceedings of the 10th ACM SIGCOMM conference on Internet measurement
Exact temporal characterization of 10 Gbps optical wide-area network
IMC '10 Proceedings of the 10th ACM SIGCOMM conference on Internet measurement
Predicting and tracking internet path changes
Proceedings of the ACM SIGCOMM 2011 conference
Rigorous statistical analysis of internet loss measurements
IEEE/ACM Transactions on Networking (TON)
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Packet delay and loss are two fundamental measures of performance. Using active probing to measure delay and loss typically involves sending Poisson probes, on the basis of the PASTA property (Poisson Arrivals See Time Averages), which ensures that Poisson probing yields unbiased estimates. Recent work, however, has questioned the utility of PASTA for probing and shown that, for delay measurements, i) a wide variety of processes other than Poisson can be used to probe with zero bias and ii) Poisson probing does not necessarily minimize the variance of delay estimates. In this paper, we determine optimal probing processes that minimize the mean-square error of measurement estimates for both delay and loss. Our contributions are twofold. First, we show that a family of probing processes, specifically Gamma renewal probing processes, has optimal properties in terms of bias and variance. The optimality result is general, and only assumes that the target process we seek to optimally measure via probing, such as a loss or delay process, has a convex auto-covariance function. Second, we use empirical datasets to demonstrate the applicability of our results in practice, specifically to show that the convexity condition holds true and that Gamma probing is indeed superior to Poisson probing. Together, these results lead to explicit guidelines on designing the best probe streams for both delay and loss estimation.