Stochastic analysis of algorithms for collecting longitudinal data
Résumé
This paper proposes and analyses the performance and the vulnerability to attacks of three algorithms for collecting longitudinal data in a large scale system. A monitoring device is in charge of continuously collecting measurements from end-devices. The communication graph is connected but not necessarily complete. For scalability reasons, at each collect, a single end-device is randomly selected among all the end-devices to send the content of its local buffer of data to the monitoring device. Once sent, the enddevice resets its buffer, and resumes its measurement process. Two of the three algorithms are randomized algorithms while the third one is deterministic. The difference between the randomized algorithms stems from the random choice policy: in the first algorithm, choice is uniform while in the second one the random choice is weighted by the current amount of measurements at end-devices. The third algorithm is deterministic. End-devices are successively chosen in a round robin way. We study the transient and stationary maximum load distribution at end-devices when collects are made using the first and third algorithm, and by providing bounds via a coupling argument when the second algorithm is used. While the third algorithm provides the best performance, it is highly vulnerable to attacks. keywords Collecting longitudinal data, coupling technique, balls and urn models.
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