Estimating Logarithmic and Exponential Functions to Track Network Traffic Entropy in P4

The evaluation of network traffic entropy is very useful for management purposes, since it helps to keep track of changes in network flow distribution. Nowadays, network traffic entropy is usually estimated in centralized monitoring collectors, which require a significant amount of information to be retrieved from switches. The advent of programmable data planes in Software-Defined Networks helps mitigate this issue, opening the door to the possibility of estimating entropy directly in the switches' data plane. Unfortunately, the most widely-adopted programming language used to program the data plane, called P4, lacks supporting many arithmetic operations such as logarithm and exponential function computation, which are necessary for entropy estimation. In this paper we propose two new algorithms, called P4Log and P4Exp, to fill this gap: these algorithms can estimate logarithms and exponential functions with a given precision by only using P4-supported arithmetic operations. Additionally, we leverage them to propose a novel strategy, called P4Entropy, to estimate traffic entropy entirely in the switch data plane. Results show that P4Entropy has comparable accuracy as an existing solution but without (i) constraining the number of packets in an observation interval and (ii) requiring the usage of TCAM, which is a scarce resource.