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+.. This work is licensed under a Creative Commons Attribution 4.0 International
+.. License.
+.. http://creativecommons.org/licenses/by/4.0
+.. (c) Cisco Systems, Inc
+
+NDR/PDR Binary Search
+=====================
+
+The NDR/PDR binary search algorithm used by NFVbench is based on the algorithm used by the
+FD.io CSIT project, with some additional optimizations.
+
+Algorithm Outline
+-----------------
+
+The ServiceChain class (nfvbench/service_chain.py) is responsible for calculating the NDR/PDR
+or all frame sizes requested in the configuration.
+Calculation for 1 frame size is delegated to the TrafficClient class (nfvbench/traffic_client.py)
+
+Call chain for calculating the NDR-PDR for a list of frame sizes:
+
+- ServiceChain.run()
+ - ServiceChain._get_chain_results()
+ - for every frame size:
+ - ServiceChain.__get_result_per_frame_size()
+ - TrafficClient.get_ndr_pdr()
+ - TrafficClient.__range_search() recursive binary search
+
+The search range is delimited by a left and right rate (expressed as a % of line rate per direction).
+The search always start at line rate per port, e.g. in the case of 2x10Gbps, the first iteration
+will send 10Gbps of traffic on each port.
+
+The load_epsilon configuration parameter defines the accuracy of the result as a % of line rate.
+The default value of 0.1 indicates for example that the measured NDR and PDR are within 0.1% of line rate of the
+actual NDR/PDR (e.g. 0.1% of 10Gbps is 10Mbps). It also determines how small the search range must be in the binary search.
+Smaller values of load_epsilon will result in more iterations and will take more time but may not
+always be beneficial if the absolute value falls below the precision level of the measurement.
+For example a value of 0.01% would translate to an absolute value of 1Mbps (for a 10Gbps port) or
+around 10kpps (at 64 byte size) which might be too fine grain.
+
+The recursion narrows down the range by half and stops when:
+
+- the range is smaller than the configured load_epsilon value
+- or when the search hits 100% or 0% of line rate
+
+Optimization
+------------
+
+Binary search algorithms assume that the drop rate curve is monotonically increasing with the Tx rate.
+To save time, the algorithm used by NFVbench is capable of calculating the optimal Tx rate for an
+arbitrary list of target maximum drop rates in one pass instead of the usual 1 pass per target maximum drop rate.
+This saves time linearly to the number target drop rates.
+For example, a typical NDR/PDR search will have 2 target maximum drop rates:
+
+- NDR = 0.001%
+- PDR = 0.1%
+
+The binary search will then start with a sorted list of 2 target drop rates: [0.1, 0.001].
+The first part of the binary search will then focus on finding the optimal rate for the first target
+drop rate (0.1%). When found, the current target drop rate is removed from the list and
+iteration continues with the next target drop rate in the list but this time
+starting from the upper/lower range of the previous target drop rate, which saves significant time.
+The binary search continues until the target maximum drop rate list is empty.
+
+Results Granularity
+-------------------
+The binary search results contain per direction stats (forward and reverse).
+In the case of multi-chaining, results contain per chain stats.
+The current code only reports aggregated stats (forward + reverse for all chains) but could be enhanced
+to report per chain stats.
+
+
+CPU Limitations
+---------------
+One particularity of using a software traffic generator is that the requested Tx rate may not always be met due to
+resource limitations (e.g. CPU is not fast enough to generate a very high load). The algorithm should take this into
+consideration:
+
+- always monitor the actual Tx rate achieved as reported back by the traffic generator
+- actual Tx rate is always <= requested Tx rate
+- the measured drop rate should always be relative to the actual Tx rate
+- if the actual Tx rate is < requested Tx rate and the measured drop rate is already within threshold
+ (<NDR/PDR threshold) then the binary search must stop with proper warning because the actual NDR/PDR
+ might probably be higher than the reported values