- From: Tom Bergan <tombergan@chromium.org>
- Date: Tue, 24 Jan 2017 14:22:51 -0800
- To: Stefan Eissing <stefan.eissing@greenbytes.de>
- Cc: Kazu Yamamoto (山本和彦) <kazu@iij.ad.jp>, HTTP Working Group <ietf-http-wg@w3.org>
- Message-ID: <CA+3+x5EdkLSAR2gWR9TT72o2Tg4Z_xKXMh8yVREYD7mvNuLB8w@mail.gmail.com>

Thanks for the feedback. Sounds like the worst-case time really is O(n). > kazuhooku@ > the constant for O(n) would be small enough so that it cannot be used an attack vector Don't you need to ensure that n is small, otherwise even O(n) with a small constant factor can lead to degraded performance? e.g., if SETTINGS_MAX_CONCURRENT_STREAMS = 20,000, I may end up computing a sum of 20,000 numbers every few frames, which is not terribly slow, but not terribly fast either. > kazu@ > http://www.mew.org/~kazu/material/2015-http2-priority2.pdf > http://www.mew.org/~kazu/doc/paper/http2-haskell-2016.pdf Thanks. IIUC, the algorithms described in both links are still at least O(depth), which can be O(n) for dependency trees generated by certain clients such as Chrome. > stefan.eissing@ > The very same problem exists for stream processing in order to generate response data. What did you mean by "stream processing"? On Tue, Jan 24, 2017 at 12:26 AM, Stefan Eissing < stefan.eissing@greenbytes.de> wrote: > The very same problem exists for stream processing in order to generate > response data. > > > Am 24.01.2017 um 08:53 schrieb Kazu Yamamoto (山本和彦) <kazu@iij.ad.jp>: > > > > Hi Tom, > > > > Probably, this material would help you: > > > > http://www.mew.org/~kazu/material/2015-http2-priority2.pdf > > http://www.mew.org/~kazu/doc/paper/http2-haskell-2016.pdf > > > > --Kazu > > > >> Regarding your question, I am unaware of a scheduler design that is > >> better than O(n) for both dequeuing (i.e. selecting the stream to > >> send) and for rescheduling a stream (especially a stream with many > >> decendants). > >> > >> While designing the scheduler of H2O (you are right in pointing out > >> the fact that it is O(depth)), I came up with two options. One was to > >> retain the vertical (i.e. parent-children) relationship between the > >> streams. The other was to squash the vertical relationships to > >> generate a one-dimensional list of streams ordered by priority. > >> > >> By taking the latter approach, you could create a scheduler that > >> dequeues at O(1). But such scheduler would need to perform O(N) > >> operation when receiving a priority frame or a stream-level window > >> update (in this case N is number of direct and indirect decendants of > >> the reprioritized stream). > >> > >> Considering this, we chose to implement the scheduler of H2O as O(1) > >> weight-wise, and O(n) depth-wise, but that the constant for O(n) would > >> be small enough so that it cannot be used an attack vector. > >> > >> 2017-01-24 9:39 GMT+09:00 Tom Bergan <tombergan@chromium.org>: > >>> I implemented the HTTP/2 response scheduler in Go's HTTP/2 server > library. > >>> I'm trying to understand the worst-case behavior of that scheduler. I > >>> believe the worst-case behavior is necessarily O(n) operations per > frame > >>> sent on the wire, where n is the number of streams in the dependency > tree. > >>> Here is my rationale. > >>> > >>> The key operation is finding the highest-priority stream that is ready > to > >>> send data. > >>> > >>> If we don't care about weights, and we don't care about balancing > bandwidth > >>> usage across sibling nodes in a tree, then we can label each node with > two > >>> fields: "ready" (true if the stream is ready to send data) and "depth" > (the > >>> node's distance from the root of the tree). The scheduler must find a > node > >>> with the smallest depth over all nodes with ready = true. It is fairly > >>> trivial to implement this in O(log n). > >>> > >>> Now, let's introduce weights. The scheduler must allocate bandwidth to > all > >>> ready nodes, which happens recursively as follows: > >>> > >>> func allocateBandwidth(node, bw) { > >>> if (node.ready) { > >>> node.bandwidthShare = bw > >>> return > >>> } > >>> totalWeight = 0 > >>> for (n in node.children) { > >>> if (n.ready || descendantIsReady(n)) { > >>> totalWeight += n.weight > >>> } > >>> } > >>> for (n in node.children) { > >>> if (n.ready || descendantIsReady(n)) { > >>> allocateBandwidth(n, bw * n.weight / totalWeight) > >>> } > >>> } > >>> } > >>> allocateBandwidth(root, 1.0) > >>> > >>> I believe the above definition is a direct translation of RFC 7540 > Section > >>> 5.3.2 (also see this thread, which discussed bandwidth allocation). > Given a > >>> complete bandwidth allocation, the server can translate each node's > >>> bandwidthShare to a number of tokens that are updated using a token > bucket > >>> algorithm (or similar). The scheduler would then pick the node with > the most > >>> available tokens. The scheduler looks something like: > >>> > >>> func scheduleNextFrame() { > >>> if (tree changed since last frame written) { > >>> allocateBandwidth(root, 1.0) > >>> assign tokens and build a priority queue containing all nodes with > >>> allocated bandwidth > >>> } > >>> node = priorityQueue.head() > >>> node.consumeTokens() // consume up to frame size or flow-control > limit > >>> priorityQueue.update(node) > >>> return node > >>> } > >>> > >>> There are two steps in scheduleNextFrame. The first step updates the > >>> bandwidth allocation if the tree changed since the last frame was > written. > >>> This is the most expensive step. I don't believe it's possible to > implement > >>> allocateBandwidth using fewer than O(n) worst-case steps. For example, > if > >>> the tree is mostly flat, meaning that most nodes are children of the > same > >>> node, then the loop to compute totalWeight is O(n). I believe Firefox > >>> creates mostly-flat trees. Further, allocateBandwidth makes O(depth) > >>> recursive steps, where "depth" is the maximum depth of the dependency > tree. > >>> If the tree is mostly-linear, then O(depth) becomes O(n). Chrome > creates > >>> mostly-linear trees. > >>> > >>> The overall runtime depends on how often the tree changes. If the tree > >>> changes rarely, the scheduler is cheap. If the tree changes > frequently, the > >>> scheduler is worst-case O(n). A tree has "changed" if it changed shape > >>> (nodes are added/moved/removed) or if any node's ready state has > changed. > >>> Both kinds of changes can happen often in practice, suggesting that the > >>> overall scheduler is worst-case O(n). For example, consider a server > that > >>> sends small responses (one or two DATA frames per response) -- each > stream > >>> will be closed after one or two DATA frames, so on average, the tree > will > >>> change shape every few frames. Further, it's possible for ready states > to > >>> change more frequently than you might think. In Go's HTTP/2 > implementation, > >>> a stream does not become ready until the application handler calls > Write to > >>> buffer response data. After that buffered data is serialized on the > wire, > >>> the stream transitions to "not ready" because the scheduler cannot > know when > >>> the next Write call will happen. The stream will transition back to > "ready" > >>> during the next Write call. Each Write call typically buffers about > 32KB of > >>> data. This is a "push" model, where the application handler "pushes" > data > >>> into the scheduler. I'm aware of one other HTTP/2 server that works > >>> similarly. I suspect that frequent ready/not-ready transitions are > common to > >>> most HTTP/2 servers that use a "push" model. These servers will be more > >>> susceptible to the O(n) worst case. > >>> > >>> Questions: > >>> > >>> 1. Am I missing a clever implementation, or is it true that a faithful > >>> HTTP/2 scheduler necessarily requires O(n) operations per frame sent > on the > >>> wire, in the worst case? I could not find much discussion of this > question > >>> after a quick search. H2O claims to implement an O(1) scheduler, > however, > >>> the code seems to be worst-case O(depth) or O(n) -- see here, here, and > >>> here. > >>> > >>> 2. If the above is correct, should I be concerned about the O(n) worst > case? > >>> I doubt that a typical web browsing session will trigger O(n) behavior > >>> frequently, so I'm less concerned about the average case; I'm more > concerned > >>> about pathological cases or possible DoS vectors. Also, think about > cases > >>> where the "client" is actually a proxy server, meaning the HTTP/2 > connection > >>> may have many more concurrent streams than a typical browsing session. > For > >>> comparison, if you recall the predecessor to HTTP/2 (SPDY), a SPDY > scheduler > >>> could be trivially implemented in O(1), since SPDY used just eight > priority > >>> buckets. > >>> > >>> 3. If I should be concerned about an O(n) worst case, are there any > >>> suggested mitigations beyond setting SETTINGS_MAX_CONCURRENT_STREAMS > to a > >>> smallish constant? > >> > >> > >> > >> -- > >> Kazuho Oku > >> > > > > >

Received on Tuesday, 24 January 2017 22:23:27 UTC