/*
* Copyright (C) 2012 The Guava Authors
*
* Licensed under the Apache License, Version 2.0 (the "License");
* you may not use this file except in compliance with the License.
* You may obtain a copy of the License at
*
* http://www.apache.org/licenses/LICENSE-2.0
*
* Unless required by applicable law or agreed to in writing, software
* distributed under the License is distributed on an "AS IS" BASIS,
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
* See the License for the specific language governing permissions and
* limitations under the License.
*/
package com.google.common.util.concurrent;
import static java.lang.Math.min;
import static java.util.concurrent.TimeUnit.SECONDS;
import java.util.concurrent.TimeUnit;
abstract class SmoothRateLimiter extends RateLimiter {
/*
* How is the RateLimiter designed, and why?
*
* The primary feature of a RateLimiter is its "stable rate", the maximum rate that
* is should allow at normal conditions. This is enforced by "throttling" incoming
* requests as needed, i.e. compute, for an incoming request, the appropriate throttle time,
* and make the calling thread wait as much.
*
* The simplest way to maintain a rate of QPS is to keep the timestamp of the last
* granted request, and ensure that (1/QPS) seconds have elapsed since then. For example,
* for a rate of QPS=5 (5 tokens per second), if we ensure that a request isn't granted
* earlier than 200ms after the last one, then we achieve the intended rate.
* If a request comes and the last request was granted only 100ms ago, then we wait for
* another 100ms. At this rate, serving 15 fresh permits (i.e. for an acquire(15) request)
* naturally takes 3 seconds.
*
* It is important to realize that such a RateLimiter has a very superficial memory
* of the past: it only remembers the last request. What if the RateLimiter was unused for
* a long period of time, then a request arrived and was immediately granted?
* This RateLimiter would immediately forget about that past underutilization. This may
* result in either underutilization or overflow, depending on the real world consequences
* of not using the expected rate.
*
* Past underutilization could mean that excess resources are available. Then, the RateLimiter
* should speed up for a while, to take advantage of these resources. This is important
* when the rate is applied to networking (limiting bandwidth), where past underutilization
* typically translates to "almost empty buffers", which can be filled immediately.
*
* On the other hand, past underutilization could mean that "the server responsible for
* handling the request has become less ready for future requests", i.e. its caches become
* stale, and requests become more likely to trigger expensive operations (a more extreme
* case of this example is when a server has just booted, and it is mostly busy with getting
* itself up to speed).
*
* To deal with such scenarios, we add an extra dimension, that of "past underutilization",
* modeled by "storedPermits" variable. This variable is zero when there is no
* underutilization, and it can grow up to maxStoredPermits, for sufficiently large
* underutilization. So, the requested permits, by an invocation acquire(permits),
* are served from:
* - stored permits (if available)
* - fresh permits (for any remaining permits)
*
* How this works is best explained with an example:
*
* For a RateLimiter that produces 1 token per second, every second
* that goes by with the RateLimiter being unused, we increase storedPermits by 1.
* Say we leave the RateLimiter unused for 10 seconds (i.e., we expected a request at time
* X, but we are at time X + 10 seconds before a request actually arrives; this is
* also related to the point made in the last paragraph), thus storedPermits
* becomes 10.0 (assuming maxStoredPermits >= 10.0). At that point, a request of acquire(3)
* arrives. We serve this request out of storedPermits, and reduce that to 7.0 (how this is
* translated to throttling time is discussed later). Immediately after, assume that an
* acquire(10) request arriving. We serve the request partly from storedPermits,
* using all the remaining 7.0 permits, and the remaining 3.0, we serve them by fresh permits
* produced by the rate limiter.
*
* We already know how much time it takes to serve 3 fresh permits: if the rate is
* "1 token per second", then this will take 3 seconds. But what does it mean to serve 7
* stored permits? As explained above, there is no unique answer. If we are primarily
* interested to deal with underutilization, then we want stored permits to be given out
* /faster/ than fresh ones, because underutilization = free resources for the taking.
* If we are primarily interested to deal with overflow, then stored permits could
* be given out /slower/ than fresh ones. Thus, we require a (different in each case)
* function that translates storedPermits to throtting time.
*
* This role is played by storedPermitsToWaitTime(double storedPermits, double permitsToTake).
* The underlying model is a continuous function mapping storedPermits
* (from 0.0 to maxStoredPermits) onto the 1/rate (i.e. intervals) that is effective at the given
* storedPermits. "storedPermits" essentially measure unused time; we spend unused time
* buying/storing permits. Rate is "permits / time", thus "1 / rate = time / permits".
* Thus, "1/rate" (time / permits) times "permits" gives time, i.e., integrals on this
* function (which is what storedPermitsToWaitTime() computes) correspond to minimum intervals
* between subsequent requests, for the specified number of requested permits.
*
* Here is an example of storedPermitsToWaitTime:
* If storedPermits == 10.0, and we want 3 permits, we take them from storedPermits,
* reducing them to 7.0, and compute the throttling for these as a call to
* storedPermitsToWaitTime(storedPermits = 10.0, permitsToTake = 3.0), which will
* evaluate the integral of the function from 7.0 to 10.0.
*
* Using integrals guarantees that the effect of a single acquire(3) is equivalent
* to { acquire(1); acquire(1); acquire(1); }, or { acquire(2); acquire(1); }, etc,
* since the integral of the function in [7.0, 10.0] is equivalent to the sum of the
* integrals of [7.0, 8.0], [8.0, 9.0], [9.0, 10.0] (and so on), no matter
* what the function is. This guarantees that we handle correctly requests of varying weight
* (permits), /no matter/ what the actual function is - so we can tweak the latter freely.
* (The only requirement, obviously, is that we can compute its integrals).
*
* Note well that if, for this function, we chose a horizontal line, at height of exactly
* (1/QPS), then the effect of the function is non-existent: we serve storedPermits at
* exactly the same cost as fresh ones (1/QPS is the cost for each). We use this trick later.
*
* If we pick a function that goes /below/ that horizontal line, it means that we reduce
* the area of the function, thus time. Thus, the RateLimiter becomes /faster/ after a
* period of underutilization. If, on the other hand, we pick a function that
* goes /above/ that horizontal line, then it means that the area (time) is increased,
* thus storedPermits are more costly than fresh permits, thus the RateLimiter becomes
* /slower/ after a period of underutilization.
*
* Last, but not least: consider a RateLimiter with rate of 1 permit per second, currently
* completely unused, and an expensive acquire(100) request comes. It would be nonsensical
* to just wait for 100 seconds, and /then/ start the actual task. Why wait without doing
* anything? A much better approach is to /allow/ the request right away (as if it was an
* acquire(1) request instead), and postpone /subsequent/ requests as needed. In this version,
* we allow starting the task immediately, and postpone by 100 seconds future requests,
* thus we allow for work to get done in the meantime instead of waiting idly.
*
* This has important consequences: it means that the RateLimiter doesn't remember the time
* of the _last_ request, but it remembers the (expected) time of the _next_ request. This
* also enables us to tell immediately (see tryAcquire(timeout)) whether a particular
* timeout is enough to get us to the point of the next scheduling time, since we always
* maintain that. And what we mean by "an unused RateLimiter" is also defined by that
* notion: when we observe that the "expected arrival time of the next request" is actually
* in the past, then the difference (now - past) is the amount of time that the RateLimiter
* was formally unused, and it is that amount of time which we translate to storedPermits.
* (We increase storedPermits with the amount of permits that would have been produced
* in that idle time). So, if rate == 1 permit per second, and arrivals come exactly
* one second after the previous, then storedPermits is _never_ increased -- we would only
* increase it for arrivals _later_ than the expected one second.
*/
/**
* This implements the following function:
*
* ^ throttling
* |
* 3*stable + /
* interval | /.
* (cold) | / .
* | / . <-- "warmup period" is the area of the trapezoid between
* 2*stable + / . halfPermits and maxPermits
* interval | / .
* | / .
* | / .
* stable +----------/ WARM . }
* interval | . UP . } <-- this rectangle (from 0 to maxPermits, and
* | . PERIOD. } height == stableInterval) defines the cooldown period,
* | . . } and we want cooldownPeriod == warmupPeriod
* |---------------------------------> storedPermits
* (halfPermits) (maxPermits)
*
* Before going into the details of this particular function, let's keep in mind the basics:
* 1) The state of the RateLimiter (storedPermits) is a vertical line in this figure.
* 2) When the RateLimiter is not used, this goes right (up to maxPermits)
* 3) When the RateLimiter is used, this goes left (down to zero), since if we have storedPermits,
* we serve from those first
* 4) When _unused_, we go right at the same speed (rate)! I.e., if our rate is
* 2 permits per second, and 3 unused seconds pass, we will always save 6 permits
* (no matter what our initial position was), up to maxPermits.
* If we invert the rate, we get the "stableInterval" (interval between two requests
* in a perfectly spaced out sequence of requests of the given rate). Thus, if you
* want to see "how much time it will take to go from X storedPermits to X+K storedPermits?",
* the answer is always stableInterval * K. In the same example, for 2 permits per second,
* stableInterval is 500ms. Thus to go from X storedPermits to X+6 storedPermits, we
* require 6 * 500ms = 3 seconds.
*
* In short, the time it takes to move to the right (save K permits) is equal to the
* rectangle of width == K and height == stableInterval.
* 4) When _used_, the time it takes, as explained in the introductory class note, is
* equal to the integral of our function, between X permits and X-K permits, assuming
* we want to spend K saved permits.
*
* In summary, the time it takes to move to the left (spend K permits), is equal to the
* area of the function of width == K.
*
* Let's dive into this function now:
*
* When we have storedPermits <= halfPermits (the left portion of the function), then
* we spend them at the exact same rate that
* fresh permits would be generated anyway (that rate is 1/stableInterval). We size
* this area to be equal to _half_ the specified warmup period. Why we need this?
* And why half? We'll explain shortly below (after explaining the second part).
*
* Stored permits that are beyond halfPermits, are mapped to an ascending line, that goes
* from stableInterval to 3 * stableInterval. The average height for that part is
* 2 * stableInterval, and is sized appropriately to have an area _equal_ to the
* specified warmup period. Thus, by point (4) above, it takes "warmupPeriod" amount of time
* to go from maxPermits to halfPermits.
*
* BUT, by point (3) above, it only takes "warmupPeriod / 2" amount of time to return back
* to maxPermits, from halfPermits! (Because the trapezoid has double the area of the rectangle
* of height stableInterval and equivalent width). We decided that the "cooldown period"
* time should be equivalent to "warmup period", thus a fully saturated RateLimiter
* (with zero stored permits, serving only fresh ones) can go to a fully unsaturated
* (with storedPermits == maxPermits) in the same amount of time it takes for a fully
* unsaturated RateLimiter to return to the stableInterval -- which happens in halfPermits,
* since beyond that point, we use a horizontal line of "stableInterval" height, simulating
* the regular rate.
*
* Thus, we have figured all dimensions of this shape, to give all the desired
* properties:
* - the width is warmupPeriod / stableInterval, to make cooldownPeriod == warmupPeriod
* - the slope starts at the middle, and goes from stableInterval to 3*stableInterval so
* to have halfPermits being spend in double the usual time (half the rate), while their
* respective rate is steadily ramping up
*/
static final class SmoothWarmingUp extends SmoothRateLimiter {
private final long warmupPeriodMicros;
/**
* The slope of the line from the stable interval (when permits == 0), to the cold interval
* (when permits == maxPermits)
*/
private double slope;
private double halfPermits;
SmoothWarmingUp(SleepingStopwatch stopwatch, long warmupPeriod, TimeUnit timeUnit) {
super(stopwatch);
this.warmupPeriodMicros = timeUnit.toMicros(warmupPeriod);
}
@Override
void doSetRate(double permitsPerSecond, double stableIntervalMicros) {
double oldMaxPermits = maxPermits;
maxPermits = warmupPeriodMicros / stableIntervalMicros;
halfPermits = maxPermits / 2.0;
// Stable interval is x, cold is 3x, so on average it's 2x. Double the time -> halve the rate
double coldIntervalMicros = stableIntervalMicros * 3.0;
slope = (coldIntervalMicros - stableIntervalMicros) / halfPermits;
if (oldMaxPermits == Double.POSITIVE_INFINITY) {
// if we don't special-case this, we would get storedPermits == NaN, below
storedPermits = 0.0;
} else {
storedPermits = (oldMaxPermits == 0.0)
? maxPermits // initial state is cold
: storedPermits * maxPermits / oldMaxPermits;
}
}
@Override
long storedPermitsToWaitTime(double storedPermits, double permitsToTake) {
double availablePermitsAboveHalf = storedPermits - halfPermits;
long micros = 0;
// measuring the integral on the right part of the function (the climbing line)
if (availablePermitsAboveHalf > 0.0) {
double permitsAboveHalfToTake = min(availablePermitsAboveHalf, permitsToTake);
micros = (long) (permitsAboveHalfToTake * (permitsToTime(availablePermitsAboveHalf)
+ permitsToTime(availablePermitsAboveHalf - permitsAboveHalfToTake)) / 2.0);
permitsToTake -= permitsAboveHalfToTake;
}
// measuring the integral on the left part of the function (the horizontal line)
micros += (stableIntervalMicros * permitsToTake);
return micros;
}
private double permitsToTime(double permits) {
return stableIntervalMicros + permits * slope;
}
}
/**
* This implements a "bursty" RateLimiter, where storedPermits are translated to
* zero throttling. The maximum number of permits that can be saved (when the RateLimiter is
* unused) is defined in terms of time, in this sense: if a RateLimiter is 2qps, and this
* time is specified as 10 seconds, we can save up to 2 * 10 = 20 permits.
*/
static final class SmoothBursty extends SmoothRateLimiter {
/** The work (permits) of how many seconds can be saved up if this RateLimiter is unused? */
final double maxBurstSeconds;
SmoothBursty(SleepingStopwatch stopwatch, double maxBurstSeconds) {
super(stopwatch);
this.maxBurstSeconds = maxBurstSeconds;
}
@Override
void doSetRate(double permitsPerSecond, double stableIntervalMicros) {
double oldMaxPermits = this.maxPermits;
maxPermits = maxBurstSeconds * permitsPerSecond;
if (oldMaxPermits == Double.POSITIVE_INFINITY) {
// if we don't special-case this, we would get storedPermits == NaN, below
storedPermits = maxPermits;
} else {
storedPermits = (oldMaxPermits == 0.0)
? 0.0 // initial state
: storedPermits * maxPermits / oldMaxPermits;
}
}
@Override
long storedPermitsToWaitTime(double storedPermits, double permitsToTake) {
return 0L;
}
}
/**
* The currently stored permits.
*/
double storedPermits;
/**
* The maximum number of stored permits.
*/
double maxPermits;
/**
* The interval between two unit requests, at our stable rate. E.g., a stable rate of 5 permits
* per second has a stable interval of 200ms.
*/
double stableIntervalMicros;
/**
* The time when the next request (no matter its size) will be granted. After granting a
* request, this is pushed further in the future. Large requests push this further than small
* requests.
*/
private long nextFreeTicketMicros = 0L; // could be either in the past or future
private SmoothRateLimiter(SleepingStopwatch stopwatch) {
super(stopwatch);
}
@Override
final void doSetRate(double permitsPerSecond, long nowMicros) {
resync(nowMicros);
double stableIntervalMicros = SECONDS.toMicros(1L) / permitsPerSecond;
this.stableIntervalMicros = stableIntervalMicros;
doSetRate(permitsPerSecond, stableIntervalMicros);
}
abstract void doSetRate(double permitsPerSecond, double stableIntervalMicros);
@Override
final double doGetRate() {
return SECONDS.toMicros(1L) / stableIntervalMicros;
}
@Override
final long queryEarliestAvailable(long nowMicros) {
return nextFreeTicketMicros;
}
@Override
final long reserveEarliestAvailable(int requiredPermits, long nowMicros) {
resync(nowMicros);
long returnValue = nextFreeTicketMicros;
double storedPermitsToSpend = min(requiredPermits, this.storedPermits);
double freshPermits = requiredPermits - storedPermitsToSpend;
long waitMicros = storedPermitsToWaitTime(this.storedPermits, storedPermitsToSpend)
+ (long) (freshPermits * stableIntervalMicros);
this.nextFreeTicketMicros = nextFreeTicketMicros + waitMicros;
this.storedPermits -= storedPermitsToSpend;
return returnValue;
}
/**
* Translates a specified portion of our currently stored permits which we want to
* spend/acquire, into a throttling time. Conceptually, this evaluates the integral
* of the underlying function we use, for the range of
* [(storedPermits - permitsToTake), storedPermits].
*
* This always holds: {@code 0 <= permitsToTake <= storedPermits}
*/
abstract long storedPermitsToWaitTime(double storedPermits, double permitsToTake);
private void resync(long nowMicros) {
// if nextFreeTicket is in the past, resync to now
if (nowMicros > nextFreeTicketMicros) {
storedPermits = min(maxPermits,
storedPermits + (nowMicros - nextFreeTicketMicros) / stableIntervalMicros);
nextFreeTicketMicros = nowMicros;
}
}
}
