On Queuing, Marking, and Dropping

There is extensive history in the set of algorithms collectively referred to as "Fair Queuing". The model was initially discussed in , which proposed it hypothetically as a solution to the TCP Silly Window Syndrome issue in BSD 4.1. The problem was that, due to a TCP implementation bug, some senders would settle into sending a long stream of very short segments, which unnecessarily consumed bandwidth on TCP and IP headers and occupied short packet buffers, thereby disrupting competing sessions. Nagle suggested that if packet streams were sorted by their source address and the sources treated in a round robin fashion, a sender's effect on end-to-end latency and increased loss rate would primarily affect only itself. This touched off perhaps a decade of work by various researchers on what was and is termed "Fair Queuing," philosophical discussions of the meaning of the word "fair," operational reasons that one might want a "weighted" or "predictably unfair" queuing algorithm, and so on.

Conceptually, any Fair Queuing algorithm attempts to implement some approximation to the Generalized Processor Sharing model. The GPS model, in its essence, presumes that a set of identified data streams, called "flows", pass through an interface. Each flow has a rate when measured over a period of time; A voice session might, for example, require 64 kbps plus whatever overhead is necessary to deliver it, and a TCP session might have variable throughput depending on where it is in its evolution. The premise of Generalized Processor Sharing is that on all time scales, the flow occupies a predictable bit rate, so that if there is enough bandwidth for the flow in the long term, it also lacks nothing in the short term. "All time scales" is obviously untenable in a packet network - and even in a traditional TDM circuit switch network - because a timescale shorter than the duration of a packet will only see one packet at a time. But it provides an ideal for other models to be compared against. There are a number of attributes of approximations to the GPS model that bear operational consideration, including at least the transmission quanta, the definition of a "flow", and the unit of measurement. Implementation approaches have different practical impacts as well.

The most obvious comparison between the GPS model and common approximations to it is that real world data is not delivered uniformly, but in some quantum. The smallest quantum, in a packet network, is a packet. But quanta can be larger; for example, in video applications it is common to describe data flow in frames per second, where a frame describes a picture on a screen or the changes made from a previous one. A single video frame is commonly on the order of tens of packets. If a codec is delivering thirty frames per second, it is conceivable that the packets comprising a frame might be sent as thirty bursts per second, with each burst sent at the interface rate of the camera or other sender. Similarly, TCP exchanges have an initial window, common values of which include 1, 2, 3, 4 , and 10 , and there are also reports of bursts of 64 kB at the relevant MSS, which is to say about 45 packets in one burst, presumably coming from TCP Segment Offload (TSO, also called TOE) engines (at least one implementation is known to be able to send a burst of 256 kB). After that initial burst, TCP senders commonly send pairs of packets, but may send either smaller or larger bursts .

An important engineering trade-off relevant to GPS is the definition of a "flow". A flow is, by definition, a defined data stream. Common definitions include: Packets in a single transport layer session ("microflow"), identified by a five-tuple , Packets between a single pair of addresses, identified by a source and destination address or prefix, Packets from a single source address or prefix , Packets to a single destination address or prefix, Packets to or from a single subscriber, customer, or peer . In Service Provider operations, this might be a neighboring Autonomous System; in broadband, a residential customer. The difference should be apparent. Consider a comparison between sorting by source address or destination address, to pick two examples, in the case that a given router interface has N application sessions going through it between N/2 local destinations and N remote sources. Sorting by source, or in this case by source/destination pair, would give each remote peer an upper bound guarantee of 1/N of the available capacity, which might be distributed very unevenly among the local destinations. Sorting by destination would give each local destination an upper bound guarantee of 2/N of the available capacity, which might be distributed very unevenly among the remote systems and correlated sessions. Who is one fair to? In both cases, they deliver equal service by their definition, but that might not be someone else's definition. Flow fairness, and the implications of TCP's congestion avoidance algorithms, is discussed extensively in .

And finally, there is the question of what is measured for rate. If the only objective is to force packet streams to not dominate each other, it is sufficient to count packets. However, if the issue is the bit rate of an SLA, one must consider the sizes of the packets (the aggregate throughput of a flow, measured in bits or bytes). And if predictable unfairness is a consideration, the value must be weighted accordingly. discusses measurement.

Carrying the matter further, a queuing algorithm may also be termed "Work Conserving" or "Non Work Conserving". A queue in a "work conserving" algorithm, by definition, is either empty, in which case no attempt is being made to dequeue data from it, or contains something, in which case the algorithm continuously tries to empty the queue. A work conserving queue that contains queued data, at an interface with a given rate, will deliver data at that rate until it empties. A non-work-conserving queue might stop delivering even though it still contains data. A common reason for doing this is to impose an artificial upper bound on a class of traffic that is lower than the rate of the underlying physical interface.

In the discussion following, we assume a basic definition of a queuing algorithm. A queuing algorithm has, at minimum: Some form of internal storage for the elements kept in the queue, If it has multiple internal classifications, a method for classifying elements, additional storage for the classifier and implied classes, potentially, a method for creating the queue, potentially, a method for destroying the queue, an enqueuing method, for placing packets into the queue or queuing system a dequeuing method, for removing packets from the queue or queuing system There may also be other information or methods, such as the ability to inspect the queue. It also often has inspectable external attributes, such as the total volume of packets or bytes in queue, and may have limit thresholds, such as a maximum number of packets or bytes the queue might hold. For example, a simple FIFO queue has a linear data structure, enqueues packets at the tail, and dequeues packets from the head. It might have a maximum queue depth and a current queue depth, maintained in packets or bytes.

One class of implementation approaches, generically referred to as "Weighted Round Robin" (WRR), implements the structure of the queue as an array or ring of sub-queues associated with flows, for whatever definition of a flow is important. The arriving packet must, of course, first be classified. If a hash is used as a classifier, the modulus of the hash might be used as an array index, selecting the sub-queue that the packet will go into. One can imagine other classifiers, such as using a Differentiated Services Code Point (DSCP) value as an index into an array containing the queue number for a flow, or more complex access list implementations. In any event, a sub-queue contains the traffic for a flow, and data is sent from each sub-queue in succession. On enqueue, the enqueue method places a classified packet into a simple FIFO sub-queue. On dequeue, the sub-queues are searched in round-robin order, and when a sub-queue is identified that contains data, the dequeue method removes a specified quantum of data from it. That quantum is at minimum a packet, but it may be more. If the system is intended to maintain a byte rate, there will be memory between searches of the excess previously dequeued.

|1| | +-+ | | | +-+ +-+ | |1| +>|3| | +-+ | +-+ | | | | | +-+ +-+ | +-+ | |1| +>|2| | |3| | +-+ | +-+ | +-+ | A | A | A | | | | | | ++--++ ++--++ ++--++ +->| Q |-->| Q |-->| Q |--+ | +----+ +----+ +----+ | +----------------------------+ ]]>

Another class of implementation approaches, generically referred Calendar Queue Implementations, implements the structure of the queue as an array or ring of sub-queues (often called "buckets") associated with time or sequence; Each bucket contains the set of packets, which may be null, intended to be sent at a certain time or following the emptying of the previous bucket. The queue structure includes a look-aside table that indicates the current depth (which is to say, the next bucket) of any given class of traffic, which might similarly be identified using a hash, a DSCP, an access list, or any other classifier. Conceptually, the queues each contain zero or more packets from each class of traffic. One is the queue being emptied "now"; the rest are associated with some time or sequence in the future. On enqueue, the enqueue method, considering a classified packet, determines the current depth of that class with a view to scheduling it for transmission at some time or sequence in the future. If the unit of scheduling is a packet and the queuing quantum is one packet per sub-queue, a burst of packets arrives in a given flow, and at the start the flow has no queued data, the first packet goes into the "next" queue, the second into its successor, and so on; if there was some data in the class, the first packet in the burst would go into the bucket pointed to by the look-aside table. If the unit of scheduling is time, the explanation in might be simplest to follow, but the bucket selected will be the bucket corresponding to a given transmission time in the future. A necessary side-effect, memory being finite, is that there exist a finite number of "future" buckets. If enough traffic arrives to cause a class to wrap, one is forced to drop something (tail-drop). On dequeue, the buckets are searched at their stated times or in their stated sequence, and when a bucket is identified that contains data, the dequeue method removes a specified quantum of data from it and, by extension, from the associated traffic classes. A single bucket might contain data from a number of classes simultaneously.

|1| | +-+ | | | +-+ +-+ | |2| +>|2| | +-+ | +-+ | | | | | +-+ | +-+ +-+ | |3| | |1| +>|1| | +-+ | +-+ | +-+ | A | A | A | | | | | | ++--++ ++--++ ++--++ "now"+->| Q |-->| Q |-->| Q |-->... +----+ +----+ +----+ A A A |3 |2 |1 +++++++++++++++++++++++ |||| Flow |||| +++++++++++++++++++++++ ]]> In any event, a sub-queue contains the traffic for a point in time or a point in sequence, and data is sent from each sub-queue in succession. If sub-queues are associated with time, an interesting end case develops: If the system is draining a given sub-queue, and the time of the next sub-queue arrives, what should the system do? One potentially valid line of reasoning would have it continue delivering the data in the present queue, on the assumption that it will likely trade off for time in the next. Another potentially valid line of reasoning would have it discard any waiting data in the present queue and move to the next.

Stochastic Fairness Queuing is an example of a work conserving algorithm. This algorithm measures packets, and considers a "flow" to be an equivalence class of traffic defined by a hashing algorithm over the source and destination IPv4 addresses. As packets arrive, the enqueue method performs the indicated hash and places the packet into the indicated sub-queue. The dequeue method operates as described in ; sub-queues are inspected in round-robin sequence, and if they contain one or more packets, a packet is removed. Deficit Round Robin model modifies the quanta to bytes, and deals with variable length packets. A sub-queue descriptor contains a waiting quantum (the amount intended to be dequeued on the previous dequeue attempt that was not satisfied), a per-round quantum (the sub-queue is intended to dequeue a certain number of bytes each round), and a maximum to permit (some multiple of the MTU). In each dequeue attempt, the dequeue method sets the waiting quantum to the smaller of the maximum quantum and the sum of the waiting and incremental quantum. It then dequeues up to the waiting quantum, in bytes, of packets in the queue, and reduces the waiting quantum by the number of bytes dequeued. Since packets will not normally be exactly the size of the quantum, some dequeue attempts will dequeue more than others, but they will over time average the incremental quantum per round if there is data present. and could be implemented as described in . The weakness of a WRR approach is the search time expended when the queuing system is relatively empty or the overhead of obviating that issue, which the calendar queue model also obviates.

Virtual Clock is an example of a non-work-conserving algorithm. It is trivially implemented as described in . It associates buckets with intervals in time, with durations on the order of microseconds to tens of milliseconds. Each flow is assigned a rate in bytes per interval. The flow entry maintains a point in time the "next" packet in the flow should be scheduled. On enqueue, the method determines whether the "next schedule" time is "in the past"; if so, the packet is scheduled "now", and if not, the packet is scheduled at that time. It then calculates the new "next schedule" time, as the current "next schedule" time plus the length of the packet divided by the rate; if the resulting time is also in the past, the "next schedule" time is set to "now", and otherwise to the calculated time. As noted in , there is an interesting point regarding "too much time in the future"; if a packet is scheduled too far into the future, it may be marked or dropped in the AQM procedure, and if it runs beyond the end of the queuing system, may be defensively tail dropped. On dequeue, the bucket associated with the time "now" is inspected. If it contains a packet, the packet is dequeued and transmitted. If the bucket is empty and the time for the next bucket has not arrived, the system waits, even if there is a packet in the next bucket. As noted in , there is an interesting point regarding the queue associated with "now". If a subsequent bucket, even if it is actually empty, would be delayed by the transmission of a packet, one could imagine marking the packet ECN CE or dropping the packet.

Queuing, marking, and dropping are integrated in any system that has a queue. If nothing else, as memory is finite, a system has to drop as discussed in and in order to protect itself. However, host transports interpret drops as signals, so AQM algorithms use that as a mechanism to signal. It is useful to think of the effects of queuing as a signal as well. The receiver sends acknowledgements as data is received, so the arrival of acknowledgements at the sender paces the sender at approximately the average rate it is able to achieve through the network. This is true even if the sender keeps an arbitrarily large amount of data stored in network queues, and is the basis for delay-based congestion control algorithms. So, delaying a packet momentarily in order to permit another session to improve its operation has the effect of signaling a slightly lower capacity to the sender.

In the default case, in which a FIFO queue is used with defensive tail-drop only, the effect is therefore to signal to the sender in two ways: Ack Clocking, pacing the sender to send at approximately the rate it can deliver data to the receiver, and Defensive loss, when a sender sends faster than available capacity (such as by probing network capacity when fully utilizing that capacity) and overburdens a queue.

In any case wherein a queuing algorithm is used along with CoDel, the sequence of events is that a packet is time-stamped, enqueued, dequeued, compared to a subsequent reading of the clock, and then acted on, whether by dropping it, marking and forwarding it, or simply forwarding it. This is to say that the only drop algorithm inherent in queuing is the defensive drop when the queue's resources are overrun. However, the intention of marking or dropping is to signal to the sender much earlier, when a certain amount of delay has been observed. In a FIFO+CoDel, Virtual Clock+CoDel, or FlowQueue-Codel implementation, the queuing algorithm is completely separate from the AQM algorithm. Using them in series results in four signals to the sender: Ack Clocking, pacing the sender to send at approximately the rate it can deliver data to the receiver through a queue, Lossless signaling that a certain delay threshold has been reached, if ECN is in use, Intentional signaling via loss that a certain delay threshold has been reached, if ECN is not in use, and Defensive loss, when a sender sends faster than available capacity (such as by probing network capacity when fully utilizing that capacity) and overburdens a queue.

In any case wherein a queuing algorithm is used along with PIE, RED, or other such algorithms, the sequence of events is that a queue is inspected, a packet is dropped, marked, or left unchanged, enqueued, dequeued, compared to a subsequent reading of the clock, and then forwarded on. This is to say that the AQM Mark/Drop Algorithm precedes enqueue; if it has not been effective and as a result the queue is out of resources anyway, the defensive drop algorithm steps in, and failing that, the queue operates in whatever way it does. Hence, in a FIFO+PIE, SFQ+PIE, or Virtual Clock+PIE implementation, the queuing algorithm is again completely separate from the AQM algorithm. Using them in series results in four signals to the sender: Ack Clocking, pacing the sender to send at approximately the rate it can deliver data to the receiver through a queue, Lossless signaling that a queue depth that corresponds to a certain delay threshold has been reached, if ECN is in use, Intentional signaling via loss that a queue depth that corresponds to a certain delay threshold has been reached, if ECN is not in use, and Defensive loss, when a sender sends faster than available capacity (such as by probing network capacity when fully utilizing that capacity) and overburdens a queue.