| Network Working Group | X. Zhu |
| Internet-Draft | R. Pan |
| Intended status: Experimental | M. Ramalho |
| Expires: April 11, 2016 | S. Mena |
| P. Jones | |
| J. Fu | |
| Cisco Systems | |
| S. D'Aronco | |
| EPFL | |
| C. Ganzhorn | |
| October 9, 2015 |
NADA: A Unified Congestion Control Scheme for Real-Time Media
draft-ietf-rmcat-nada-01
This document describes NADA (network-assisted dynamic adaptation), a novel congestion control scheme for interactive real-time media applications, such as video conferencing. In the proposed scheme, the sender regulates its sending rate based on either implicit or explicit congestion signaling, in a unified approach. The scheme can benefit from explicit congestion notification (ECN) markings from network nodes. It also maintains consistent sender behavior in the absence of such markings, by reacting to queuing delays and packet losses instead.
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Interactive real-time media applications introduce a unique set of challenges for congestion control. Unlike TCP, the mechanism used for real-time media needs to adapt quickly to instantaneous bandwidth changes, accommodate fluctuations in the output of video encoder rate control, and cause low queuing delay over the network. An ideal scheme should also make effective use of all types of congestion signals, including packet loss, queuing delay, and explicit congestion notification (ECN) [RFC3168] markings. The requirements for the congestion control algorithm are outlined in [I-D.ietf-rmcat-cc-requirements].
This document describes an experimental congestion control scheme called network-assisted dynamic adaptation (NADA). The NADA design benefits from explicit congestion control signals (e.g., ECN markings) from the network, yet also operates when only implicit congestion indicators (delay and/or loss) are available. In addition, it supports weighted bandwidth sharing among competing video flows. The signaling mechanism consists of standard RTP timestamp [RFC3550] and standard RTCP feedback reports.
The key words "MUST", "MUST NOT", "REQUIRED", "SHALL", "SHALL NOT", "SHOULD", "SHOULD NOT", "RECOMMENDED", "MAY", and "OPTIONAL" in this document are to be interpreted as described [RFC2119].
Figure 1 shows the end-to-end system for real-time media transport that NADA operates in.
+---------+ r_vin +--------+ +--------+ +----------+
| Media |<--------| RTP | |Network | | RTP |
| Encoder |========>| Sender |=======>| Node |====>| Receiver |
+---------+ r_vout +--------+ r_send +--------+ +----------+
/|\ |
| |
+---------------------------------+
RTCP Feedback Report
Figure 1: System Overview
Like TCP-Friendly Rate Control (TFRC) [Floyd-CCR00] [RFC5348], NADA is a rate-based congestion control algorithm. In its simplest form, the sender reacts to the collection of network congestion indicators in the form of an aggregated congestion signal, and operates in one of two modes:
This section introduces the list of mathematical notations and describes the core congestion control algorithm at the sender and receiver, respectively. Additional details on recommended practical implementations are described in Section 5.1 and Section 5.2.
This section summarizes the list of variables and parameters used in the NADA algorithm.
+--------------+-------------------------------------------------+
| Notation | Variable Name |
+--------------+-------------------------------------------------+
| t_curr | Current timestamp |
| t_last | Last time sending/receiving a feedback |
| delta | Observed interval between current and previous |
| | feedback reports: delta = t_curr-t_last |
| r_n | Reference rate based on network congestion |
| r_send | Sending rate |
| r_recv | Receiving rate |
| r_vin | Target rate for video encoder |
| r_vout | Output rate from video encoder |
| d_base | Estimated baseline delay |
| d_fwd | Measured and filtered one-way delay |
| d_n | Estimated queueing delay |
| d_tilde | Equivalent delay after non-linear warping |
| p_mark | Estimated packet ECN marking ratio |
| p_loss | Estimated packet loss ratio |
| x_n | Aggregate congestion signal |
| x_prev | Previous value of aggregate congestion signal |
| x_diff | Change in aggregate congestion signal w.r.t. |
| | its previous value: x_diff = x_n - x_prev |
| rmode | Rate update mode: (0 = accelerated ramp-up; |
| | 1 = gradual update) |
| gamma | Rate increase multiplier in accelerated ramp-up |
| | mode |
| rtt | Estimated round-trip-time at sender |
| buffer_len | Rate shaping buffer occupancy measured in bytes |
+--------------+-------------------------------------------------+
Figure 2: List of variables.
+---------------+---------------------------------+----------------+
| Notation | Parameter Name | Default Value |
+--------------+----------------------------------+----------------+
| PRIO | Weight of priority of the flow | 1.0
| RMIN | Minimum rate of application | 150 Kbps |
| | supported by media encoder | |
| RMAX | Maximum rate of application | 1.5 Mbps |
| | supported by media encoder | |
| X_REF | Reference congestion level | 20ms |
| KAPPA | Scaling parameter for gradual | 0.5 |
| | rate update calculation | |
| ETA | Scaling parameter for gradual | 2.0 |
| | rate update calculation | |
| TAU | Upper bound of RTT in gradual | 500ms |
| | rate update calculation | |
| DELTA | Target feedback interval | 100ms |
| LOGWIN | Observation window in time for | 500ms |
| | calculating packet summary | |
| | statistics at receiver | |
| QEPS | Threshold for determining queuing| 10ms |
| | delay build up at receiver | |
+..............+..................................+................+
| QTH | Delay threshold for non-linear | 100ms |
| | warping | |
| QMAX | Delay upper bound for non-linear | 400ms |
| | warping | |
| DLOSS | Delay penalty for loss | 1.0s |
| DMARK | Delay penalty for ECN marking | 200ms |
+..............+..................................+................+
| GAMMA_MAX | Upper bound on rate increase | 20% |
| | ratio for accelerated ramp-up | |
| QBOUND | Upper bound on self-inflicted | 50ms |
| | queuing delay during ramp up | |
+..............+..................................+................+
| FPS | Frame rate of incoming video | 30 |
| BETA_S | Scaling parameter for modulating | 0.1 |
| | outgoing sending rate | |
| BETA_V | Scaling parameter for modulating | 0.1 |
| | video encoder target rate | |
| ALPHA | Smoothing factor in exponential | 0.1 |
| | smoothing of packet loss and | |
| | marking ratios |
+--------------+----------------------------------+----------------+
Figure 3: List of algorithm parameters.
The receiver-side algorithm can be outlined as below:
On initialization:
set d_base = +INFINITY
set p_loss = 0
set p_mark = 0
set r_recv = 0
set both t_last and t_curr as current time
On receiving a media packet:
obtain current timestamp t_curr
obtain from packet header sending time stamp t_sent
obtain one-way delay measurement: d_fwd = t_curr - t_sent
update baseline delay: d_base = min(d_base, d_fwd)
update queuing delay: d_n = d_fwd - d_base
update packet loss ratio estimate p_loss
update packet marking ratio estimate p_mark
update measurement of receiving rate r_recv
On time to send a new feedback report (t_curr - t_last > DELTA):
calculate non-linear warping of delay d_tilde if packet loss exists
calculate aggregate congestion signal x_n
determine mode of rate adaptation for sender: rmode
send RTCP feedback report containing values of: rmode, x_n, and r_recv
update t_last = t_curr
In order for a delay-based flow to hold its ground when competing against loss-based flows (e.g., loss-based TCP), it is important to distinguish between different levels of observed queuing delay. For instance, a moderate queuing delay value below 100ms is likely self-inflicted or induced by other delay-based flows, whereas a high queuing delay value of several hundreds of milliseconds may indicate the presence of a loss-based flow that does not refrain from increased delay.
When packet losses are observed, the estimated queuing delay follows a non-linear warping inspired by the delay-adaptive congestion window backoff policy in [Budzisz-TON11]:
/ d_n, if d_n<QTH;
|
| (QMAX - d_n)^4
d_tilde = < QTH ----------------, if QTH<d_n<QMAX (1)
| (QMAX - QTH)^4
|
\ 0, otherwise.
Here, the queuing delay value is unchanged when it is below the first threshold QTH; it is scaled down following a non-linear curve when its value falls between QTH and QMAX; above QMAX, the high queuing delay value no longer counts toward congestion control.
The aggregate congestion signal is:
x_n = d_tilde + p_mark*DMARK + p_loss*DLOSS. (2)
Here, DMARK is prescribed delay penalty associated with ECN markings and DLOSS is prescribed delay penalty associated with packet losses. The value of DLOSS and DMARK does not depend on configurations at the network node, but does assume that ECN markings, when available, occur before losses. Furthermore, the values of DLOSS and DMARK need to be set consistently across all NADA flows for them to compete fairly.
In the absence of packet marking and losses, the value of x_n reduces to the observed queuing delay d_n. In that case the NADA algorithm operates in the regime of delay-based adaptation.
Given observed per-packet delay and loss information, the receiver is also in a good position to determine whether the network is underutilized and recommend the corresponding rate adaptation mode for the sender. The criteria for operating in accelerated ramp-up mode are:
Otherwise the algorithm operates in graduate update mode.
The sender-side algorithm is outlined as follows:
on initialization:
set r_n = RMIN
set rtt = 0
set x_prev = 0
set t_last and t_curr as current time
on receiving feedback report:
obtain current timestamp: t_curr
obtain values of rmode, x_n, and r_recv from feedback report
update estimation of rtt
measure feedback interval: delta = t_curr - t_last
if rmode == 0:
update r_n following accelerated ramp-up rules
else:
update r_n following gradual update rules
clip rate r_n within the range of [RMIN, RMAX]
x_prev = x_n
t_last = t_curr
In accelerated ramp-up mode, the rate r_n is updated as follows:
QBOUND
gamma = min(GAMMA_MAX, -----------) (3)
rtt+DELTA
r_n = (1+gamma) r_recv (4)
The rate increase multiplier gamma is calculated as a function of upper bound of self-inflicted queuing delay (QBOUND), round-trip-time (rtt), and target feedback interval DELTA. It has a maximum value of GAMMA_MAX. The rationale behind (3)-(4) is that the longer it takes for the sender to observe self-inflicted queuing delay build-up, the more conservative the sender should be in increasing its rate, hence the smaller the rate increase multiplier.
In gradual update mode, the rate r_n is updated as:
x_offset = x_n - PRIO*X_REF*RMAX/r_n (5)
x_diff = x_n - x_prev (6)
delta x_offset
r_n = r_n - KAPPA*-------*------------*r_n
TAU TAU
x_diff
- KAPPA*ETA*---------*r_n (7)
TAU
The rate changes in proportion to the previous rate decision. It is affected by two terms: offset of the aggregate congestion signal from its value at equilibrium (x_offset) and its change (x_diff). Calculation of x_offset depends on maximum rate of the flow (RMAX), its weight of priority (PRIO), as well as a reference congestion signal (X_REF). The value of X_REF is chosen that the maximum rate of RMAX can be achieved when the observed congestion signal level is below PRIO*X_REF.
At equilibrium, the aggregated congestion signal stablizes at x_n = PRIO*X_REF*RMAX/r_n. This ensures that when multiple flows share the same bottleneck and observe a common value of x_n, their rates at equilibrium will be proportional to their respective priority levels (PRIO) and maximum rate (RMAX).
As mentioned in the sender-side algorithm, the final rate is clipped within the dynamic range specified by the application:
r_n = min(r_n, RMAX) (8) r_n = max(r_n, RMIN) (9)
The above operations ignore many practical issues such as clock synchronization between sender and receiver, filtering of noise in delay measurements, and base delay expiration. These will be addressed in later sections describing practical implementation of the NADA algorithm.
The receiver continuously monitors end-to-end per-packet statistics in terms of delay, loss, and/or ECN marking ratios. It then aggregates all forms of congestion indicators into the form of an equivalent delay and periodically reports this back to the sender. In addition, the receiver tracks the receiving rate of the flow and includes that in the feedback message.
The delay estimation process in NADA follows a similar approach as in earlier delay-based congestion control schemes, such as LEDBAT [RFC6817]. NADA estimates the forward delay as having a constant base delay component plus a time varying queuing delay component. The base delay is estimated as the minimum value of one-way delay observed over a relatively long period (e.g., tens of minutes), whereas the individual queuing delay value is taken to be the difference between one-way delay and base delay.
The individual sample values of queuing delay should be further filtered against various non-congestion-induced noise, such as spikes due to processing "hiccup" at the network nodes. Current implementation employs a 15-tab minimum filter over per-packet queuing delay estimates.
The receiver detects packet losses via gaps in the RTP sequence numbers of received packets. Packets arriving out-of-order are discarded, and count towards losses. The instantaneous packet loss ratio p_inst is estimated as the ratio between the number of missing packets over the number of total transmitted packets within the recent observation window LOGWIN. The packet loss ratio p_loss is obtained after exponential smoothing:
p_loss = ALPHA*p_inst + (1-ALPHA)*p_loss. (10)
The filtered result is reported back to the sender as the observed packet loss ratio p_loss.
Estimation of packet marking ratio p_mark follows the same procedure as above. It is assumed that ECN marking information at the IP header can be passed to the transport layer by the receiving endpoint.
It is fairly straighforward to estimate the receiving rate r_recv. NADA maintains a recent observation window with time span of LOGWIN, and simply divides the total size of packets arriving during that window over the time span. The receiving rate (r_recv) is included as part of the feedback report.
Figure 4 provides a detailed view of the NADA sender. Upon receipt of an RTCP feedback report from the receiver, the NADA sender calculates the reference rate r_n as specified in Section 4.3. It further adjusts both the target rate for the live video encoder r_vin and the sending rate r_send over the network based on the updated value of r_n and rate shaping buffer occupancy buffer_len.
The NADA sender behavior stays the same in the presence of all types of congestion indicators: delay, loss, and ECN marking. This unified approach allows a graceful transition of the scheme as the network shifts dynamically between light and heavy congestion levels.
+----------------+
| Calculate | <---- RTCP report
| Reference Rate |
-----------------+
| r_n
+------------+-------------+
| |
\|/ \|/
+-----------------+ +---------------+
| Calculate Video | | Calculate |
| Target Rate | | Sending Rate |
+-----------------+ +---------------+
| /|\ /|\ |
r_vin | | | |
\|/ +-------------------+ |
+----------+ | buffer_len | r_send
| Video | r_vout -----------+ \|/
| Encoder |--------> |||||||||=================>
+----------+ -----------+ RTP packets
Rate Shaping Buffer
Figure 4: NADA Sender Structure
The operation of the live video encoder is out of the scope of the design for the congestion control scheme in NADA. Instead, its behavior is treated as a black box.
A rate shaping buffer is employed to absorb any instantaneous mismatch between encoder rate output r_vout and regulated sending rate r_send. Its current level of occupancy is measured in bytes and is denoted as buffer_len.
A large rate shaping buffer contributes to higher end-to-end delay, which may harm the performance of real-time media communications. Therefore, the sender has a strong incentive to prevent the rate shaping buffer from building up. The mechanisms adopted are:
The target rate for the live video encoder deviates from the network congestion control rate r_n based on the level of occupancy in the rate shaping buffer:
r_vin = r_n - BETA_V*8*buffer_len*FPS. (11)
The actual sending rate r_send is regulated in a similar fashion:
r_send = r_n + BETA_S*8*buffer_len*FPS. (12)
In (11) and (12), the first term indicates the rate calculated from network congestion feedback alone. The second term indicates the influence of the rate shaping buffer. A large rate shaping buffer nudges the encoder target rate slightly below -- and the sending rate slightly above -- the reference rate r_n.
Intuitively, the amount of extra rate offset needed to completely drain the rate shaping buffer within the duration of a single video frame is given by 8*buffer_len*FPS, where FPS stands for the frame rate of the video. The scaling parameters BETA_V and BETA_S can be tuned to balance between the competing goals of maintaining a small rate shaping buffer and deviating the system from the reference rate point.
The current design works with relative one-way-delay (OWD) as the main indication of congestion. The value of the relative OWD is obtained by maintaining the minimum value of observed OWD over a relatively long time horizon and subtract that out from the observed absolute OWD value. Such an approach cancels out the fixed difference between the sender and receiver clocks. It has been widely adopted by other delay-based congestion control approaches such as [RFC6817]. As discussed in [RFC6817], the time horizon for tracking the minimum OWD needs to be chosen with care: it must be long enough for an opportunity to observe the minimum OWD with zero queuing delay along the path, and sufficiently short so as to timely reflect "true" changes in minimum OWD introduced by route changes and other rare events.
The potential drawback in relying on relative OWD as the congestion signal is that when multiple flows share the same bottleneck, the flow arriving late at the network experiencing a non-empty queue may mistakenly consider the standing queuing delay as part of the fixed path propagation delay. This will lead to slightly unfair bandwidth sharing among the flows.
Alternatively, one could move the per-packet statistical handling to the sender instead and use relative round-trip-time (RTT) in lieu of relative OWD, assuming that per-packet acknowledgements are available. The main drawback of RTT-based approach is the noise in the measured delay in the reverse direction.
Note that the choice of either delay metric (relative OWD vs. RTT) involves no change in the proposed rate adaptation algorithm. Therefore, comparing the pros and cons regarding which delay metric to adopt can be kept as an orthogonal direction of investigation.
Like other delay-based congestion control schemes, performance of NADA depends on the accuracy of its delay measurement and estimation module. Appendix A in [RFC6817] provides an extensive discussion on this aspect.
The current recommended practice of simply applying a 15-tab minimum filter suffices in guarding against processing delay outliers observed in wired connections. For wireless connections with a higher packet delay variation (PDV), more sophisticated techniques on de-noising, outlier rejection, and trend analysis may be needed.
More sophisticated methods in packet loss ratio calculation, such as that adopted by [Floyd-CCR00], will likely be beneficial. These alternatives are currently under investigation.
In the gradual rate update mode, the parameter TAU indicates the upper bound of round-trip-time (RTT) in feedback control loop. Typically, the observed feedback interval delta is close to the target feedback interval DELTA, and the relative ratio of delta/TAU versus ETA dictates the relative strength of influence from the aggregate congestion signal offset term (x_offset) versus its recent change (x_diff), respectively. These two terms are analogous to the integral and proportional terms in a proportional-integral (PI) controller. The recommended choice of TAU=500ms, DELTA=100ms and ETA = 2.0 corresponds to a relative ratio of 1:10 between the gains of the integral and proportional terms. Consequently, the rate adaptation is mostly driven by the change in the congestion signal with a long-term shift towards its equilibrium value driven by the offset term. Finally, the scaling parameter KAPPA determines the overall speed of the adaptation and needs to strike a balance between responsiveness and stability.
The choice of the target feedback interval DELTA needs to strike the right balance between timely feedback and low RTCP feedback message counts. A target feedback interval of DELTA=100ms is recommended, corresponding to a feedback bandwidth of 16Kbps with 200 bytes per feedback message --- less than 0.1% overhead for a 1 Mbps flow. Furthermore, both simulation studies and frequency-domain analysis have established that a feedback interval below 250ms will not break up the feedback control loop of NADA congestion control.
In calculating the non-linear warping of delay in (1), the current design uses fixed values of QTH and QMAX. It is possible to adapt the value of both based on past observations of queuing delay in the presence of packet losses.
In calculating the aggregate congestion signal x_n, the choice of DMARK and DLOSS influence the steady-state packet loss/marking ratio experienced by the flow at a given available bandwidth. Higher values of DMARK and DLOSS result in lower steady-state loss/marking ratios, but are more susceptible to the impact of individual packet loss/marking events. While the value of DMARK and DLOSS are fixed and predetermined in the current design, a scheme for automatically tuning these values based on desired bandwidth sharing behavior in the presence of other competing loss-based flows (e.g., loss-based TCP) is under investigation.
[Editor's note: Choice of start value: is this in scope of congestion control, or should this be decided by the application?]
In the current design, the aggregated congestion signal x_n is calculated at the receiver, keeping the sender operation completely independent of the form of actual network congestion indications (delay, loss, or marking). Alternatively, one can move the logics of (1) and (2) to the sender. Such an approach requires slightly higher overhead in the feedback messages, which should contain individual fields on queuing delay (d_n), packet loss ratio (p_loss), packet marking ratio (p_mark), receiving rate (r_recv), and recommended rate adaptation mode (rmode).
One nice property of NADA is the consistent video endpoint behavior irrespective of network node variations. This facilitates gradual, incremental adoption of the scheme.
To start off with, the proposed congestion control mechanism can be implemented without any explicit support from the network, and relies solely on observed one-way delay measurements and packet loss ratios as implicit congestion signals.
When ECN is enabled at the network nodes with RED-based marking, the receiver can fold its observations of ECN markings into the calculation of the equivalent delay. The sender can react to these explicit congestion signals without any modification.
Ultimately, networks equipped with proactive marking based on token bucket level metering can reap the additional benefits of zero standing queues and lower end-to-end delay and work seamlessly with existing senders and receivers.
The NADA scheme has been implemented in [ns-2] and [ns-3] simulation platforms. Extensive ns-2 simulation evaluations of an earlier version of the draft are documented in [Zhu-PV13]. Evaluation results of the current draft over several test cases in [I-D.ietf-rmcat-eval-test] have been presented at recent IETF meetings [IETF-90][IETF-91].
The scheme has also been implemented and evaluated in a lab setting as described in [IETF-90]. Preliminary evaluation results of NADA in single-flow and multi-flow scenarios have been presented in [IETF-91].
This document makes no request of IANA.
The authors would like to thank Randell Jesup, Luca De Cicco, Piers O'Hanlon, Ingemar Johansson, Stefan Holmer, Cesar Ilharco Magalhaes, Safiqul Islam, Mirja Kuhlewind, and Karen Elisabeth Egede Nielsen for their valuable questions and comments on earlier versions of this draft.
| [RFC2119] | Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, DOI 10.17487/RFC2119, March 1997. |
| [RFC3168] | Ramakrishnan, K., Floyd, S. and D. Black, "The Addition of Explicit Congestion Notification (ECN) to IP", RFC 3168, DOI 10.17487/RFC3168, September 2001. |
| [RFC3550] | Schulzrinne, H., Casner, S., Frederick, R. and V. Jacobson, "RTP: A Transport Protocol for Real-Time Applications", STD 64, RFC 3550, DOI 10.17487/RFC3550, July 2003. |
| [I-D.ietf-rmcat-eval-criteria] | Singh, V. and J. Ott, "Evaluating Congestion Control for Interactive Real-time Media", Internet-Draft draft-ietf-rmcat-eval-criteria-03, March 2015. |
| [I-D.ietf-rmcat-eval-test] | Sarker, Z., Singh, V., Zhu, X. and M. Ramalho, "Test Cases for Evaluating RMCAT Proposals", Internet-Draft draft-ietf-rmcat-eval-test-02, September 2015. |
| [I-D.ietf-rmcat-cc-requirements] | Jesup, R. and Z. Sarker, "Congestion Control Requirements for Interactive Real-Time Media", Internet-Draft draft-ietf-rmcat-cc-requirements-09, December 2014. |
NADA can work with different network queue management schemes and does not assume any specific network node operation. As an example, this appendix describes three variants of queue management behavior at the network node, leading to either implicit or explicit congestion signals.
In all three flavors described below, the network queue operates with the simple first-in-first-out (FIFO) principle. There is no need to maintain per-flow state. The system can scale easily with a large number of video flows and at high link capacity.
In a conventional network with drop tail or RED queues, congestion is inferred from the estimation of end-to-end delay and/or packet loss. Packet drops at the queue are detected at the receiver, and contributes to the calculation of the aggregated congestion signal x_n. No special action is required at network node.
In this mode, the network node randomly marks the ECN field in the IP packet header following the Random Early Detection (RED) algorithm [RFC2309]. Calculation of the marking probability involves the following steps:
on packet arrival:
update smoothed queue size q_avg as:
q_avg = w*q + (1-w)*q_avg.
calculate marking probability p as:
/ 0, if q < q_lo;
|
| q_avg - q_lo
p= < p_max*--------------, if q_lo <= q < q_hi;
| q_hi - q_lo
|
\ p = 1, if q >= q_hi.
Here, q_lo and q_hi corresponds to the low and high thresholds of queue occupancy. The maximum marking probability is p_max.
The ECN markings events will contribute to the calculation of an equivalent delay x_n at the receiver. No changes are required at the sender.
Advanced network nodes may support random early marking based on a token bucket algorithm originally designed for Pre-Congestion Notification (PCN) [RFC6660]. The early congestion notification (ECN) bit in the IP header of packets are marked randomly. The marking probability is calculated based on a token-bucket algorithm originally designed for the Pre-Congestion Notification (PCN) [RFC6660]. The target link utilization is set as 90%; the marking probability is designed to grow linearly with the token bucket size when it varies between 1/3 and 2/3 of the full token bucket limit.
* upon packet arrival, meter packet against token bucket (r,b);
* update token level b_tk;
* calculate the marking probability as:
/ 0, if b-b_tk < b_lo;
|
| b-b_tk-b_lo
p = < p_max* --------------, if b_lo<= b-b_tk <b_hi;
| b_hi-b_lo
|
\ 1, if b-b_tk>=b_hi.
Here, the token bucket lower and upper limits are denoted by b_lo and b_hi, respectively. The parameter b indicates the size of the token bucket. The parameter r is chosen to be below capacity, resulting in slight under-utilization of the link. The maximum marking probability is p_max.
The ECN markings events will contribute to the calculation of an equivalent delay x_n at the receiver. No changes are required at the sender. The virtual queuing mechanism from the PCN-based marking algorithm will lead to additional benefits such as zero standing queues.