| RTP Media Congestion Avoidance Techniques (rmcat) | S. Islam |
| Internet-Draft | M. Welzl |
| Intended status: Experimental | S. Gjessing |
| Expires: March 19, 2018 | University of Oslo |
| September 15, 2017 |
Coupled congestion control for RTP media
draft-ietf-rmcat-coupled-cc-07
When multiple congestion controlled Real-time Transport Protocol (RTP) sessions traverse the same network bottleneck, combining their controls can improve the total on-the-wire behavior in terms of delay, loss and fairness. This document describes such a method for flows that have the same sender, in a way that is as flexible and simple as possible while minimizing the amount of changes needed to existing RTP applications. It specifies how to apply the method for the Network-Assisted Dynamic Adaptation (NADA) congestion control algorithm, and provides suggestions on how to apply it to other congestion control algorithms.
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When there is enough data to send, a congestion controller attempts to increase its sending rate until the path's capacity has been reached. Some controllers detect path capacity by increasing the sending rate further, until packets are ECN-marked [RFC8087] or dropped, and then decreasing the sending rate until that stops happening. This process inevitably creates undesirable queuing delay when multiple congestion-controlled connections traverse the same network bottleneck, and each connection overshoots the path capacity as it determines its sending rate.
The Congestion Manager (CM) [RFC3124] couples flows by providing a single congestion controller. It is hard to implement because it requires an additional congestion controller and removes all per-connection congestion control functionality, which is quite a significant change to existing RTP based applications. This document presents a method to combine the behavior of congestion control mechanisms that is easier to implement than the Congestion Manager [RFC3124] and also requires less significant changes to existing RTP based applications. It attempts to roughly approximate the CM behavior by sharing information between existing congestion controllers. It is able to honor user-specified priorities, which is required by rtcweb [I-D.ietf-rtcweb-overview] [RFC7478].
The described mechanisms are believed safe to use, but are experimental and are presented for wider review and operational evaluation.
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 in RFC 2119.
Figure 1 shows the elements of the architecture for coupled congestion control: the Flow State Exchange (FSE), Shared Bottleneck Detection (SBD) and Flows. The FSE is a storage element that can be implemented in two ways: active and passive. In the active version, it initiates communication with flows and SBD. However, in the passive version, it does not actively initiate communication with flows and SBD; its only active role is internal state maintenance (e.g., an implementation could use soft state to remove a flow's data after long periods of inactivity). Every time a flow's congestion control mechanism would normally update its sending rate, the flow instead updates information in the FSE and performs a query on the FSE, leading to a sending rate that can be different from what the congestion controller originally determined. Using information about/from the currently active flows, SBD updates the FSE with the correct Flow Group Identifiers (FGIs).
This document describes both active and passive versions. While the passive algorithm works better for congestion controls with RTT-independent convergence, it can still produce oscillations on short time scales. The passive algorithm, described in Appendix C, is therefore considered as highly experimental and not safe to deploy outside of testbed environments. Figure 2 shows the interaction between flows and the FSE, using the variable names defined in Section 5.2.
------- <--- Flow 1 | FSE | <--- Flow 2 .. ------- <--- .. Flow N ^ | | ------- | | SBD | <-------| -------
Figure 1: Coupled congestion control architecture
Flow#1(cc) FSE Flow#2(cc)
---------- --- ----------
#1 JOIN ----register--> REGISTER
REGISTER <--register-- JOIN #1
#2 CC_R(1) ----UPDATE----> UPDATE (in)
#3 NEW RATE <---FSE_R(1)-- UPDATE (out) --FSE_R(2)-> #3 NEW RATE
Figure 2: Flow-FSE interaction
Since everything shown in Figure 1 is assumed to operate on a single host (the sender) only, this document only describes aspects that have an influence on the resulting on-the-wire behavior. It does not, for instance, define how many bits must be used to represent FGIs, or in which way the entities communicate.
Implementations can take various forms: for instance, all the elements in the figure could be implemented within a single application, thereby operating on flows generated by that application only. Another alternative could be to implement both the FSE and SBD together in a separate process which different applications communicate with via some form of Inter-Process Communication (IPC). Such an implementation would extend the scope to flows generated by multiple applications. The FSE and SBD could also be included in the Operating System kernel. However, only one type of coupling algorithm should be used for all flows. Combinations of multiple algorithms at different aggregation levels (e.g., the Operating System coupling application aggregates with one algorithm, and applications coupling their flows with another) have not been tested and are therefore not recommended.
This section gives an overview of the roles of the elements of coupled congestion control, and provides an example of how coupled congestion control can operate.
SBD uses knowledge about the flows to determine which flows belong in the same Flow Group (FG), and assigns FGIs accordingly. This knowledge can be derived in three basic ways:
The methods above have some essential trade-offs: e.g., multiplexing is a completely reliable measure, however it is limited in scope to two end points (i.e., it cannot be applied to couple congestion controllers of one sender talking to multiple receivers). A measurement-based SBD mechanism is described in [I-D.ietf-rmcat-sbd]. Measurements can never be 100% reliable, in particular because they are based on the past but applying coupled congestion control means to make an assumption about the future; it is therefore recommended to implement cautionary measures, e.g. by disabling coupled congestion control if enabling it causes a significant increase in delay and/or packet loss. Measurements also take time, which entails a certain delay for turning on coupling (refer to [I-D.ietf-rmcat-sbd] for details). Using system configuration to decide about shared bottlenecks can be more efficient (faster to obtain) than using measurements, but it relies on assumptions about the network environment.
The FSE contains a list of all flows that have registered with it. For each flow, it stores the following: [I-D.ietf-rtcweb-transports] by simply using the values 1, 2, 4 and 8, respectively.
Note that the absolute range of priorities does not matter: the algorithm works with a flow's priority portion of the sum of all priority values. For example, if there are two flows, flow 1 with priority 1 and flow 2 with priority 2, the sum of the priorities is 3. Then, flow 1 will be assigned 1/3 of the aggregate sending rate and flow 2 will be assigned 2/3 of the aggregate sending rate. Priorities can be mapped to the "very-low", "low", "medium" or "high" priority levels described in
In the FSE, each FG contains one static variable S_CR which is the sum of the calculated rates of all flows in the same FG. This value is used to calculate the sending rate.
The information listed here is enough to implement the sample flow algorithm given below. FSE implementations could easily be extended to store, e.g., a flow's current sending rate for statistics gathering or future potential optimizations.
Flows register themselves with SBD and FSE when they start, deregister from the FSE when they stop, and carry out an UPDATE function call every time their congestion controller calculates a new sending rate. Via UPDATE, they provide the newly calculated rate and optionally (if the algorithm supports it) the desired rate. The desired rate is less than the calculated rate in case of application-limited flows; otherwise, it is the same as the calculated rate.
Below, two example algorithms are described. While other algorithms could be used instead, the same algorithm must be applied to all flows. Names of variables used in the algorithms are explained below.
This algorithm was designed to be the simplest possible method to assign rates according to the priorities of flows. Simulations results in [fse] indicate that it does however not significantly reduce queuing delay and packet loss.
S_CR = S_CR + CC_R(f) - FSE_R(f)
S_P = 0
for all flows i in FG do
S_P = S_P + P(i)
end for
for all flows i in FG do
FSE_R(i) = (P(i)*S_CR)/S_P
send FSE_R(i) to the flow i
end for
This algorithm extends algorithm 1 to conservatively emulate the behavior of a single flow by proportionally reducing the aggregate rate on congestion. Simulations results in [fse] indicate that it can significantly reduce queuing delay and packet loss.
if Timer has expired or not set then
DELTA = CC_R(f) - FSE_R(f)
if DELTA < 0 then // Reduce S_CR proportionally
S_CR = S_CR * CC_R(f) / FSE_R(f)
Set Timer for 2 RTTs
else
S_CR = S_CR + DELTA
end if
end if
S_P = 0
for all flows i in FG do
S_P = S_P + P(i)
end for
for all flows i in FG do
FSE_R(i) = (P(i)*S_CR)/S_P
send FSE_R(i) to the flow i
end for
This section specifies how the FSE can be applied to specific congestion control mechanisms and makes general recommendations that facilitate applying the FSE to future congestion controls.
Network-Assisted Dynamic Adapation (NADA) [I-D.ietf-rmcat-nada] is a congestion control scheme for rtcweb. It calculates a reference rate r_ref upon receiving an acknowledgment, and then, based on the reference rate, it calculates a video target rate r_vin and a sending rate for the flows, r_send.
When applying the FSE to NADA, the UPDATE function call described in Section 5.3 gives the FSE NADA's reference rate r_ref. The recommended algorithm for NADA is the Active FSE in Section 5.3.1. In step 3 (c), when the FSE_R(i) is "sent" to the flow i, this means updating r_ref(r_vin and r_send) of flow i with the value of FSE_R(i).
This section provides general advice for applying the FSE to congestion control mechanisms.
The algorithm described in this memo has so far been evaluated using simulations covering all the tests for more than one flow from [I-D.ietf-rmcat-eval-test] (see [IETF-93], [IETF-94]). Experiments should confirm these results using at least the NADA congestion control algorithm with real-life code (e.g., browsers communicating over an emulated network covering the conditions in [I-D.ietf-rmcat-eval-test]. The tests with real-life code should be repeated afterwards in real network environments and monitored. Experiments should investigate cases where the media coder's output rate is below the rate that is calculated by the coupling algorithm (FSE_R(i) in algorithms 1 and 2, section 5.3). Implementers and testers are invited to document their findings in an Internet draft.
This document has benefitted from discussions with and feedback from Andreas Petlund, Anna Brunstrom, Colin Perkins, David Hayes, David Ros (who also gave the FSE its name), Ingemar Johansson, Karen Nielsen, Kristian Hiorth, Mirja Kuehlewind, Martin Stiemerling, Spencer Dawkins, Varun Singh, Xiaoqing Zhu, and Zaheduzzaman Sarker. The authors would like to especially thank Xiaoqing Zhu and Stefan Holmer for helping with NADA and GCC.
This work was partially funded by the European Community under its Seventh Framework Programme through the Reducing Internet Transport Latency (RITE) project (ICT-317700).
This memo includes no request to IANA.
In scenarios where the architecture described in this document is applied across applications, various cheating possibilities arise: e.g., supporting wrong values for the calculated rate, the desired rate, or the priority of a flow. In the worst case, such cheating could either prevent other flows from sending or make them send at a rate that is unreasonably large. The end result would be unfair behavior at the network bottleneck, akin to what could be achieved with any UDP based application. Hence, since this is no worse than UDP in general, there seems to be no significant harm in using this in the absence of UDP rate limiters.
In the case of a single-user system, it should also be in the interest of any application programmer to give the user the best possible experience by using reasonable flow priorities or even letting the user choose them. In a multi-user system, this interest may not be given, and one could imagine the worst case of an "arms race" situation, where applications end up setting their priorities to the maximum value. If all applications do this, the end result is a fair allocation in which the priority mechanism is implicitly eliminated, and no major harm is done.
Implementers should also be aware of the Security Considerations sections of [RFC3124], [RFC5348], and [RFC7478].
| [I-D.ietf-rmcat-nada] | Zhu, X., Pan, R., Ramalho, M., Cruz, S., Jones, P., Fu, J. and S. D'Aronco, "NADA: A Unified Congestion Control Scheme for Real-Time Media", Internet-Draft draft-ietf-rmcat-nada-04, March 2017. |
| [RFC2119] | Bradner, S., "Key words for use in RFCs to Indicate Requirement Levels", BCP 14, RFC 2119, DOI 10.17487/RFC2119, March 1997. |
| [RFC3124] | Balakrishnan, H. and S. Seshan, "The Congestion Manager", RFC 3124, DOI 10.17487/RFC3124, June 2001. |
| [RFC5348] | Floyd, S., Handley, M., Padhye, J. and J. Widmer, "TCP Friendly Rate Control (TFRC): Protocol Specification", RFC 5348, DOI 10.17487/RFC5348, September 2008. |
| [anrw2016] | Islam, S. and M. Welzl, "Start Me Up:Determining and Sharing TCP’s Initial Congestion Window", ACM, IRTF, ISOC Applied Networking Research Workshop 2016 (ANRW 2016) , 2016. |
| [fse] | Islam, S., Welzl, M., Gjessing, S. and N. Khademi, "Coupled Congestion Control for RTP Media", ACM SIGCOMM Capacity Sharing Workshop (CSWS 2014) and ACM SIGCOMM CCR 44(4) 2014; extended version available as a technical report from http://safiquli.at.ifi.uio.no/paper/fse-tech-report.pdf , 2014. |
| [fse-noms] | Islam, S., Welzl, M., Hayes, D. and S. Gjessing, "Managing Real-Time Media Flows through a Flow State Exchange", IEEE NOMS 2016, Istanbul, Turkey , 2016. |
| [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-05, April 2017. |
| [I-D.ietf-rmcat-gcc] | Holmer, S., Lundin, H., Carlucci, G., Cicco, L. and S. Mascolo, "A Google Congestion Control Algorithm for Real-Time Communication", Internet-Draft draft-ietf-rmcat-gcc-02, July 2016. |
| [I-D.ietf-rmcat-sbd] | Hayes, D., Ferlin, S., Welzl, M. and K. Hiorth, "Shared Bottleneck Detection for Coupled Congestion Control for RTP Media.", Internet-Draft draft-ietf-rmcat-sbd-08, July 2017. |
| [I-D.ietf-rtcweb-overview] | Alvestrand, H., "Overview: Real Time Protocols for Browser-based Applications", Internet-Draft draft-ietf-rtcweb-overview-18, March 2017. |
| [I-D.ietf-rtcweb-transports] | Alvestrand, H., "Transports for WebRTC", Internet-draft draft-ietf-rtcweb-transports-17.txt, October 2016. |
| [IETF-93] | Islam, S., Welzl, M. and S. Gjessing, "Updates on Coupled Congestion Control for RTP Media", July 2015. |
| [IETF-94] | Islam, S., Welzl, M. and S. Gjessing, "Updates on Coupled Congestion Control for RTP Media", November 2015. |
| [RFC7478] | Holmberg, C., Hakansson, S. and G. Eriksson, "Web Real-Time Communication Use Cases and Requirements", RFC 7478, DOI 10.17487/RFC7478, March 2015. |
| [RFC7656] | Lennox, J., Gross, K., Nandakumar, S., Salgueiro, G. and B. Burman, "A Taxonomy of Semantics and Mechanisms for Real-Time Transport Protocol (RTP) Sources", RFC 7656, DOI 10.17487/RFC7656, November 2015. |
| [RFC8087] | Fairhurst, G. and M. Welzl, "The Benefits of Using Explicit Congestion Notification (ECN)", RFC 8087, DOI 10.17487/RFC8087, March 2017. |
| [rtcweb-rtp-usage] | Perkins, C., Westerlund, M. and J. Ott, "Web Real-Time Communication (WebRTC): Media Transport and Use of RTP", Internet-draft draft-ietf-rtcweb-rtp-usage-26.txt, March 2016. |
| [transport-multiplex] | Westerlund, M. and C. Perkins, "Multiple RTP Sessions on a Single Lower-Layer Transport", Internet-draft draft-westerlund-avtcore-transport-multiplexing-07.txt, October 2013. |
Google Congestion Control (GCC) [I-D.ietf-rmcat-gcc] is another congestion control scheme for RTP flows that is under development. GCC is not yet finalised, but at the time of this writing, the rate control of GCC employs two parts: controlling the bandwidth estimate based on delay, and controlling the bandwidth estimate based on loss. Both are designed to estimate the available bandwidth, A_hat.
When applying the FSE to GCC, the UPDATE function call described in Section 5.3 gives the FSE GCC's estimate of available bandwidth A_hat. The recommended algorithm for GCC is the Active FSE in Section 5.3.1. In step 3 (c), when the FSE_R(i) is "sent" to the flow i, this means updating A_hat of flow i with the value of FSE_R(i).
When flows originate from the same host, it would be possible to use only one single sender-side congestion controller which determines the overall allowed sending rate, and then use a local scheduler to assign a proportion of this rate to each RTP session. This way, priorities could also be implemented as a function of the scheduler. The Congestion Manager (CM) [RFC3124] also uses such a scheduling function.
Active algorithms calculate the rates for all the flows in the FG and actively distribute them. In a passive algorithm, UPDATE returns a rate that should be used instead of the rate that the congestion controller has determined. This can make a passive algorithm easier to implement; however, when round-trip times of flows are unequal, shorter-RTT flows may (depending on the congestion control algorithm) update and react to the overall FSE state more often than longer-RTT flows, which can produce unwanted side effects. This problem is more significant when the congestion control convergence depends on the RTT. While the passive algorithm works better for congestion controls with RTT-independent convergence, it can still produce oscillations on short time scales. The algorithm described below is therefore considered as highly experimental and not safe to deploy outside of testbed environments. Results of a simplified passive FSE algorithm with both NADA and GCC can be found in [fse-noms].
This passive version of the FSE stores the following information in addition to the variables described in Section 5.2:
The passive version of the FSE contains one static variable per FG called TLO (Total Leftover Rate -- used to let a flow 'take' bandwidth from application-limited or terminated flows) which is initialized to 0. For the passive version, S_CR is limited to increase or decrease as conservatively as a flow's congestion controller decides in order to prohibit sudden rate jumps.
for all flows i in FG do
new_S_CR = new_S_CR + FSE_R(i)
end for
DELTA = CC_R(f) - FSE_R(f)
FSE_R(f) = CC_R(f)
if DELTA > 0 then // the flow's rate has increased
S_CR = S_CR + DELTA
else if DELTA < 0 then
S_CR = new_S_CR + DELTA
end if
DR(f) = min(new_DR(f),FSE_R(f))
for all flows i in FG do
if P(i)<0 then
delete flow
else
S_P = S_P + P(i)
end if
end for
if DR(f) < FSE_R(f) then
TLO = TLO + (P(f)/S_P) * S_CR - DR(f))
end if
Rate(f) = min(new_DR(f), (P(f)*S_CR)/S_P + TLO)
if Rate(f) != new_DR(f) and TLO > 0 then
TLO = 0 // f has 'taken' TLO
end if
if Rate(f) > DR(f) then
DR(f) = Rate(f)
end if
FSE_R(f) = Rate(f)
The goals of the flow algorithm are to achieve prioritization, improve network utilization in the face of application-limited flows, and impose limits on the increase behavior such that the negative impact of multiple flows trying to increase their rate together is minimized. It does that by assigning a flow a sending rate that may not be what the flow's congestion controller expected. It therefore builds on the assumption that no significant inefficiencies arise from temporary application-limited behavior or from quickly jumping to a rate that is higher than the congestion controller intended. How problematic these issues really are depends on the controllers in use and requires careful per-controller experimentation. The coupled congestion control mechanism described here also does not require all controllers to be equal; effects of heterogeneous controllers, or homogeneous controllers being in different states, are also subject to experimentation.
This algorithm gives all the leftover rate of application-limited flows to the first flow that updates its sending rate, provided that this flow needs it all (otherwise, its own leftover rate can be taken by the next flow that updates its rate). Other policies could be applied, e.g. to divide the leftover rate of a flow equally among all other flows in the FGI.
In order to illustrate the operation of the passive coupled congestion control algorithm, this section presents a toy example of two flows that use it. Let us assume that both flows traverse a common 10 Mbit/s bottleneck and use a simplistic congestion controller that starts out with 1 Mbit/s, increases its rate by 1 Mbit/s in the absence of congestion and decreases it by 2 Mbit/s in the presence of congestion. For simplicity, flows are assumed to always operate in a round-robin fashion. Rate numbers below without units are assumed to be in Mbit/s. For illustration purposes, the actual sending rate is also shown for every flow in FSE diagrams even though it is not really stored in the FSE.
Flow #1 begins. It is a bulk data transfer and considers itself to have top priority. This is the FSE after the flow algorithm's step 1:
----------------------------------------
| # | FGI | P | FSE_R | DR | Rate |
| | | | | | |
| 1 | 1 | 1 | 1 | 1 | 1 |
----------------------------------------
S_CR = 1, TLO = 0
Its congestion controller gradually increases its rate. Eventually, at some point, the FSE should look like this:
-----------------------------------------
| # | FGI | P | FSE_R | DR | Rate |
| | | | | | |
| 1 | 1 | 1 | 10 | 10 | 10 |
-----------------------------------------
S_CR = 10, TLO = 0
Now another flow joins. It is also a bulk data transfer, and has a lower priority (0.5):
------------------------------------------
| # | FGI | P | FSE_R | DR | Rate |
| | | | | | |
| 1 | 1 | 1 | 10 | 10 | 10 |
| 2 | 1 | 0.5 | 1 | 1 | 1 |
------------------------------------------
S_CR = 11, TLO = 0
Now assume that the first flow updates its rate to 8, because the total sending rate of 11 exceeds the total capacity. Let us take a closer look at what happens in step 3 of the flow algorithm.
CC_R(1) = 8. new_DR(1) = infinity.
3 a) new_S_CR = 11; DELTA = 8 - 10 = -2.
3 b) FSE_R(1) = 8. DELTA is negative, hence S_CR = 9;
DR(1) = 8.
3 c) S_P = 1.5.
3 d) new sending rate Rate(1) = min(infinity, 1/1.5 * 9 + 0) = 6.
3 e) FSE_R(1) = 6.
The resulting FSE looks as follows:
-------------------------------------------
| # | FGI | P | FSE_R | DR | Rate |
| | | | | | |
| 1 | 1 | 1 | 6 | 8 | 6 |
| 2 | 1 | 0.5 | 1 | 1 | 1 |
-------------------------------------------
S_CR = 9, TLO = 0
The effect is that flow #1 is sending with 6 Mbit/s instead of the 8 Mbit/s that the congestion controller derived. Let us now assume that flow #2 updates its rate. Its congestion controller detects that the network is not fully saturated (the actual total sending rate is 6+1=7) and increases its rate.
CC_R(2) = 2. new_DR(2) = infinity.
3 a) new_S_CR = 7; DELTA = 2 - 1 = 1.
3 b) FSE_R(2) = 2. DELTA is positive, hence S_CR = 9 + 1 = 10;
DR(2) = 2.
3 c) S_P = 1.5.
3 d) Rate(2) = min(infinity, 0.5/1.5 * 10 + 0) = 3.33.
3 e) DR(2) = FSE_R(2) = 3.33.
The resulting FSE looks as follows:
-------------------------------------------
| # | FGI | P | FSE_R | DR | Rate |
| | | | | | |
| 1 | 1 | 1 | 6 | 8 | 6 |
| 2 | 1 | 0.5 | 3.33 | 3.33 | 3.33 |
-------------------------------------------
S_CR = 10, TLO = 0
The effect is that flow #2 is now sending with 3.33 Mbit/s, which is close to half of the rate of flow #1 and leads to a total utilization of 6(#1) + 3.33(#2) = 9.33 Mbit/s. Flow #2's congestion controller has increased its rate faster than the controller actually expected. Now, flow #1 updates its rate. Its congestion controller detects that the network is not fully saturated and increases its rate. Additionally, the application feeding into flow #1 limits the flow's sending rate to at most 2 Mbit/s.
CC_R(1) = 7. new_DR(1) = 2.
3 a) new_S_CR = 9.33; DELTA = 1.
3 b) FSE_R(1) = 7, DELTA is positive, hence S_CR = 10 + 1 = 11;
DR(1) = min(2, 7) = 2.
3 c) S_P = 1.5; DR(1) < FSE_R(1), hence TLO = 1/1.5 * 11 - 2 = 5.33.
3 d) Rate(1) = min(2, 1/1.5 * 11 + 5.33) = 2.
3 e) FSE_R(1) = 2.
The resulting FSE looks as follows:
-------------------------------------------
| # | FGI | P | FSE_R | DR | Rate |
| | | | | | |
| 1 | 1 | 1 | 2 | 2 | 2 |
| 2 | 1 | 0.5 | 3.33 | 3.33 | 3.33 |
-------------------------------------------
S_CR = 11, TLO = 5.33
Now, the total rate of the two flows is 2 + 3.33 = 5.33 Mbit/s, i.e. the network is significantly underutilized due to the limitation of flow #1. Flow #2 updates its rate. Its congestion controller detects that the network is not fully saturated and increases its rate.
CC_R(2) = 4.33. new_DR(2) = infinity.
3 a) new_S_CR = 5.33; DELTA = 1.
3 b) FSE_R(2) = 4.33. DELTA is positive, hence S_CR = 12;
DR(2) = 4.33.
3 c) S_P = 1.5.
3 d) Rate(2) = min(infinity, 0.5/1.5 * 12 + 5.33 ) = 9.33.
3 e) FSE_R(2) = 9.33, DR(2) = 9.33.
The resulting FSE looks as follows:
-------------------------------------------
| # | FGI | P | FSE_R | DR | Rate |
| | | | | | |
| 1 | 1 | 1 | 2 | 2 | 2 |
| 2 | 1 | 0.5 | 9.33 | 9.33 | 9.33 |
-------------------------------------------
S_CR = 12, TLO = 0
Now, the total rate of the two flows is 2 + 9.33 = 11.33 Mbit/s. Finally, flow #1 terminates. It sets P(1) to -1 and DR(1) to 0. Let us assume that it terminated late enough for flow #2 to still experience the network in a congested state, i.e. flow #2 decreases its rate in the next iteration.
CC_R(2) = 7.33. new_DR(2) = infinity.
3 a) new_S_CR = 11.33; DELTA = -2.
3 b) FSE_R(2) = 7.33. DELTA is negative, hence S_CR = 9.33;
DR(2) = 7.33.
3 c) Flow 1 has P(1) = -1, hence it is deleted from the FSE.
S_P = 0.5.
3 d) Rate(2) = min(infinity, 0.5/0.5*9.33 + 0) = 9.33.
3 e) FSE_R(2) = DR(2) = 9.33.
The resulting FSE looks as follows:
-------------------------------------------
| # | FGI | P | FSE_R | DR | Rate |
| | | | | | |
| 2 | 1 | 0.5 | 9.33 | 9.33 | 9.33 |
-------------------------------------------
S_CR = 9.33, TLO = 0