Host-to-host congestion control is an important technology that avoids network congestion and improves network transmission performance by controlling the transmission rate. However, it is difficult for host-to-host congestion control mechanisms to remain effective in dynamic networks due to factors such as imperfect feedback information, error-prone congestion detection, slow convergence control algorithm, etc. In order to provide a basis for the development of new mechanisms, this paper provides a comprehensive review of control models, congestion detection and control algorithms, as well as evaluation indicators and the main challenges associated with such networks. Furthermore, the paper discusses the potential of intelligent algorithms and edge-host cooperation in host-to-host congestion control. host-to-host congestion control, control model, congestion detection algorithm Communication networks have seen a revolutionary shift in recent decades, largely due to soaring data consumption and the widespread adoption of connected devices [1]. As the number of devices and data usage surge, network congestion is emerging as a critical concern once again. Moreover, applications like live broadcasting and gaming, which are increasingly popular, demand stringent requirements for low latency, high bandwidth, and stable host-to-host communication [2, 3]. Consequently, refining the host-to-host congestion control mechanism has become an urgent practical matter.
through network feedback signals, the paper effectively compares their strengths and weaknesses.
We highlight the main challenges in mechanism design, delving into how intelligent algorithm and edge computing technologies could address issues like hosts collaboration, feedback delay, and inaccuracy.
The structure of the paper unfolds as follows: Section 2 classifies and compares control models, while Section 3 provides a summary of congestion detection. Section 4 delves into the analysis of control algorithms, and Section 5 introduces the evaluation indicators. Section 6 elucidates the main challenges faced in mechanism design. Section 7 discusses potential future directions, and the paper concludes in Section 8.
Host-to-host congestion control models can be categorized based on the involvement of switches into implicit feedback model and explicit feedback model. The implicit feedback model operates without direct communication from switches, whereas the explicit feedback model relies on direct signals or data from switches to manage congestion. This distinction is vital for understanding the underlying mechanisms and effectiveness of each approach in different network environments.
The implicit feedback model is shown as Figure 1. This model is fundamentally composed of the sender and the receiver. The basic operation process can be outlined in the following steps: 1. The sender initiates the process by transmitting packets at a predetermined rate. 2. Upon receiving these packets, the receiver generates ACKs (acknowledge packets). 3. The receiver then sends these ACKs back to the sender. 4. The sender, upon receiving the ACKs, analyzes them to extract the network state. 5. Based on the results of this congestion detection, the sender implements a control algorithm. 6. The sender adjusts its packet sending rate according to the outputs of the control algorithm.
The emergence of the implicit feedback model can be traced back to post-1986
developments, driven by the early switches’ limitations in providing network status
information to terminals. This led to the development of various host-to-host congestion
control mechanisms based on this model, such as Tahoe [
As illustrated in Figure 2, the explicit feedback model is composed of three key components: the sender, the switch, and the receiver. The operation process unfolds as follows: 1. The sender starts by transmitting packets at a predetermined rate. 2. As packets pass through, the switch embeds network status information into them. 3. The receiver, upon receiving enhanced packets, adds network status information into ACKs. 4. The receiver then sends these ACKs back to the sender. 5. The sender analyzes the ACKs to extract network status information. 6. Based on the congestion detection, the sender implements a specific control algorithm. 7. The sender adjusts its transmission rate according to the results of the control algorithm.
The explicit feedback model gained prominence following the introduction of ECN
(Explicit Congestion Notification) in 2001, as per RFC 3168 [
Through the above analysis, the implicit feedback model is characterized by its straightforward structure, ease of implementation, and excellent scalability. However, it has a limitation in collecting detailed network feedback, such as queue size and link utilization.
The explicit feedback model enhances the implicit model by providing more detailed link information, such as queue size and link utilization, for a deeper network understanding. However, it has scalability and deployment challenges due to higher network device capability requirements.
Network status collection is crucial for detecting congestion effectively. Here’s a summary of the five primary methods for collecting network status information: 1. Using Packet Transmission Status: This basic method uses sent packets and received ACKs to calculate RTT (round-trip time), infer available bandwidth from ACK rates, and detect packet loss from ACKs. It’s simple, but limited in the data it can collect. 2. Using SDN Controller [22]: In SDN networks, the controller provides a full view, collecting data like queue size and delay from switches. For instance, TCCS mechanism [23] uses OpenFlow protocol to collect switch queue size for addressing TCP incast issues. However, larger networks and loads can affect the timeliness of data collection.
Congestion detection algorithms categorize the network into congested and uncongested states using network status information. The normalized representation can be described as follows: fcongestion = tfraulsee condition1 otherwise
The condition1 denotes boundary conditions and its setting depends on the specific network feedback information. Congestion detection algorithms can be categorized into seven types based on the network status information they utilize.
The Loss-Based detection algorithm uses packet loss as a key indicator of network
congestion. Packet loss is typically identified by observing duplicate ACKs. Notable
LossBased congestion detection mechanisms include TCP Tahoe [28], TCP Reno [29], and TCP
NewReno [
otherwise NACKi represents the number of times ACKi.
The queue size measures network congestion, and RTT mirrors this by reflecting the time from packet send to ACK receipt. RTT fluctuates due to network queuing, with its average ( ) rising with queue size. The RTT range widens with network load (ratio of packet arrival to departure rate), given as (−(1 − ) − 1 (1 − ) − 1 ), where is a window factor. Thus, RTT serves to evaluate network congestion. The RTT is calculated using the following formula: (1) (2)
R(tc ) = tc − ts −σ fcongestion = tfraulsee
R ≥ Thigh otherwise
Here denotes the sending time of packet i, represents the time when the sender receives ACKi, and stands for an error factor.
There exist two types of congestion detection algorithms based on RTT:
1. Instantaneous RTT-Based Congestion Detection
represents the most recent measured value of RTT, and ℎ ℎ is a threshold factor.
There are congestion detection mechanisms grounded in instantaneous RTT, examples
being TIMELY [
2. Average RTT-Based Congestion Detection
RS = αRS + (1 −α )R, fcongestion = tfraulsee
RS ≥ Thigh otherwise
Similar to the instantaneous RTT approach, denotes the estimated value of RTT [28], the variable α represents a smoothing factor. Schemes based on average RTT include Vegas [31] and FAST TCP [32], among others.
In the congestion control pipeline model, Figure 3 illustrates the interrelationships among
RTT, delivery rate, and the amount of data in flight (i.e., data sent but not yet acknowledged)
[
The Figure 3 shows that the optimal network transmission performance occurs where the blue and green lines intersect, indicating the lowest RTT and highest delivery rate. In (3) (4) (5) Rα (t) = min(R(t)),
∀t ∈ [t − WR ,t]
( ) denotes the latest measured RTT, and represents a window factor.
The formula for calculating the maximum delivery rate [
B(t) = max(Rd(t)),
∀t ∈ [t − WB ,t] ( ) = /∆ , where is the number of ACKs received during ∆ . is a window factor.
In accordance with the definition of BDP, the BDP-Based congestion detection formula is: fcongestion = tfraulsee
N flight ≥ Rα ⋅ B
otherwise
ℎ represents the amount of data in flight, is the minimum RTT, and is the
maximum delivery rate. BDP-Based congestion detection mechanisms, such as BBR [
fcongestion = tfraulsee getCNP = true otherwise fcongestion = tfraulsee
Rsum / C ≥ ϕ
otherwise
the BDP-Based Detection Algorithm, the blue line’s region signifies no network congestion,
while other areas suggest congestion. The Bandwidth-Delay Product (BDP) is calculated as
the product of the minimum RTT and the maximum delivery rate, using statistical data for
these values. The formula for the minimum RTT [
ECN-Based congestion detection mechanisms, such as DCTCP [25] and D2TCP [34], utilize these principles to effectively detect and respond to network congestion.
represents the total traffic of the bottleneck link, represents the bandwidth of
the bottleneck link, and is a threshold factor. Link-Utilization-Based congestion
detection mechanisms, such as HPCC [
ECN is a mechanism that uses the last two bits of the DSCP (Differentiated Services Code Point) field in the IP header to signal congestion. When a switch’s queue size exceeds a set threshold, it marks subsequent packets with ECN. Upon receiving an ECN-marked packet, the receiver generates a Congestion Notification Packet (CNP) and forwards it to the sender. This process allows the detection of network congestion, and the formula is as follows:
In the context of network congestion, link utilization serves as a direct indicator of the congestion level. The congestion detection formula based on link utilization is expressed as:
Equation-based congestion detection evaluates network state by constructing a utility function. The formula based on equations is expressed as: (11) (12) true fcongestion = false
F(x1, x2 ,..., xN ) ≥ Thigh otherwise represents the utility function. 1, 2 represent network status. ℎ ℎ is a threshold factor. Equation-based congestion detection mechanisms allow for customizable design to fit specific requirements. For instance, the network performance-oriented congestion control framework [36] assesses network status by constructing a utility function based on throughput, loss rate, and delay.
Practical congestion control mechanisms often employ a combination of algorithms. The congestion detection formula based on composite approach is expressed as: fcongestion = tfraulsee f1 = true or f2 = true otherwise 1 and 2 represent the results of certain detection algorithms. Composite-ApproachBased Detection mechanisms leverage these principles to combining the advantages of multiple detection methods. For example, TCP Africa [37] integrates both loss-based and RTT-based algorithms for effective congestion detection.
Loss-Based Detection Algorithm: The Loss-Based detection algorithm operates on a simple principle and can be implemented in the implicit feedback model. It effectively determines network congestion, serving as the fundamental detection algorithm for TCP. However, it lacks the ability to differentiate between packet loss due to damage and congestion, performing poorly in high-error-rate networks like wireless networks. It exhibits low sensitivity in low congestion levels, leading to potential buffer overflow issues.
RTT-Based Detection Algorithm: The RTT-Based detection algorithm is implementable in the implicit feedback model, allowing the adaptation of congestion detection thresholds to different environments. Yet, its accuracy is influenced by the randomness of RTT, and it suffers from a feedback time delay problem. As congestion intensifies, the RTT feedback duration increases, resulting in delayed congestion control.
BDP-Based Detection Algorithm: Implementable in the implicit feedback model, the BDP-Based detection algorithm is insensitive to packet loss, avoiding misjudgments caused by damage-related losses in the Loss-Based detection. It effectively determines worsening congestion based on RTT sensitivity. However, it heavily relies on RTT and has a long detection period, leading to poor performance in highly dynamic environments, such as wireless networks.
ECN-Based and Link-Utilization-Based Detection Algorithms: Both ECN-Based and Link-Utilization-Based detection algorithms can only be implemented in the explicit feedback model. They accurately determine network congestion and proactively control congestion through factor settings. However, they require network devices to support corresponding protocols, resulting in poor scalability.
Equation-Based and Composite-Approach-Based Detection Algorithms: The Equation-Based detection algorithm establishes a mapping between network status information and congestion using complex functions, offering fine granularity. The Composite-Approach-Based detection algorithm combines the advantages of multiple detection methods to improve adaptability. However, these algorithms have high complexity, and their performance is challenging to guarantee in dynamic environments.
Disadvantages Misjudgment during packet loss;
Buffer overflow problems.
Limited accuracy due to delay;
Feedback delay problem.
Heavy reliance on RTT;
Long detection period; Poor performance in dynamic
environments.
Complex structure;
Poor scalability.
High complexity; Unstable performance in dynamic environments.
High complexity; Unstable performance in dynamic environments.
The control algorithm computes the new sending rate based on congestion detection. The basic strategy is to decrease the sending rate when congestion occurs and increase the sending rate when there is no congestion. Its normalized representation is RC ⋅ A − B Rnew = RC ⋅C + D fcongestion = true fcongestion = false , represents the new sending rate. represents the current sending rate. , , and are the control parameters whose values depend on the network feedback information. It should be noted that there is a corresponding linear relationship between the sending rate and the congestion window, and that adjusting the congestion window can be converted equivalently to adjusting the sending rate. According to the network feedback information and calculation rules, six typical control algorithms are selected to be analysed in this section. (13)
The TCP Reno algorithm encompasses several key components, including the slow start, congestion avoidance, timeout retransmit, fast retransmit, and fast recovery algorithms. 1. Slow start algorithm
When the congestion window (cwnd) is less than the slow-start threshold (ssthtesh), and a new ACK is received, cwnd is incremented by 1 (in MSS, Maximum Segment Size units). 2. Congestion avoidance algorithm When cwnd ≥ ssthtesh, upon receiving a new ACK, cwnd=cwnd+1/cwnd. 3. Timeout retransmission algorithm
If RTT>RTO (the retransmission timeout), ssthtesh=max(2, cwnd/2), and cwnd=1, entering the slow-start state.
4. Fast retransmit algorithm 5. Fast recovery algorithm
Upon receiving 3 duplicate ACKs, ssthtesh=max(2, cwnd/2), and cwnd=cwnd/2. This triggers the fast recovery state.
In response to duplicate ACKs, cwnd=cwnd+1; upon receiving a new ACK, cwnd=ssthresh, transitioning into the congestion avoidance state.
0, p(t) = pmax ⋅(q(t) − Kmin), 1, q(t) ≤ Kmin
Kmin < q(t) ≤Kmax q(t) > Kmax (14) (15)
Ri (t) = τ i (t) = q(t) C
Wi (t) τi
i + Dprop dWi(t) = dt
1 − Wi(t) τi(t) 2
Ri(t)p(t)
1. Stability and Proof remains constant. Assuming
If the algorithm is stable, there must be a point where the sending rate of all flows = 0, the equations at the stable point can be derived as (16) (17) (18) (19) (20) 2 = Wi2 ⋅ p ∑iN=1 τ i
Wi = C
The equations with two unknowns have a unique solution. Furthermore, the unique solution satisfies 1 = 2 = ⋯ = , indicating the stability of the TCP Reno algorithm. 2. Unfairness and Proof
Assuming flow A and B share the same path, with ( ) > ( ), let ( ) = ( ) − ( ). Utilizing equation (18), we can derive: dWA(t) − dWB(t) = p(t) dt 2τ (t)
(WB2(t) − WA2(t)) < 0
The decreasing function ( ) leads to equal congestion windows 1 = 2 = ⋯ = across flows, showing algorithm convergence. However, because ( ) = ( )/ , the algorithm does not ensure fair bandwidth sharing, lacking inherent fairness.
Patched TIMELY algorithm consists of two parts: RTT algorithm and rate algorithm. 1. RTT algorithm
RTT = tc − ts − seg.size
NICrate refers to the time when packet is sent, and indicates the time when the is received. NICrate denotes the bandwidth capacity of the Network Interface Card (NIC), while seg.size represents the size of an individual data burst.
2. Rate algorithm R + δ R = R ⋅ (1 − β ⋅ (1 − Thigh / newRTT )) δ ⋅ (1 − weight) + R ⋅ (1 − β ⋅ error ⋅ weight) newRTT < Tlow newRTT > Thigh otherwise
represents the newly measured round-trip time. The acts as a step modifier in the algorithm. and ℎ ℎ
are critical threshold factors that guide the rate adjustment. Additionally, error and weight function as regulatory factors in this context. The algorithm employs specific formulas, incorporating and ∗ as further regulatory elements.
g = r(t) / DminRTT , r(t) = (1 −α )r(t −τ *) +α∆RTT , error = newRTT − Tlow ,
Tlow weight = 2g + 0.5 0 1 4.2.2. Fluid model α τ* (−gi (t) + q(t − τ') − q(t − τ' − τ*)
C ⋅ DminRTT
) 0 wi = 12gi + 0.5
1. Stability and Proof Bandwidth of 13 ottleneck link Multiplicative decrease factor
Considering the characteristics of a constant transmission rate and a stable queue size at equilibrium, setting equation (24, 25) to zero leads to the following conclusion: Ri = C
N q* = NδCTlow + CTlow
βC The unique solution implies that the algorithm demonstrates stability.
2. Fairness and Proof ∗
< < ∗ ℎ ℎ, The derivative of ( ) = ( ) − ( ) is: In the scenario where flows A and B share a bottleneck link, with ( ) > ( ) and dt τ* convergence. This ensures fair bandwidth sharing among flows in the Patched TIMELY algorithm model, reflecting its fairness characteristic.
TCP BBR consists of four main algorithms: Start-up, Drain, ProbeBW, and ProbeRTT. For an in-depth understanding of the round-trip propagation time ( ) and the methods used to measure the bottleneck bandwidth (BW), one should refer to Section 3.2.3. 1. Start-up algorithm
Start-up phase fills the network pipe and transitions to Drain when the bandwidth estimate stabilizes (no more than 1.25x increase over three assessments). During this phase, (30) (31) R(t) = ln 2 2 ⋅ BW (t), cwnd(t) = ln 2 2 ⋅ BW (t) ⋅ Dprop(t) 2. Drain algorithm
In Drain, once the inflight data falls beneath the BDP threshold, the algorithm transitions to the ProbeBW state. In this state, the calculations for rate and congestion window are as 3. ProbeBW algorithm
ProbeBW algorithm regularly evaluates the bottleneck link’s bandwidth, typically every 8 round-trip propagation times. If
increases within a 10-second window, the algorithm moves to the ProbeRTT state. In ProbeBW, the rate and congestion window are calculated as follows: the sending rate (R) and congestion window (cwnd) are calculated with the following considerations: (32) (33) (34) (35) (36) (37) (38) R(t) = Rgain ⋅ BW(t)
Rgain = [1.25,0.75,1,1,1,1,1,1], cwnd(t) = 2 ⋅ BW (t) ⋅ Dprop(t) 4. ProbeRTT algorithm
The ProbeRTT algorithm runs for a maximum of 200 milliseconds before transitioning. It switches back to Start-up or ProbeBW based on network load. During this state, the algorithm calculates rate and congestion window as follows:
R(t) = BW (t), cwnd(t) = 4(MSS) dq dt Ti (t) =
N i=1 q(t)
C
1. Stability and Proof Bandwidth of bottleneck link
Propagation time of flow i Setting equation (38) to zero yields a specific result: N ∑ Ri (t) = C qi=(1t) = 0
The result shows that the equations have multiple solutions, indicating that TCP BBR has numerous stable points and confirming its inherent stability.
2. Unfairness and Proof be made:
Given ( ) > ( ) for flows A and B on the same path, the following observation can d(RA(t) − RB(t)) = q(t − Dpirop) − q(t) dt
This leads to the conclusion that the rate difference between flows A and B is growing, suggesting that flow A continues to dominate bandwidth at the bottleneck. This behavior indicates a lack of fairness in the algorithm.
DCQCN consists of switch, receiver and sender algorithms.
1. Switch algorithm p(t) = 0 1 q(t) − Kmin Pmax Kmax − Kmin q(t) ≤ Kmin be sent per N microseconds.
Here represents the marking probability. and define the minimum and maximum thresholds, respectively, and denotes the maximum probability limit.
After receiving an ECN-marked packet, the receiver sends a CNP. Maximum one CNP can (39) (40) (41) 3. Sender algorithm
The sender algorithm primarily governs the packet transmission rate ( ) utilizing factors such as α (initial value is 1), ′, , , Timer , and Byte counter . When the sender receives a CNP,
RT = R ,
C
RC = RC (1 −α / 2), α = (1 − g)α + g If sender gets no CNP for ′, If no CNP is received and max(NT, NBC) ≤ F occurs, If no CNP is received and min(NT, NBC) > F occurs, α = (1 − g)α
RC = (RT + RC ) / 2
In other cases,
RT = RT + iRAI i = NT or NBC ,
RC = (RC + RT ) / 2 RT = RT + RAI ,
RC = (RC + RT ) / 2
0 p(t) = q(t) − Kmin pmax Kmax − Kmin 1 q(t) ≤ Kmin dα(i) = g ((1 − (1 − p(t −τ * ))τ'R(Ci) (t−τ* )) − α(i)(t)) dt τ' dRC(i) = − RC(i)(t)α(i)(t) dt
(1 − (1 − p(t − τ*))τRC(i)(t−τ*) ) RT(i)(t) −2τRC(i)(t) RC(i)(t − τ*)p(t − τ*)
2 (1 − p(t − τ*))−B − 1 RT(i)(t) − RC(i)(t) RC(i)(t − τ*)p(t − τ*)
2 (1 − p(t − τ*))−TRC(i)(t−τ*) − 1 dRT(i) = − RT(i)(t) − RC(i )(t) (1 − (1 − p(t − τ*))τRC(i)(t−τ*) ) dt + +
τ RAI RC(i)(t − τ*) RAI RC(i)(t − τ*) (1 − p(t − τ*))FBp(t − τ*)
(1 − p(t − τ*))−B − 1 (1 − p(t − τ*))FTRC(i)(t−τ*)p(t − τ*) (1 − p(t − τ*))−TRC(i)(t−τ*) − 1 (42) (43) (44) (45) (46) (47) (48) (49) (50) (51) DCQCN Model Equation Parameters
Current rate Target rate Decrease factor Time Low threshold High threshold Probability factor Decrease factor Queue size of bottleneck link ∗ ′
1. Stability and Proof
Initially, if the bandwidth is underutilized, the sending rate increases. If it surpasses the bottleneck capacity, congestion occurs, and the sending rate decreases. Therefore, at the stable point, the bottleneck link bandwidth must be fully occupied and the queue size will remain constant. Assuming the queue size at stable time is ∗, the following equations can be obtained.
Combining equation (49-51), we see that Here ( )∗, a, b, c, d, e is denoted as follows： N ∑ RC(i)(t) = C i=1 p* = dα dt
q * −Kmin Kmax − Kmin
Pmax dt dRT = 0 , dR dt
C = 0 a2α (i)* τ 2RAI (b + c)(d + e) = 0 , RC(i) =
, α (i)∗ = 1 − (1 − p* )τ ’RC(i) a = 1 − (1 − p* )τRC(i)
b = ((1 − p* )−B − 1)−1 p* , , c = ((1 − p* )−TRC(i) − 1)−1 p*
d = ((1 − p* )−B − 1)−1(1 − p* )FB p* e = ((1 − p* )−TRC(i) − 1)−1(1 − p* )FTRC(i) p* .
, (52) (53) (54) Let f (p* ) = τ 2RAI (b + c)(d + e)
a2α (i)* flows share ∗, it follows that
R(1)* = R(2)* = ⋅⋅⋅ = R(N)* = C / N
C C C . the continuity principle, when ( ) > 0, there exists ∗ such that
Based on the above analysis, the DCQCN algorithm has a unique stable point, where all flows have equal sending rates. Therefore, the DCQCN algorithm is stable. f (p* ) = R(i)*
C . Since all . When ( ) > 0, (0) = 0 and (1) → +∞. According to
The DCQCN algorithm’s fairness isn’t directly discernible from equation (51) due to the interplay between RC and RT. To prove fairness, the paper uses a discrete method, examining RC changes between CNPs. Here, we first prove two theorems.
Theorem 1. In DCQCN algorithm, the smaller the sending rate of flow i is, the more additive growth occurs between adjacent CNPs.
Proof of Theorem 1. The switch algorithm estimates a flow collects CNPs at a rate of p*RC*∆t. When a CNP is collected, the average packet sending rate is 1/p packets. This means that the sending rates of adjacent CNPs for each flow are the same. DCQCN controls this rate via a timer and byte counter. For equal data sent, the increment of the byte counter is the same, but the timer increments more with smaller sending rates. Therefore, for flows with smaller sending rates, the additive growth between adjacent CNPs occurs more frequently.
Theorem 2. In DCQCN algorithm, ( ) is a converging function.
Proof of Theorem 2. If the time interval between adjacent CNPs of flow i is ∆t, then α (i)(t + ∆t) = (1 − g)∆t/τ '((1 − g)α (i)(t) + g) < (1 − g)1+∆t/τ 'α (i)(t) < α (i)(t) (55)
The function ( ) is monotonically decreasing. Given that ( ) > 0 and 0<g<1, it follows that ( )( + ∆ )>0. By induction, ( ) >0 for all t>0. As ( ) is monotonically decreasing with an upper bound, it must converge.
Below, we study the changes between adjacent CNPs. Let the receiving times of adjacent CNPs be t and t+∆t, besides, the rate decreases at + ( → 0) and then experiences additive growth for ( ) times.
Let ( )( + ) = (1 − 2−1 ( )( ) ( )( ) and ( ) = ∗( ∗ > 0) , according to the DCQCN algorithm and Theorem 2, we get that when the rate increase occurs 0 times, ( )[0] = ( )( ), ( )[0] = ( )( + ), ∆ = ( )[0] − ( )( ) = −2−1 ( )( ) ∗ .By induction, we can obtain that at t+∆t, after N(i) growth times, ∆ = 1 − 2− ( ) − 2− ( )−1 ( )( ) ∗.
Assuming the number of rate increases between adjacent CNPs at the stable point ( ) =
, ∆ = 0 is ( ). According to Theorem 1, if ( )( ) > / for flow i, ( ) < ( ) . We can get that ∆ ( ) = 1 − 2− ( ) −2− ( )−1 ( )( ) ∗ < ∆ ( ) = 0 . So ( )( ) will converge to the stable point where ( )( ) = / . When ( )( ) < / , the
In summary, in the DCQCN algorithm, all flows will share the bottleneck bandwidth. So proof method is the same. the algorithm is fair.
HPCC consists of bottleneck link utilization and congestion window algorithms. 1. Bottlenck link utilization algorithm
U = max(Uj ) Uj = qj + txRatej × T
= C × T q
j C × T + txRatej
C txRatej = ack1.txBytesj − ack0.txBytesj ack1.tsj − ack0.tsj (56) (57) (58) (59) (60) (61)
U represents the bottleneck link utilization, 1 and 0 are two ACKs, T denotes the minimun RTT. For link , , , , . and represent the bandwidth utilization, queue size, sending rate, sending data volume, timestamp and bandwidth, respectively.
2. Congestion window algorithm is a step factor, and η is generally set to 0.95.
W =
W U /η
+ WAI Ra(t) = U j(t) = C1 ∑i Ri(t)
Wa(t)
τ η dWa(t) = (U j(t −τ ) dt −1) Wa(t −τ ) + WAI τ τ
Sending rate of flow a Congestion window size of flow a Control loop delay Bottlenck link of flow a the utilization of link j flow at bottleneck link j Sending rate of flow i Threshold Bandwidth of bottlenck link Additive increase step
1. Stability and Proof Let the left side of equation (58) be zero, then
Wa(t) =
U j(t −τ )WAI
U j(t −τ ) −η For any ( − ), ( ) has a unique solution, so the algorithm is stable. 2. Unfairness and Proof
The increasing function ( ) contradicts the fairness assumption. Thus, HPCC algorithm is unfair.
TCP Drinc leverages deep reinforcement learning to regulate transmission rate. It defines event S as a series of states, represented as = [ 0, 1, . . . , ]. The state space is defined as = [∆ ( ), ( ), ( ), ( ), ( )] . Here, ∆ ( ) indicates the variation in the congestion window size, ( ) signifies the round-trip time, ( ) is the ratio of propagation time to RTT, ( ) highlights the disparity between RTT and propagation time, and ( ) refers to the interval between successive ACKs.
The action space is defined as = [ = + 1; = − 1; = + −1; = − −1; = ]. is the congestion widow size.
The reward is defined as ( ) = ( + ( + ( ))) − ( ). Related functions are listed below:
Assuming the algorithm is fair, for flows with different initial rates, the rate difference between them will decrease over time. If flows A and B have the same path and ( ) > ( ), < . Let ( ) = ( ) > ( ), then (62) (63) U(t) = Uα (z(t)) − βUα (τ RTT (t))
t+L−1 z(t) = ∑ x(l) ⋅ (1 −η )
1 −η L+1 ⋅η l−t l=t log(l) Uα (l) = l1−α 1 −α α = 1 otherwise , ,
In the aforementioned equations, ( ) symbolizes the network throughput at time , which is derived from the congestion window and RTT. The variables , , and are introduced as adjustment factors to fine-tune the algorithm. Importantly, this algorithm is characterized by a dynamic relationship between its inputs and outputs, precluding the formulation of a fluid model equation for analytical purposes.
From the standpoint of control models, algorithms based on packet loss, RTT, and Bandwidth-Delay Product (BDP) are straightforward in their approach, allowing implementation within an implicit feedback model. In contrast, algorithms reliant on ECN and link utilization necessitate an explicit feedback model, entailing more complex protocols.
Regarding algorithm characteristics, the input-output relationship in the first five types of algorithms is typically fixed. Algorithms based on packet loss, RTT, BDP, and ECN struggle to calculate the ideal regulation rate, often resorting to heuristic strategies for incremental adjustments. This approach introduces a degree of latency. Conversely, algorithms focusing on link utilization avoid this drawback but demand significant network feedback data, thus incurring higher bandwidth and computational resource costs.
Control algorithms integrating machine learning exhibit a dynamic control model contingent on specific network feedback signals. These algorithms excel in adapting to network environment changes, automatically adjusting relevant factors to optimize regulation strategies and enhance performance. However, the complexity of designing appropriate reward functions, ensuring swift convergence, and managing unpredictable outcomes makes them inherently complex.
The criteria for assessing host-to-host congestion control are derived from network performance metrics as outlined in [41]. Despite variations in emphasis among different schemes, four key indicators are universally recognized: Throughput, Delay, Packet Loss Rate, and Fairness Index, as referenced in [42].
1. Throughput 2. Delay
Throughput is defined as the quantity of data successfully transmitted over a network per unit of time. This metric serves as a direct indicator of a control mechanism's efficacy. Generally, higher throughput equates to superior performance. The formula for calculating throughput is as follows:
In this formula, ∆t represents the duration of the operational period, while N denotes the total amount of data successfully received by the receiver.
x = N / ∆t (64)
Delay is the total time for a packet's transmission and reception, including sending, transmission, processing, and queuing delays. Optimal network performance is characterized by low delay and its stability, which is often associated with higher throughput and stable transmission quality. For practical measurement, the smoothed RTT is commonly used. The formula is as follows:
T(t) = αT(t) + (1 −α )(t − ts) (65) is the send time for packet i, t is the receipt time, and α is the smoothing factor. 3. Packet Loss Rate
Packet Loss Rate is the ratio of lost packets to the total packets sent over a period, key for analyzing data flows. Higher loss rates may signal network congestion and are critical for assessing congestion control. The lower the rate, the better the performance, ideally. The formula for Packet Loss Rate is as follows: 4. Fairness Index
The Fairness Index serves as a measure of how equitably congestion control mechanisms distribute network resources under congested conditions, quantitatively assessing fairness in resource allocation. A common formula for calculating the Fairness Index [43] is as follows:
is the amount of data successfully received by the receiver in time interval ∆ , and Nsend is the amount of data sent by the sender in the same period.
represents the throughput for the flow . The Fairness Index ranges from 0 to 1, with higher values indicating better fairness. Achieving a high Fairness Index is important for protocol coexistence on the Internet, making it a key metric for assessing congestion control protocols.
A systematic analysis reveals three critical aspects of host-to-host congestion control: realtime collection of network status, precise congestion detection, and efficient packet sending rate control. To address these aspects, host-to-host congestion control mechanisms encounter several challenges: 1. Hosts Coordination
Host-to-host congestion control operates as a distributed system without a central control authority. Each host independently executes control algorithms. Inconsistencies or conflicts in the behavior of different hosts can lead to uneven bandwidth allocation, creating fairness issues. This disparity can also trigger network congestion, adversely impacting network transmission performance. Thus, achieving effective coordination among hosts represents a significant challenge.
2. Feedback Delay
Host-to-host congestion control relies on a feedback mechanism, requiring hosts to gather network feedback and adjust their sending rates accordingly. This process inherently introduces a delay, especially during periods of network congestion, potentially hindering the timely acquisition of current network status. Such delays can result in suboptimal decision-making, affecting congestion control efficacy. Addressing feedback delay is, therefore, a pivotal challenge.
3. Inaccurate Feedback
Beyond the issues caused by feedback delay, the accuracy of feedback in host-to-host congestion control is also compromised by factors like network noise, packet loss, and inherent randomness (e.g., RTT variation). These elements can lead to erroneous congestion control decisions. Consequently, resolving the issue of inaccurate feedback is another crucial challenge.
Through the examination of existing research and considering the latest technological trends, we identify two key areas that hold significant potential for future exploration. 1. Edge-host Collaboration Control Model
Using the idea of edge computing, the Edge-host collaboration control model could offload some of the congestion detection and control functions to the edge switches. In terms of distribution, edge switches exhibit a more centralized nature compared to hosts, offering several advantages for congestion detection and control. Firstly, edge switches can aggregate information from multiple hosts, thereby providing more comprehensive data for congestion detection. Secondly, the feedback path can be shortened by leveraging edge switches. Thirdly, the utilization of edge switches can minimize the redundant collection of network state information, consequently reducing transmission overhead. Lastly, the integration of edge switches can effectively coordinate host behavior locally and address local fairness issues. Hence, the Edge-Host Collaboration Control Model signifies a promising research direction.
2. Intelligent Congestion Detection and Control Algorithm
Intelligent congestion detection and control algorithm has emerged as a prominent area of research in recent years, yielding substantial advancements. Innovative mechanisms like Orca [44] and Sage [45] employ deep reinforcement learning to craft intelligent algorithms, facilitating efficient data transmission in intricate network environments. This algorithm, rooted in mathematical and statistical principles, discerns the patterns of network congestion changes. Through logical reasoning, it calculates the optimal sending rate based on network feedback information, thereby enhancing congestion control performance.
Despite current challenges in applying intelligent algorithms to congestion control— such as intricate model training, complex reward function design, and slow convergence— their successes in fields like computer vision, speech recognition, and AIGC underscore their capability to address complex issues. With ongoing technological progress, intelligent algorithms are poised to access more extensive network information and adeptly learn network characteristics and congestion control strategies. Consequently, the Intelligent Congestion Detection and Control Algorithm is set to significantly enhance its efficiency and adaptability, establishing itself as a pivotal area for future research.
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