# A Multi-Parameter Comprehensive Optimized Algorithm for MPTCP Networks

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## Abstract

**:**

## 1. Introduction

## 2. Path Management, Congestion Control and Buffer Configuration

#### 2.1. Path Management Algorithms

#### 2.2. Congestion Control Algorithms

#### 2.3. Buffer Function and Configuration

## 3. MPCOA Algorithm

- TOP: = [Site Name, Internet Service Provider, Bandwidth], a topology structure information set of heterogeneous transmission network;
- PM: = {PCDC, FullMesh}, a set of path management policies, an enumerated value;
- CC: = {Cubic, OLIA, Hybla, Reno, Scalable, Vegas}, a set of congestion control algorithms, an enumerated value.

- OTP: = the relative maximum throughput, which is the main constraint of this algorithm;
- OBS: = the relative minimum buffer size;
- OCC: = the suitable CC algorithm, one of CC;
- OPM: = the suitable PM policy, one of PM.
- These four parameters are output simultaneously.

_{1}, …, f

_{5}, which can be seen in Equations (3)–(8) respectively. The corresponding algorithm execution steps are illustrated in Figure 2.

- According to the topology of the MPTCP network, the available subflow’s set is obtained,$$\begin{array}{l}sp={f}_{1}\left(top\right),sp\in SP,top\in TOP\\ SP=\left\{s{p}_{1},\cdots ,s{p}_{i},\cdots ,s{p}_{N}\right\},N={N}_{s}\times {M}_{r}\end{array}$$
_{s}is the number of interfaces at the sending side (i.e., the number of local ISPs); M_{r}is the number of interfaces at the receiving side (i.e., the number of remote ISPs). Actually, this available subflows of SP are all used for transmission in FullMesh policy; - Based on the set of input parameters, the throughput TP of each available subflow can be measured,$$\begin{array}{l}tp={f}_{2}\left(sp,cc\right),tp\in TP,cc\in CC\\ TP=\left\{T{P}_{1},\cdots ,T{P}_{i},\cdots \right\},i=1,2,\cdots ,N\end{array}$$
- With the obtained TP, the IF value Ω of all available subflows are calculated by:$${\Omega}_{i}={f}_{3}\left(tp\right)=1-\frac{{\displaystyle \sum _{t=T+1}^{2T}T{P}_{i}\left(t\right)}}{{\displaystyle \sum _{t=0}^{T}T{P}_{0}\left(t\right)}}$$
_{i}is the IF value of i-th subflow, TP_{0}(t) is the total throughput at the time t, TP_{i}(t) is the throughput at time t when the i-th subflow does not participate in transmission, and T is the transmission time, see Figure 3. In Figure 3, from time 0 to time T, all subflows participate in transmission, and the throughput TP_{0}(t) at each time is calculated, which is a function of time t (t$\in $[0, T]). From time T to time 2T, the i-th subflow (i$\in $[1, N]) does not participate in the transmission, other subflows continue to transmit data, and the throughput TP_{i}(t) is calculated which is also a function of time t (t$\in $[T, 2T]). Then the IF value Ω can be calculated by Equation (5); - Using IF value, the available subflow set SP is divided into optional subflow subset SP* and standby subflow subset. The optional subflow SP* is used for transmission in PCDC,$$\begin{array}{l}osp={f}_{4}\left(s{p}_{i},{\Omega}_{i}\right),osp\in SP\ast \\ SP\ast =\left\{s{p}_{1},\cdots ,s{p}_{i},\cdots s{p}_{N}\right\}\backslash \left\{s{p}_{i}|{\Omega}_{i}<0\right\}\end{array}$$
- According to the SP* sets obtained in Step 4 and CC, remeasure the throughput to obtain TP* (for FullMesh, throughput does not need to remeasure, TP is TP*),$$rtp={f}_{2}\left(osp,cc\right),rtp\in TP\ast $$
- Based on the result of Step 5, taking the input parameter set CC, PM, TP* and BS as input, a prediction model between buffer size BS and throughput TP, which varies with CC and PM, can be established by using multiple regression analysis method through a scikit-learn tool [26]. The model shows like function f
_{5}, see Equation (8). When the most essential two criteria values of prediction model after N times run: once R-Squarer and p-value have reached the idea range (R-Square ≥ 0.90 (interval [0, 1]) and p-value ≤ 0.05), which means that this prediction model is a commonly accepted in statistical society. The detail of model construction can be seen in [4],$$\begin{array}{c}tp={\phi \left(bs,pm,cc\right)|}_{\begin{array}{l}pm=P{M}_{i}\\ cc=C{C}_{j}\end{array}}={{f}_{5}\left(bs\right)|}_{\left(P{M}_{i},C{C}_{j}\right)}\\ P{M}_{i}\in PM\left(i=1,2\right),C{C}_{j}\in CC\left(j=1,2,\cdots ,6\right)\end{array}$$ - Obtain the comprehensive optimized outputs. The final goal of this algorithm is to find the minimum buffer size BS when maximizing the throughput TP, and determine the corresponding PM and CC accordingly,$$\{\begin{array}{l}{{f}_{5}|}_{\left(P{M}_{i},C{C}_{j}\right)}:BS\to TP\\ \begin{array}{cc}s.t.& bs\in BS\left(BS=\left\{0.5,1.0,1.5,\cdots ,30.0\right\}\right),tp\in TP,\end{array}\\ \underset{bs}{\mathrm{min}}\left(\mathrm{arg}\mathrm{max}\left({{f}_{5}|}_{\left(P{M}_{i},C{C}_{j}\right)}\right)\right)\end{array}$$

Algorithm 1:MPCOA | |

1: | Inputs: CC = {Cubic,OLIA,Hybla,Reno,Scalable,Vegas}, PM = {PCDC, FullMesh}, TOP = [Site Name, ISP, Bandwidth] |

2: | Outputs: OTP, OBS, OCC, OPM |

3: | Initialize: BS = {0.5,1.0,1.5,…,30.0}, SP* = {}, δ = 0.07 |

4: | Start: |

5: | Obtain SP from TOP |

6: | For cc in CC do |

7: | For pm in PM do |

8: | If pm is PCDC then |

9: | Calculate TP_{i} for each subflow sp_{i} in SP, then obtain Ω_{i} |

10: | ${\Omega}_{i}=1-\frac{{\displaystyle {\sum}_{t=T+1}^{2T}T{P}_{i}\left(t\right)}}{{\displaystyle {\sum}_{t=0}^{T}T{P}_{0}\left(t\right)}}$ |

11: | If Ω_{i} > 0 then |

12: | SP* = SP* + sp_{i} |

13: | End If |

14: | Else If pm is FullMesh then |

15: | SP* = SP |

16: | End If |

17: | End For |

18: | Measure and obtain the throughput TP* |

19: | Using sklearn.LinearRegression(BS,PM,TP*), get the regression model |

20: | $tp={f}_{5}\left(bs\right)$ |

21: | Calculate the maximum tp_{cc} of TP |

22: | Calculate the minimum bs_{cc} in [(1-δ)tp_{cc,} tp_{cc}] according to the inverse function ${f}_{5}^{-1}$ |

23: | End For |

24: | bs_{min} = min(bs_{cc}) |

25: | OBS = bs_{min} |

26: | Making use of OBS and the function ${f}_{5}$, obtain OTP, OCC and OPM |

27: | Outputs: OTP, OBS, OCC, OPM |

## 4. Measurement Scenario

- Ubuntu Linux 16.04 “Xenial Xerus” LTS with Linux kernel version 4.19.128;
- Linux MPTCP version 0.95;
- Buffer size limit set to 30 MiB, unless otherwise specified, to prevent throughput limitations by lack of buffer space [2].

## 5. Result Analysis

- An inter-continental setup (between Norway and China) in Section 5.1;
- A regional setup (between two cities in Norway) in Section 5.2;
- A trans-continental setup (between two cities in different countries of Europe) in Section 5.3.

#### 5.1. SRL to HU

_{1}= 1, CC

_{2}= CC

_{3}= CC

_{4}= CC

_{5}= CC

_{6}= 0, then tp = 3.49 + 4.85bs−0.15bs

^{2}).

_{max}= 80.27 Mbit/s, and the corresponding BS is bs = 18.12 MiB, PM is PCDC and CC is Hybla. Considering Equation (10), with sacrificing δ = 7% the throughput, the throughput is 74.65 Mbit/s, and the corresponding buffer size is 12.36 MiB. 7% is the empirical value obtained through many experiments. Since buffer resources are more precious, we can reduce the waste of buffer resources by sacrificing a little throughput without affecting network performance. Therefore, the final output of the MPCOA algorithm is OBS = 12.36 MiB, OPM = PCDC, OCC = Hybla, and OTP = 74.65 Mbit/s.

#### 5.2. UNIS to HiN

_{max}= 286.73 Mbit/s, and the corresponding BS is bs = 17.83 MiB when PM is PCDC and CC is Cubic. Considering Equation (10), by sacrificing δ = 7% throughput, the final output of the MPCOA algorithm is OBS = 9.22 MiB, OPM = PCDC, OCC = Cubic and OTP = 266.66 Mbit/s. Figure 7 presents the throughput test results on NorNet Core testbed for both path managers and all CC algorithms without considering MPCOA algorithm, where the buffer size is set to be 30 MiB. The test results show that the combination of PCDC and Cubic with the maximum throughput of 274.2 Mbit/s is the best choice, which is consistent with the MPCOA output.

#### 5.3. UiT to HAW

_{max}= 0.87 Mbit/s, and the corresponding BS is bs = 30 MiB when CC is Scalable, and PM could be either FullMesh or PCDC. Actually, from Table 1, we can see that the two ISPs of UiT almost have the same bandwidth, and therefore the networks between UiT and HAW are homogeneous networks, where the IFs of all subflows are positive, see Table 2. In this case, PCDC is equivalent to FullMesh. In other words, both PM algorithms can achieve almost the same performance. Since PCDC is more complicated than FullMesh, we can directly choose to use FullMesh in a homogeneous network. According to Table 4, when bs decreases, tp does not change too much. Therefore, considering Equation (10), by sacrificing δ = 7% throughput, the final output of MPCOA algorithm is OBS = 0.5 MiB, OPM = FullMesh, OCC = Scalable and OTP = 0.81 Mbit/s. Comparing BS = 30 MiB and OBS = 0.5 MiB, it can be seen that a lot of buffer resource is saved by using Equation (10).

#### 5.4. Optimized Solutions

## 6. Conclusions and Outlook

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 5.**Relationship between buffer size and throughput for SRL to HU with: (

**a**) FullMesh; (

**b**) PCDC.

**Figure 6.**Throughput test results on NorNet Core testbed for SRL to HU with different PM and CC, without MPCOA.

**Figure 7.**Throughput test results on NorNet Core testbed for UNIS to HiN with different PM and CC, without MPCOA.

**Figure 8.**Throughput test results on NorNet Core testbed for UiT to HAW with different PM and CC, without MPCOA.

Site | Location (City, Province, Country) | Internet Service Provider (ISP) | Bandwidth (Down/Up) Kbit/s |
---|---|---|---|

Simula Research Laboratory (SRL) | Fornebu, Viken, Norway | Uninett (U) | 100,000/100,000 |

Kvantel (K) | 1,000,000/1,000,000 | ||

PowerTech (P) | 6000/256 | ||

Telenor (T) | 3000/768 | ||

Hainan University (HU) | Haikou, Hainan, China | CERNET (C) | 100,000/100,000 |

CnUnicom (CU) | 20,000/20,000 | ||

Universitetet på Svalbard (UNIS) | Longyearbyen, Svalbard, Norway | Uninett (U) | 100,000/100,000 |

Telenor (T) | 10,000/10,000 | ||

Høgskolen i Narvik (HiN) | Narvik, Nordland, Norway | Uninett (U) | 100,000/100,000 |

PowerTech (P) | 6000/512 | ||

Broadnet (B) | 16,000/768 | ||

Universitetet i Tromsø (UiT) | Tromsø, Troms, Norway | PowerTech (P) | 6000/512 |

Telenor (T) | 2000/384 | ||

Hochschule Hamburg (HAW) | Hamburg, Hamburg, Germany | DFN (D) | 100,000/100,000 |

Scenario | From ISP | To ISP | Subflow | Ω | |||||
---|---|---|---|---|---|---|---|---|---|

Cubic | OLIA | Hybla | Reno | Scalable | Vegas | ||||

SRL-HU | Kvantel | CERNET | K-C | 0.496 | 0.376 | 0.396 | 0.469 | 0.292 | 0.356 |

Kvantel | CnUnicom | K-CU | 0.248 | 0.359 | 0.174 | −0.027 | 0.19 | 0.135 | |

PowerTech | CERNET | P-C | −0.313 | 0.098 | −23.667 | 0.174 | −0.324 | 0.086 | |

PowerTech | CnUnicom | P-CU | 0.184 | 0.172 | −0.366 | −0.496 | 0.24 | 0.077 | |

Telenor | CERNET | T-C | 0.032 | −0.54 | −40.713 | 0.14 | 0.057 | 0.08 | |

Telenor | CnUnicom | T-CU | 0.046 | 0.105 | −13.235 | 0.085 | 0.02 | 0.057 | |

Uninett | CERNET | U-C | 0.239 | 0.305 | 0.209 | 0.235 | 0.301 | 0.325 | |

Uninett | CnUnicom | U-CU | 0.063 | 0.113 | 0.258 | 0.165 | 0.072 | 0.189 | |

UNIS-HiN | Telenor | Broadnet | T-B | −0.014 | 0.017 | −0.019 | 0.061 | −0.154 | 0.014 |

Telenor | PowerTech | T-P | −0.063 | 0.002 | 0.001 | 0.028 | −0.03 | −0.004 | |

Telenor | Uninett | T-U | −0.011 | −0.047 | −0.013 | −0.034 | 0.036 | 0.027 | |

Uninett | Broadnet | U-B | −0.046 | 0.025 | −0.025 | 0.02 | −0.008 | 0.094 | |

Uninett | PowerTech | U-P | −0.075 | 0.054 | −0.003 | −0.001 | 0.004 | −0.13 | |

Uninett | Uninett | U-U | 0.897 | 0.916 | 0.921 | 0.92 | 0.923 | 0.852 | |

UiT-HAW | PowerTech | DFN | P-D | 0.59 | 0.61 | 0.55 | 0.57 | 0.61 | 0.58 |

Telenor | DFN | T-D | 0.44 | 0.46 | 0.44 | 0.43 | 0.45 | 0.44 |

CC | Optional Subflow Subset | ||
---|---|---|---|

SRL-HU | UNIS-HiN | UiT-HAW | |

Cubic | {K-C, K-CU, P-CU, T-C, T-CU, U-C, U-CU} | {U-U} | {P-D, T-D} |

OLIA | {K-C, K-CU, P-C, P-CU, T-CU, U-C, U-CU} | {T-B, T-P, U-B, U-P, U-U} | {P-D, T-D} |

Hybla | {K-C, K-CU, U-C, U-CU} | {T-P, U-U} | {P-D, T-D} |

Reno | {K-C, P-C, T-C, T-CU, U-C, U-CU} | {T-B, T-P, U-B, U-U} | {P-D, T-D} |

Scalable | {K-C, K-CU, P-CU, T-C, T-CU, U-C, U-CU} | {T-U, U-P, U-U} | {P-D, T-D} |

Vegas | {K-C, K-CU, P-C, P-CU, T-C, T-CU, U-C, U-CU} | {T-B, T-U, U-B, U-U} | {P-D, T-D} |

**Table 4.**Maximum throughput calculation with different PM and CC for SRL to HU, UNIS to HiN, and UiT to HAW.

Scenario | Relationship among Different Congestion Control (CC), Path Management (PM), Throughput and Buffer Size Obtained from the Prediction Models | R and P | Calculation Results | ||
---|---|---|---|---|---|

CC | PM | ||||

FullMesh | PCDC | ||||

SRL-HU | Cubic | tp = 3.49 + 4.85bs − 0.15bs^{2} | tp = 6.31 + 5.45bs − 0.17bs^{2} | R-square = 0.80 p-value < 0.00001 | tp_{max} = 80.27bs = 18.12 |

OLIA | tp = 7.01 + 5.26bs − 0.15bs^{2} | tp = 2.41 + 6.51bs − 0.17bs^{2} | |||

Hybla | tp = 5.91 + 5.00bs − 0.15bs^{2} | tp = 24.49 + 6.16bs − 0.17bs^{2} | |||

Reno | tp = 4.47 + 4.59bs − 0.15bs^{2} | tp = 3.49 + 5.30bs − 0.17bs^{2} | |||

Scalable | tp = 3.49 + 4.85bs − 0.15bs^{2} | tp = 1.99 + 5.64bs − 0.17bs^{2} | |||

Vegas | tp = 4.67 + 4.63bs − 0.15bs^{2} | tp = 0.47 + 5.38bs − 0.17bs^{2} | |||

UNIS-HiN | Cubic | tp = 171.62 + 11.08bs − 0.29bs^{2} | tp = 200.82 + 9.63bs − 0.27bs^{2} | R-square = 0.94 p-value < 0.00001 | tp_{max} = 286.73bs = 17.83 |

OLIA | tp = 102.04 + 13.16bs − 0.29bs^{2} | tp = 118.6 + 12.25bs − 0.27bs^{2} | |||

Hybla | tp = 109 + 13.48bs − 0.29bs^{2} | tp = 159.5 + 11.42bs − 0.27bs^{2} | |||

Reno | tp = 111.74 + 13.54bs − 0.29bs^{2} | tp = 138.3 + 12.17bs − 0.27bs^{2} | |||

Scalable | tp = 130.48 + 12.95bs − 0.29bs^{2} | tp = 178.56 + 10.74bs − 0.27bs^{2} | |||

Vegas | tp = 55.28 + 9.85bs − 0.29bs^{2} | tp = 66.8 + 7.77bs − 0.27bs^{2} | |||

UiT-HAW | Cubic | tp = 0.763 + 0.002bs | tp = 0.764 + 0.002bs | R-square = 0.95 p-value < 0.00001 | tp_{max} = 0.87bs = 30 |

OLIA | tp = 0.675 + 0.004bs | tp = 0.68 + 0.003bs | |||

Hybla | tp = 0.795 + 0.002bs | tp = 0.796 + 0.002bs | |||

Reno | tp = 0.753 + 0.002bs | tp = 0.754 + 0.002bs | |||

Scalable | tp = 0.807 + 0.002bs | tp = 0.808 + 0.002bs | |||

Vegas | tp = 0.743 + 0.002bs | tp = 0.744 + 0.002bs |

Scenario | Optimized Solutions | Traditional Solutions of BS |
---|---|---|

SRL-HU | OPM = PCDC, OCC = Hybla, OBS = 12.36 MiB, OTP = 74.65 Mbit/s | B ≥ 329 MiB (RTT_{max} = 1.800 s, RTO _{max} = 2.000 s) |

UNIS-HiN | OPM = PCDC, OCC = Cubic, OBS = 9.22 MiB, OTP = 266.66 Mbit/s | B ≥ 54 MiB (RTT_{max} = 0.020 s,RTO _{max} = 1.000 s) |

UiT-HAW | OPM = FullMesh, OCC = Scalabale, OBS = 0.50 MiB, OTP = 0.81 Mbit/s | B ≥ 1.22 MiB (RTT_{max} = 1.800 s,RTO _{max} = 2.000 s) |

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## Share and Cite

**MDPI and ACS Style**

Chen, M.; Raza, M.W.; Zhou, X.; Dreibholz, T.; Tan, Y.
A Multi-Parameter Comprehensive Optimized Algorithm for MPTCP Networks. *Electronics* **2021**, *10*, 1942.
https://doi.org/10.3390/electronics10161942

**AMA Style**

Chen M, Raza MW, Zhou X, Dreibholz T, Tan Y.
A Multi-Parameter Comprehensive Optimized Algorithm for MPTCP Networks. *Electronics*. 2021; 10(16):1942.
https://doi.org/10.3390/electronics10161942

**Chicago/Turabian Style**

Chen, Min, Muhammad Waleed Raza, Xing Zhou, Thomas Dreibholz, and Yuyin Tan.
2021. "A Multi-Parameter Comprehensive Optimized Algorithm for MPTCP Networks" *Electronics* 10, no. 16: 1942.
https://doi.org/10.3390/electronics10161942