# Performance research on time-triggered Ethernet based on network calculus

- Yu Xiang
^{1}, - Wei Wang
^{1}Email author, - Xiang Zhang
^{1}and - Zhenwei Li
^{1}

**2014**:12

https://doi.org/10.1186/1687-1499-2014-12

© Xiang et al.; licensee Springer. 2014

**Received: **18 September 2013

**Accepted: **17 December 2013

**Published: **19 January 2014

## Abstract

In the paper, we research on the performance of time-triggered Ethernet based on network calculus. Three kinds of data with different priority are imported to research on time-triggered Ethernet. Firstly, we adopt network calculus to obtain the theory-bound value of the network performance parameters. Then, we design and implement the time-triggered Ethernet clock synchronization, redundancy fault-tolerant, multi-data communication, service-performance model, node model, and network model successfully in two different topologies. Lastly, we compare the simulation value with the network calculus value and obtain the comparison result. The result shows that the performance parameters of time-triggered Ethernet well meet the theory value, and time-triggered Ethernet specification is feasible.

## Keywords

## 1. Introduction

In recent years, the development of real-time tasks based on the existing Ethernet has become a hot-spot issue. In the fierce competition, the time-triggered Ethernet (TTE) stands out, which combines time-triggered technology certainty, fault-tolerant mechanisms, and real-time performance with the ordinary Ethernet's performances, like flexibility, dynamism, and best effort [1, 2]. TTE provides support for synchronous, highly reliable embedded computing and networking, fault-tolerant design. Because of its characteristics, TTE is widely used in the safety-critical system, such as aviation electronic technology, transport system, and industrial automation. It is a new method to analyze TTE using network calculus, and there is no existing research result.

‘Time-triggered’ [3] means predictable and deterministic, which means all activities in the network would run in a planned way over time. The definition of the time-triggered Ethernet is as follows [4, 5]:

TTE = Ethernet + Clock synchronization + Time-triggered communication + Rate-constrained traffic + Guaranteed transport.

In this article, we firstly construct a service-performance network calculus model which is triggered by time. Meanwhile, we construct a simulation model and realize the TTE clock synchronization algorithm, protocol, and network components and then we use the simulation model to analyze the performance and parameters of the TTE. Lastly, we compare the simulation results with the network calculus results based on network calculus model and simulation model. Conclusions show that TTE can well meet the needs of safety-critical systems.

## 2. The service-performance model of TTE based on network calculus

Network calculus is a newly developed network quality of service (QoS) theory, and it is based on the Idempotent Mathematics and Residuation Theory [6]. The foundation of network calculus lies in the mathematical theory of algebra, the min-plus algebra, and the max-plus algebra. Network calculus can give out the network performance boundary. Deterministic network calculus makes use of arrival curve and service curve to work out the deterministic boundary of the network performance parameters [7, 8], such as the maximum delay of the network data flow, the cache backlog data in the network communication nodes, and backlog length.

### 2.1 The service-performance model parameter of TTE

Based on the network calculus theory, we give some definitions as follows. The micro-data stream is defined as the data bit stream of the same type from the transmitting node.

### 2.2 Network service curve and service delay

We assume that the arrival curve of the micro-data stream with the priority *p*(*j*) is *α*_{j }(*t*) = *r*_{
j
}*t* + *b*_{
j
}. So, *A*_{j }(*t*) = ∑ _{{i : p(i) = p(j)}}*α*_{i }(*t*) is the arrival curve of aggregated flow *G*_{
j
}, and ${A}_{j}^{H}={\displaystyle {\sum}_{\left\{i:p\left(i\right)>p\left(j\right)\right\}}{\alpha}_{i}}\left(t\right)$ is the arrival curve of aggregated flow.

*β*

_{R,T }(

*t*) =

*C*[

*t*− 0]

^{+}. Based on corollary 6.2.1 [9], we obtain the service curve of the aggregated flow as formula 1:

*G*

_{ j }as formula 2:

*G*

_{ j }are, respectively, formulas 4 and 5:

Generally, when ${R}_{j}^{G}>0$, the switch forwards the type of data stream *G*_{
j
}. When ${R}_{j}^{G}=0$, the value is the minimum value, and the switch will have no ability to forward the data *G*_{
j
}. It will be no sense when ${R}_{j}^{G}>0$.

*F*

_{ j }, all the micro-data in the stream

*G*

_{ j }is serviced in the order of FIFO. In this way, we can deduce the service curve of the micro-data stream

*F*

_{ j }. ${\beta}_{{R}_{j}^{G},{T}_{j}^{G}}\left({G}_{j},\theta \right)=\left(\theta -{T}_{j}^{G}\right){R}_{j}^{G}={A}_{j}\left(0\right)-{b}_{j},\theta ={T}_{j}^{G}+\left({A}_{j}\left(0\right)-{b}_{j}\right)/{R}_{j}^{G}$. Based on the assumption 6.2.1 [9], the service curve of the micro-data stream

*F*

_{ j }is as follows:

*F*

_{ j }are, respectively, as formulas 7 and 8:

Generally, when *R*_{
j
} > 0, the switch forwards the type of data stream *F*_{
j
}. When *R*_{
j
} = 0, the value is the minimum value, and the switch will have no ability forward the data *F*_{
j
}. It will be no sense when *R*_{
j
} < 0.

The network calculus value is the upper bound of the switch processing delay. According to the above reasoning process, we can apply the theory into the TTE network scenario to deduce the upper deterministic boundary of the delay in star topology.

## 3. The design and realization of the simulation model

### 3.1 The design of TTE simulation model

TTE consists of two kinds of network devices including TTE switches and TTE terminals. With the difference of TTE network nodes' position and role in TTE clock synchronization, TTE network nodes are divided into three different roles: synchronization master(SM), compression master (CM), and synchronization client (SC). The TTE switches can be as the role of SM, CM, and SC, while the TTE terminals can be as the role of SM and SC.

#### 3.1.1 TTE switches

The most important two differences between the TTE switches and traditional switches are clock synchronization module and admission control module.

#### 3.1.2 TTE terminals

### 3.2 TTE simulation performance

#### 3.2.1 The constituent part of the TTE end-to-end delay

*x*axis refers to the simulation time, and the

*y*axis refers to the value of end-to-end delay. It also applies to Figures 5 and 6.

The conclusion is that the TTE end-to-end delay of the above topology is the total sending delay of node_1, node_3, and node_0, and the total processing delay of node_3 and node_0.

## 4 Comparison analysis of the simulation results and network calculus results

In the second section, we analyze and derivate the maximum delay of the TTE data in a specified network topology with the use of the theory of network calculus. Then, we conduct the statistical analysis on time-triggered Ethernet network performance parameters with simulation tools. Here, we use the results of the two research tools to conduct comparative analysis to verify whether the results of the TTE simulation can meet the delay constraints of the maximum delay derived from network calculus.

### 4.1 The star topology

#### 4.1.1 The network calculus process

In the star topology network simulation model, there are three types of data traffic (time-triggered real-time data (TT), RC, and BE).The rules of the terminal nodes sending frames are as follows (all the frames are standard Ethernet frames):

For the TT data stream, node_1, node_2, and node_3 send two frames per 0.025 s; node_4, node_5, node_6, and node_7 send one frame per 0.025 s; the TT data frame size varies from 100 to 500bytes. For the RC data stream, each node sends one frame per second; the frame size of the RC data stream varies from 100 to 500bytes. For the BE data stream, each node sends 10,000 frames per second; the frame size of the BE data varies from 100 to 500bytes.

So, the parameters are as follows:

*r*_{TT} = 4, 000, *b*_{TT} = 100, *r*_{RC} = 8, 000, *b*_{RC} = 100, *r*_{BE} = 4, 000, *b*_{BE} = 4, 000, *n* = 7 (the number of the micro-data).

*F*

_{ j }(TT, RC, and BE) supported by switch is

#### 4.1.2 Comparison analysis

##### 4.1.2.1 The comparison analysis of the end-to-end delay of the three kinds of data

In Section 4.1.1, we obtain the calculus results of the star topology. We can obtain the simulation value of the star topology. In the star topology, the comparison analysis of the end-to-end delay of the three kinds of data is as follows (for example, packet_size = 100 bytes):

**The definitions of the symbols**

Symbol | Definition |
---|---|

| The micro-data stream through the switch |

| The length of the micro-data stream |

| The priority of the micro-data stream |

| The aggregated flow of the micro-data stream whose priority is the same with the priority of |

${G}_{j}^{H}={\displaystyle {\cup}_{\left\{i:p\left(i\right)>p\left(j\right)\right\}}{F}_{i}}$ | The aggregated flow of the micro-data stream whose priority is bigger than the priority of |

| The aggregated flow of the flow aggregated |

${l}_{max}^{j}=max\left\{{l}_{i}:p\left(i\right)<p\left(j\right)\right\}$ | The maximum length of the micro-data stream whose priority is lower than the priority of |

**The exceeding rate of the BE data**

BE data | Number of receiving data | Number of exceeding data | Exceeding rate |
---|---|---|---|

100 bytes | 62,134 | 2,993 | 4.817% |

Figure 8 is the description of the receiving and sending rate of switch. The switch services three kinds of data with different sizes.

**The comparison results of the TT data with different sizes**

TT data (bytes) | Simulation value (×10 | Average of simulation value (×10 | Network calculus value (×10 |
---|---|---|---|

100 | 2.36294 | 2.36294 | 2.363 |

150 | 3.53855 | 3.53855 | 3.54 |

200 | 4.72588 | 4.72588 | 4.73 |

250 | 5.90734 | 5.90734 | 5.91 |

300 | 7.0888 | 7.0888 | 7.1 |

**The comparison results of the RC data with different sizes**

RC data (bytes) | Average of simulation value (×10 | Network calculus value |
---|---|---|

100 | 4.6571 | 8.466 |

150 | 7.263 | 1.27 |

200 | 1.0914 | 1.694 |

250 | 1.3643 | 2.13 |

300 | 1.6371 | 2.542 |

**The comparison results of the BE data with different sizes**

BE data (bytes) | Average of simulation value | Network calculus value |
---|---|---|

100 | 1.1335 × 10 | 1.387 × 10 |

150 | 1.5419 × 10 | 2.084 × 10 |

200 | 2.6 × 10 | 2.783 × 10 |

##### 4.1.2.2 The comparison analysis of packet loss rate

**The packet loss of the TT data**

TT data (bytes) | Number of sending data | Number of receiving data | Number of losses | Loss rate (%) |
---|---|---|---|---|

100 | 20 | 20 | 0 | 0 |

150 | 20 | 20 | 0 | 0 |

200 | 20 | 20 | 0 | 0 |

250 | 20 | 20 | 0 | 0 |

300 | 20 | 20 | 0 | 0 |

**The packet loss of the RC data**

RC data (bytes) | Number of sending data | Number of receiving data | Number of losses | Loss rate (%) |
---|---|---|---|---|

100 | 28 | 28 | 0 | 0 |

150 | 28 | 28 | 0 | 0 |

200 | 28 | 28 | 0 | 0 |

250 | 28 | 28 | 0 | 0 |

300 | 28 | 28 | 0 | 0 |

**The packet loss of the BE data**

BE data (bytes) | Number of sending data | Number of receiving data | Number of losses | Loss rate (%) |
---|---|---|---|---|

100 | 3,241 | 3,182 | 59 | 1.82 |

150 | 3,241 | 3,180 | 61 | 1.882 |

200 | 3,241 | 2,866 | 375 | 11.57 |

250 | 3,241 | 2,292 | 949 | 29.28 |

300 | 3,241 | 1,909 | 1,332 | 41.098 |

In the Section 2.2, we assume that the service rate is not less than 0. When the size is up to 250 bytes, the TT and RC data are guaranteed, and the service rate of the BE data is up to 0. While, in the simulation model, different types of data are sent in different time intervals. Thus, when the size of the BE data is up to 250 bytes, there are also BE data in the TTE Ethernet. If the size of the data is larger, the loss rate is higher. We can get good simulation results when we set the size at <200 bytes.

### 4.2 The cascaded topology

The cascaded topology which is different from the star topology is shown in Figure 6a. The topology is more complex than the star topology. The analysis results of the three kinds of data are shown in Figure 6b,c,d.

According to results from the comparison chart of the three types of data stream in the cascaded topology, we can get that the actual delay of the simulation statistical results fully meets the maximum network delay obtained by network calculus, and it also verifies that the TTE simulation results are reasonable. Then, we can verify that the TTE specification is feasible.

## 5. Conclusions

As a new real-time deterministic network, time-triggered Ethernet has not yet formed a standardized protocol specification and has no mature products for the market. This paper firstly uses network calculus and network simulation to analyze and study the TTE. We present a service-performance network calculus model, which is triggered by time, and obtain the upper deterministic boundary of the delay. With the TTE clock synchronization, redundancy fault-tolerant, multi-data communication, node model and network model designed and implemented on the simulation platform, we analyze the performance of the TTE and compare the simulation results with the theoretical values from the time-triggered Ethernet network calculus. The final conclusion shows that TTE has good performance in terms of end-to-end delay and service rate, can be compatible with the traditional Ethernet [11], and meets well the needs of real-time and safety-critical systems.

## Declarations

## Authors’ Affiliations

## References

- Hermann K, Gunter G: TTP—a protocol for fault-tolerant real-time systems.
*IEEE Computer*1994, 27(1):14-23. 10.1109/2.248873View ArticleGoogle Scholar - Maier R: Event-triggered communication on top of time-triggered architecture.
*DASC*2002, 21(2):135-141.MathSciNetGoogle Scholar - Steiner W, Paulitsch M, Kopetz H:
*Multiple Failure Correction in the Time-Triggered Architecture*. Real-Time Systems Group: Technische Universitat Wien, Vienna; 2003.View ArticleGoogle Scholar - Kopetz H: Fault containment and error detection in the time-triggered architecture autonomous. Paper presented at the 6th international symposium on decentralized systems. Pisa, 9–11 April 2003Google Scholar
- TTTech: TTEthernet Specification v.9.1-22968[Z] (D-INT-S-10002, 200.11.GE). Vienna: TTTech Computertechnik AG;Google Scholar
- Firoiu V, Boudec JYL, Towsley D, Zhang Z-L: Theories and models for internet quality of service.
*Proc IEEE*2002, 90(9):1565-1591. 10.1109/JPROC.2002.802002View ArticleGoogle Scholar - Kopetz H, Ademaj A, Grillinger P, Steinhammer K: The time-triggered Ethernet (TTE) Design. In
*Paper presented at the8th IEEE international symposium on object-oriented real-time distributed computing (ISORC)*. Seattle, Washington; 18–20 May2005.Google Scholar - Cruz RL: A calculus for network delay, part 1: network analysis.
*IEEE Trans. Info. Theory*1991, 37(1):132-141. 10.1109/18.61110MathSciNetView ArticleGoogle Scholar - Boudec JYL, Thiran P:
*Network Calculus: A Theory of Deterministic Queuing System for the Internet*. Germany: Springer; 2004.Google Scholar - Li Z:
*Research on time-triggered Ethernet based on deterministic network calculus*. Masters Degree Thesis: University of Electronic Science and Technology of China; 2013.Google Scholar - Heffernan D, Doyle P: Time-triggered Ethernet based on IEEE 1588 clock synchronization.
*IEEE Trans. Computers*2004, 24(3):264-269.Google Scholar

## Copyright

This article is published under license to BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.