Reliability-based parameter design for FlexRay network in vehicles

Abstract

FlexRay has been extensively applied to safety-critical systems, such as powertrain, chassis, and X-by-wire system in vehicles. Its transmission reliability considerably influences vehicle safety. In this study, frame coding and media access control in the FlexRay protocol are analyzed, and calculation equations are deduced for the length of time slot and coded frame of FlexRay. Redundant transmission of FlexRay static frame is introduced to solve the transmission failure caused by the bit error in the physical layer, and the transmission reliability of a static segment is defined for the mechanism. Considering the demands on transmission reliability and network schedulability, the configuration of FlexRay parameters, including communication cycle, time slot allocation, and segment length, is formulated as a generalized optimization problem with constraints on predefined transmission reliability and response time of messages. A Reliability-Based Parameter Optimization algorithm and its sub-algorithms, Response Time of Dynamic Segment and Slot Allocation for the Predefined Reliability, are presented to approximately solve the optimization model. Experiment results validate the proposed method, which can efficiently improve the transmission reliability and guarantee the real-time performance of the FlexRay network.

Introduction

FlexRay bus is the next-generation automotive bus standard. It is extensively used in powertrain, chassis, and X-by-wire system in vehicles given its advantages in bandwidth, fault tolerance, and certainty. ¹ These typical safety-critical systems make stringent requirements for the communication reliability of a FlexRay network. However, in addition to communication hardware, communication reliability for the FlexRay network is greatly affected by several protocol parameters that must be selected in the network design stage. A method that can provide system performance optimization and guarantee network communication reliability is required to reduce the design complexity of these parameters.^2–4

Existing studies of the reliability of the FlexRay network are mainly concerned on three aspects, namely, the network’s real-time performance, parameter configuration, and reliable transmission. The time analysis and scheduling strategy of a message are the focus of research in terms of the real-time performance of the network. Tanasa et al. ⁵ proposed an analytical framework for the probabilistic timing analysis of an event-triggered dynamic segment (DS) of the FlexRay communication protocol. Gu et al. ⁶ considered a slot multiplexing mechanism in timing analysis and proposed a method for calculating the worst-case response time of a message under any bus loads. Kukkala et al. ⁷ proposed a novel scheduling framework that can handle jitter-affected, time-triggered, and high-priority event-triggered messages to satisfy the timing constraints in message delivery. Darbandi et al. ⁸ divided the message scheduling problem into message and task scheduling, and optimized task scheduling in accordance with the allocated time window and constraints. Dvorak and Hanzlek ⁹ decomposed the scheduling problem into the sub-problems of an electronic control unit (ECU)-to-channel assignment, and an algorithm was proposed to create a feasible schedule for channels in independent and fault-tolerant modes. Tanasa et al. ¹⁰ proposed a scheduling framework for generating fault-tolerant messages on static message segments and formulated the optimization problem into the constraint logic programming to minimize the number of message retransmissions. But they did not consider the influence on the transmission of dynamic message.

Frame packing and the optimal FlexRay parameters have still been the focus of many researchers for parameter configuration. Li et al. ¹¹ proposed a design approach of the FlexRay parameters, which can satisfy the application requirements of a hybrid transmission of static and dynamic data in the same network. Zhang et al. ¹² proposed a kind of heuristic scheduling algorithm and optimized the scheme to obtain the optimal frame identifier (FID) that can efficiently reduce the response time of the worst case of the message. Zhao et al. ¹³ used a two-dimensional (2D) bin-packing technique to maximize the bandwidth utilization in the static segment (SS) and proposed a fast heuristic and an integer linear programming approach. Wang et al. ¹⁴ formulated FlexRay frame packing problem into a generalized integer linear programming problem; a frame-packing algorithm based on transmission reliability was proposed to optimize signal combinations and static slot allocations. Gong and Chen ¹⁵ presented an automatic model coefficient matrix-generating algorithm and a phase-reserving algorithm to assign a frame identifier and a phase for each message. However, these approaches did not fully consider the transmission failure of FlexRay messages. Thus, the network reliability could not be guaranteed.

Most studies have concentrated on transmission fault detection, multi-channel redundancy, and message retransmission in terms of the reliable transmission of FlexRay. Tolentino et al. ¹⁶ presented an implementation method for an error detection/correction code for corrupted transmitted bits to be detected and corrected satisfactorily. Jovic et al. ¹⁷ proposed a solution for testing the FlexRay bus communication, which can detect the errors in processing FlexRay information transmission among multiple ECUs. Do Souto et al. ¹⁸ presented an approach to evaluating the reliability of FlexRay and time-division multiple access (TDMA) buses, such as reliable broadcast (RB). Chen and Leu ¹⁹ proposed a two-level redundancy approach for a safety-critical FlexRay bus, which can use backup nodes, mirror tasks, and task migration to maintain a system operation when an ECU fails. Lee et al. ²⁰ proposed a new fast reliability scheduling algorithm that reduced the probability of a transient fault in a clock cycle by retransmitting a message to ensure system reliability. Peng et al. ²¹ proposed a message retransmission scheduling strategy for an automobile X-by-wire system. It improved the bus bandwidth utilization and the success rate of message scheduling and minimized transmission delay. Liu et al. ²² presented a detailed prompt retransmission mechanism by acknowledging the recovery of transient errors in safety-critical, time-triggered messages. Previous methods can slightly improve the reliability of a FlexRay system. However, transmission fault detection and multi-channel redundancy are complicated and are difficult to implement in real ECUs. Existing retransmission mechanisms consider neither the optimal configuration of network parameters nor the impact on the network’s real-time performance. Therefore, the mechanism’s ability to improve network reliability is limited.

To address the problems in previous works, this study analyzes the reliability of FlexRay SS under redundant transmission and proposes an optimization design model of FlexRay network parameters. An approximate algorithm RBPO (Reliability-Based Parameter Optimization) and its sub-algorithms are presented to design the network parameters. The remainder of this article is organized as follows. First, the frame encoding, media access control, and time slot in the FlexRay communication protocol are analyzed, and the calculation of related network parameters is presented. Second, the message parameters and the reliability of the FlexRay SS are modeled for the redundant transmission of a message. Third, an optimal model for the FlexRay parameter optimization design is proposed. Fourth, the RBPO algorithm and its sub-algorithms RTDS (Response Time of Dynamic Segment) and SAPR (Slot Allocation for the Predefined Reliability) are described based on the previous optimal model, respectively. Fifth, the experimental results are analyzed and discussed. Finally, the conclusion is provided.

FlexRay communication protocol

Frame and coding

FlexRay messages include static and dynamic frames. Each frame is composed of a header, a payload segment, and a tail. The header is 5 bytes, the payload segment includes 0–254 bytes, and the tail consists of 3 bytes of frame cyclic redundancy check (CRC). The FlexRay frames must be encoded in the transmission. Figures 1 and 2 illustrate that several coding sequences, namely, transmission start sequence (TSS), frame start sequence (FSS), byte start sequence (BSS), and frame end sequences (FES), are added to the original frames. In a DS, the FES is followed by a dynamic trailing sequence (DTS), which is used for back-filling the time until the next minislot. In Figures 1 and 2, the red and blue blocks represent logical high bits (“1”) and logical low bits (“0”), respectively. ²³

Figure 1.

Static frame encoding.

Figure 2.

Dynamic frame encoding.

$l_{\mathrm{TSS}}$ , $l_{\mathrm{FSS}}$ , $l_{\mathrm{BSS}}$ , $l_{\mathrm{FES}}$ , and $l_{\mathrm{DTS}}$ are assumed to be the length of TSS, FSS, BSS, FES, and DTS, respectively. The encoding length of a message can be calculated as follows

$$\begin{array}{c}\{\begin{array}{c}{Y}_i=l_{\mathrm{TSS}}+l_{\mathrm{FSS}}+\alpha ·(l_{\mathrm{BSS}}+8)+l_{\mathrm{FES}}+\beta \hfill \\ \multicolumn{1}{c}{\alpha =\{\begin{array}{cc}{l}_s\hfill & \mathrm{if}{Y}_i=Y_s\hfill \\ \multicolumn{1}{c}{l_d}& \mathrm{if}{Y}_i=Y_d\hfill \end{array}}\\ \multicolumn{1}{c}{\beta =\{\begin{array}{cc}0\hfill & \mathrm{if}{Y}_i=Y_s\hfill \\ \multicolumn{1}{c}{l_{\mathrm{DTS}}}& \mathrm{if}{Y}_i=Y_d\hfill \end{array}}\end{array}\hfill \end{array}$$

(1)

where $l_s$ is the length of the static message, and $l_d$ is the length of the dynamic message. $Y_s$ and $Y_d$ are the encoding lengths of static message and dynamic message, respectively.

Media access control

The FlexRay bus transmits messages through a communication cycle loop. A communication cycle is defined through four timing hierarchy levels, namely, the communication cycle, arbitration grid, macrotick, and microtick levels (Figure 3). Each communication cycle contains SS, DS, symbol windows (SW), and network idle time (NIT). Several static slots with identical duration constitute DS within the SS. A single symbol can be transmitted on the network within the SW. The NIT serves as a phase during which the node calculates and applies clock correction terms. The communication cycle can be obtained by

$$T=L_{\mathrm{SS}}+L_{\mathrm{DS}}+L_{\mathrm{SW}}+L_{\mathrm{NIT}}$$

(2)

where $L_{\mathrm{SS}}$ , $L_{\mathrm{DS}}$ , $L_{\mathrm{SW}}$ , and $L_{\mathrm{NIT}}$ are the length of SS, DS, SW, and NIT, respectively. SS adopts the TDMA scheme to coordinate transmissions, while DS uses the flexible TDMA (FTDMA) scheme to arbitrate transmissions. Notably, the frame ID and slot counter are used to implement transmission arbitration. ¹⁴

Figure 3.

Timing hierarchy within the communication cycle.

Static and dynamic slot

Assume that n static messages and m dynamic messages are included in the FlexRay network. Moreover, $Y_s^i$ is the encoding length of the ith static message $W_i$ , and $Y_d^i$ is the encoding length of the ith dynamic message $M_i$ . Each static slot in the segment contains the interval from the start of the slot to the action point $(t_{\mathrm{APO}})$ , the time of frame transmission, and the channel idle $(t_{\mathrm{CID}})$ . Apparently, the static slot length $S{T}_{\mathrm{slot}}$ must not be less than the coding lengths of all static messages and can be calculated as

$$S{T}_{\mathrm{slot}}=\underset{1\le i\le n}{max}\left(Y_s^i\right)·\mathrm{gdbit}+t_{\mathrm{CID}}+t_{\mathrm{APO}}$$

(3)

where gdbit is the time of 1 bit. For the DS, the size of the dynamic slot, $D{Y}_{\mathrm{slot}}$ , depends on the length of each message given the FTDMA scheme. Thus, the $D{Y}_{\mathrm{slot}}$ of the message $M_i$ can be calculated as

$$D{Y}_{\mathrm{slot}}=(\lfloor \frac{Y_d^i·\mathrm{gdbit}}{\mathrm{gdMinislot}}\rfloor +1)·\mathrm{gdMinislot}+t_{\mathrm{CID}}+t_{\mathrm{APO}}$$

(4)

where gdMinislot is the length of one minislot.

FlexRay message and transmission reliability

Parameters of FlexRay message

In general, periodic and safety-critical messages are put into the SS for transmission, whereas aperiodic messages are transmitted in the DS. In this study, slightly different parameters are proposed for the static and dynamic messages considering the various demands of transmission reliability. Let the message set in the SS as $W_{\mathrm{st}}=\{w_1,\dots ,w_i,\dots ,w_{\mathrm{ns}}\}$ and the message set in the DS as $W_{\mathrm{dyn}}=\{m_1,\dots ,m_i,\dots ,m_{\mathrm{nd}}\}$ . Each static message $w_i\in W_{\mathrm{st}}$ is characterized by $(l_i,k_i,p_i,d_i)$ , and each dynamic message $m_i\in W_{\mathrm{dyn}}$ can be represented by $(l{m}_i,p{m}_i,d{m}_i)$ . Table 1 lists the definition of $l_i,k_i,p_i,d_i,l{m}_i,p{m}_i,\mathrm{and}d{m}_i$ . The static message has one more parameter $k_i$ than the dynamic message, thereby indicating the retransmission number of messages and is used to calculate the transmission reliability of a SS in the next section.

Table 1.

Parameter designation.

Symbol	Definition
$l_i$	Payload length of the static message $w_i$
$k_i$	Number of time slots of $w_i$ in one communication cycle
$p_i$	Message period of the static message $w_i$
$d_i$	Transmission deadline of the static message $w_i$
$l{m}_i$	Payload length of the dynamic message $m_i$
$p{m}_i$	Minimum release interval of the dynamic message $m_i$
$d{m}_i$	Transmission deadline of the dynamic message $m_i$

Transmission reliability of SS

FlexRay protocol consists of the physical, data link, and application layers. Different reliabilities are demanded by various layers. In this study, only the transmission failure of the static messages caused by a bit error in the physical layer is addressed. To ensure that static messages are transmitted reliably, additional slots must be allocated to several messages for redundant transmission, that is, $k_i\ge 1$ . Clearly, different solutions for redundant transmission can lead to various transmission reliabilities. The reliability of the SS is defined for a redundant transmission to clearly measure the reliability of static messages as follows.

Bit error is assumed to exist in the process of message transmission. ²⁴ Let $P_{\mathrm{be}}$ denote the probability of transmission failure of one bit in a static message. If the transmission of each bit is mutually independent, then the probability of success to transmit the $P_i$ of static message $w_i$ is

$$P_i=(1-P_{\mathrm{be}}{)}^{Y_s(w_i)}$$

(5)

where $Y_s(w_i)$ is the encoding length of the message.

If T denotes the communication cycle of the FlexRay, then, for the message $w_i\in W_{\mathrm{st}}$ , the probability of at least one successful transmission $P_{\mathrm{sr}}(w_i)$ is

$$P_{\mathrm{sr}}(w_i)=1-(1-(1-P_{\mathrm{be}}{)}^{Y_s(w_i)}{)}^{k_i\frac{d_i}{T}}$$

(6)

where $k_i(d_i/T)$ is the number of times, and the message $w_i$ is transmitted within its deadline.

For a given time interval $\tau$ , the whole reliability of the SS is determined by the transmission reliability of each SS message. The transmission reliability of the SS $P_{\mathrm{SR}}$ can be considered the probability of all messages that are successfully transmitted at least once in $\tau$ and is denoted as

$$P_{\mathrm{SR}}=\underset{i=1}{\overset{n}{\Pi }}{P}_{\mathrm{sr}}(w_i{)}^{\lceil \frac{\tau }{d_i}\rceil }$$

(7)

For example, four static messages, namely, $w_1,w_2,w_3,\mathrm{and}{w}_4$ , exist in the FlexRay network. Their parameters and five combinations of slot allocation are listed in Table 2, and the process of redundant transmission is depicted in Figure 4(a)–(d). According to the message parameters and equations (5)–(7), the reliability of the SS for different slot combinations is calculated and listed in Table 2. $P_{\mathrm{SR}}^1$ without redundant transmission is 0.225 and is lower than the other combinations. When k₁ = 2, k₂ = 1, k₃ = 1, and k₄ = 1, $P_{\mathrm{SR}}^2$ reaches 0.671, which is the highest, thus indicating that redundant transmission can improve the transmission reliability of the SS effectively. $P_{\mathrm{SR}}^2$ is higher than $P_{\mathrm{SR}}^3$ , $P_{\mathrm{SR}}^4$ , and $P_{\mathrm{SR}}^5$ , thereby indicating that the different slot allocations can lead to the diverse reliability of the SS, even if the total number of all static slots, Nst, in the redundant transmission is identical.

Table 2.

Reliability of different static slot combinations.

$\tau (\mathrm{ms})$	$N_{\mathrm{st}}$	Message	$w_1$	$w_2$	$w_3$	$w_4$	$P_{\mathrm{SR}}^i$
		$p_i$	0.8	0.85	0.75	0.7
		$d_i$	T	$2T$	$3T$	$3T$
		$k_i$	$k_1$	$k_2$	$k_3$	$k_4$
	4		1	1	1	1	0.225
	5		2	1	1	1	0.671
$6T$	5		1	2	1	1	0.237
	5		1	1	2	1	0.232
	5		1	1	1	2	0.236

Figure 4.

Messages transmission of different slot allocations: (a) k₁ = 2, k₂ = 1, k₃ = 1, and k₄ = 1; (b) k₁ = 1, k₂ = 2, k₃ = 1, and k₄ = 1; (c) k₁ = 1, k₂ = 1, k₃ = 2, and k₄ = 1; and (d) k₁ = 1, k₂ = 1, k₃ = 1, and k₄ = 2.

Reliability-aware network parameter design

Optimization design model

The FlexRay network parameters include communication cycle T, SS length $L_{\mathrm{SS}}$ , DS length $L_{\mathrm{DS}}$ , static slot length $S{T}_{\mathrm{slot}}$ , static slot number $N_{\mathrm{slot}}$ , and static message slot allocation set $K=\{k_1,\dots ,k_i,\dots ,k_{\mathrm{ns}}\}$ . Given $L_{\mathrm{SS}}=S{T}_{\mathrm{slot}}·N_{\mathrm{slot}}$ , $N_{\mathrm{slot}}=\sum _{k_i\in K}{k}_i$ , and $S{T}_{\mathrm{slot}}$ can be obtained using equation (3), the network parameters design is mainly the optimization design of parameters $T,L_{\mathrm{SS}},L_{\mathrm{DS}},\mathrm{and}K$ .

Assuming that the static message set is $W_{\mathrm{st}}=\{w_1,\dots ,w_i,\dots ,w_{\mathrm{ns}}\}$ , the dynamic message set is $W_{\mathrm{dyn}}=\{m_1,\dots ,m_i,\dots ,m_{\mathrm{nd}}\}$ , the predefined transmission reliability is $\rho$ , and the maximum allowable response time of DS value $\delta$ is known. The design of network parameters $T,L_{\mathrm{SS}},{L_D}_S,\mathrm{and}K$ can be formulated as a generalized optimization problem with constraints on the predefined transmission reliability and the response time of messages. The optimized model is expressed as follows

• Object

$$\Gamma =max\left(P_{\mathrm{SR}}\right)$$

(8)

such that

$$k_i\ge k_{\rho ,i},i=1,2,\dots ,\mathrm{ns}$$

(9a)

$$S{T}_{\mathrm{slot}}·\sum _{k_i\in K}{k}_i+L_{\mathrm{DS}}\le T$$

(9b)

$${\overline{T}}_R^j\le d{m}_j,j=1,2,\dots ,\mathrm{nd}$$

(9c)

$$\sum _{\mathrm{j}=1}^{\mathrm{nd}}{\overline{T}}_R^j\le \delta$$

(9d)

where $\Gamma$ is the objective function to obtain the maximum transmission reliability of the SS. Equation (9a) denotes the constraints on the transmission reliability, and $k_{\rho ,i}$ represents the number of static slots assigned to the message $w_i$ when $P_{\mathrm{SR}}=\rho$ . Equation (9b) provides the constraints on the bandwidth, that is, the total length of the static and DS must be less than the communication cycle. Equation (9c) requires that the average response time of the dynamic message ${\overline{T}}_R^j$ cannot be higher than its deadline, and equation (9d) demands that the DS response time $\sum {\overline{T}}_R^j$ must not be longer than $\delta$ .

For simplicity, let $p_i$ of each static message $w_i\in W_{\mathrm{st}}$ be equal to $d_i$ and $p{m}_i$ of each dynamic message $m_i\in W_{\mathrm{dyn}}$ be equal to $d{m}_i$ , The communication cycle of T is the common divisor of all messages and can be determined using the RBPO algorithm in the next section. The FlexRay static slot length $S{T}_{\mathrm{slot}}$ is equal to the transmission time required for messages with the maximum load segment length in $W_{\mathrm{st}}$ . The static slot length $S{T}_{\mathrm{slot}}$ depends on the maximum encoding length of the static message, and $S{T}_{\mathrm{slot}}$ can be calculated using equation (3).

For illustration, in the calculation process in this study, let $p_i$ of each static message $w_i\in W_{\mathrm{st}}$ be equal to $d_i$ and $p{m}_i$ of each dynamic message $m_i\in W_{\mathrm{dyn}}$ be equal to $d{m}_i$ . The FlexRay bus communication cycle T is the common number of all messages, and T can be determined using the RBPO algorithm in the next section. The FlexRay static slot length $S{T}_{\mathrm{slot}}$ is equal to the transmission time required for messages with the maximum load segment length in $W_{\mathrm{st}}$ .

Approximate algorithm RBPO

According to the abovementioned model, the algorithm RBPO is proposed to get approximately optimal solution. The pseudocode of the algorithm is presented in Table 3.

Table 3.

RBPO algorithm.

1. Input: static message set $W_{\mathrm{st}}$ and dynamic message set $W_{\mathrm{dyn}}$ , predefined reliability $\rho$ , communication time $\tau$ , and the maximum allowed response time $\delta$ ;

2. Set $P_{\mathrm{SR}}^b$ as the optimal transmission reliability of static segment, $K^b$ as the optimal slot allocation, $L_{\mathrm{DS}}^b$ as the optimal dynamic segment length, and $T^b$ as the optimal communication cycle;

3. Initialize $P_{\mathrm{SR}}^b=P_{\mathrm{SR}}=0$ , $T^b=T=0$ , $L_{\mathrm{DS}}^b=L_{\mathrm{DS}}=0$ , $K^b=K=\{1,1,\dots ,1\}$ ;

4. Solve common divisor set $G=\{g_1,g_2,\dots ,g_z\}$ of the deadline of messages in $W_{\mathrm{st}}\cup W_{\mathrm{dyn}}$ ;

5. for $i\in \{1,2,\dots ,z\}$ do

6.   $T=g_i$ ;

7.  LDS = Call RTDS algorithm to solve the minimum length of the dynamic segment;

8.  K = Call SAPR algorithm to solve static slot allocation with predefined reliability $\rho$ ;

9.  while $(S{T}_{\mathrm{slot}}·\sum _{k_j\in K}{k}_j+L_{\mathrm{DS}}\le T-S{T}_{\mathrm{slot}})$ do

10.   Calculate the message transmission reliability of each message $P_{\mathrm{sr}}(w)$ using equation (6);

11.   Find the static message $w_j$ with a minimum $P_{\mathrm{sr}}(w_j)$ ;

12.   Select $k_{\rho ,j}\in K$ , and let $k_{\rho ,j}=k_{\rho ,j}+1$ ;

13.   Update the set K with new $k_{\rho ,j}$ ;

14.  end while

15.  Calculate transmission reliability of static segment $P_{\mathrm{SR}}=\underset{i=1}{\overset{n}{\Pi }}{P}_{\mathrm{sr}}{\left(w_i\right)}^{\lceil \frac{\tau }{d_i}\rceil }$ ;

16.  if $(P_{\mathrm{SR}}>P_{\mathrm{sr}}^b)$

17.    $P_{\mathrm{SR}}^b=P_{\mathrm{SR}}$ , $K^b=K$ , $L_{\mathrm{DS}}^b=L_{\mathrm{DS}}$ , $T^b=T$ ;

18.  end if

19. end for

20. return $P_{\mathrm{SR}}^b$ , $K^b$ , $L_{\mathrm{DS}}^b$ , $T^b$ ;

RBPO: Reliability-Based Parameter Optimization.

First, $G=\{g_1,g_2,\dots ,g_z\}$ , the set of common divisors of the static message deadline is solved. $\forall g_i\in G$ is selected, and T is set to be equal to $g_i$ . The minimum dynamic length $L_{\mathrm{DS}}$ is determined by the RTDS algorithm, which can satisfy the real-time demands of dynamic messages. The maximum length of the SS is obtained through $L_{\mathrm{DS}}$ and T. Second, the slot for the predefined reliability is allocated by the SAPR algorithm. Third, the transmission reliability of each message is calculated using equation (5). The static message with minimum transmission reliability from the static message set is selected, and one static slot is added to the message, that is, $k_i+1$ , until the length of the SS exceeds its maximum length. The transmission reliability of the SS $P_{\mathrm{SR}}$ is calculated. Finally, the solution with maximum $P_{\mathrm{SR}}$ is considered the optimal solution when each $g_i\in G$ is selected.

The returned parameters $T^b,K^b,\mathrm{and}{L}_{\mathrm{DS}}^b$ from the algorithm can be seen as the optimal network parameters with respect to the maximum reliability $P_{\mathrm{SR}}^b$ . The optimal SS length $L_{\mathrm{SS}}^b$ can be easily deduced by $T^b-L_{\mathrm{DS}}^b$ .

Sub-algorithms RTDS and SAPR

RTDS sub-algorithm

${\overline{T}}_R^j\le d{m}_j$ and $\sum {\overline{T}}_R^j\le \delta$ are two important constraint conditions of equation (9c) and (9d). If the minimum length of the DS $L_{\mathrm{DS}}$ is found on the basis of equation (9a) and (9b), then more static slots can be allocated to the static messages, and the transmission reliability of the SS can be increased. The RTDS algorithm is used to search for the minimum length of the DS. The pseudocode of the RTDS algorithm is presented in Table 4.

Table 4.

RTDS algorithm.

1. Input: static message set $W_{\mathrm{st}}$ and dynamic message set $W_{\mathrm{dyn}}$ , communication cycle T, and the maximum allowed response time $\delta$ ;

2. Initialize $L_{\mathrm{DS}}^H=T-\mathrm{ns}·S{T}_{\mathrm{slot}}$ , $L_{\mathrm{DS}}=0$ ;

3. Calculate dynamic slot length $D{Y}_{\mathrm{slot}}$ for each message in $W_{\mathrm{dyn}}$ using equation (4);

4. Sort dynamic message in $W_{\mathrm{dyn}}$ in ascending order by the message ID;

5. for $j=1$ to nd

6.  Calculate ${\overline{T}}_R^j$ of dynamic message $m_j$ using equation (10) of the Appendix 1;

7.  while $\left(\begin{array}{ccc}{\overline{T}}_R^j>d{m}_j\hfill & \mathrm{and}\hfill & L_{\mathrm{DS}}\le L_{\mathrm{DS}}^H\hfill \end{array}\right)$

8.    $L_{\mathrm{DS}}=L_{\mathrm{DS}}+\mathrm{gdMinislot}$ ;

9.   Calculate ${\overline{T}}_R^j$ of the dynamic message $m_j$ using equation (10) of the Appendix 1;

10.  end while

11. end for

12. Calculate the response time of dynamic segment $\sum _{j=1}^{\mathrm{nd}}{\overline{T}}_R^j$ ;

13. $\mathbf{if}(\sum _{j=1}^{\mathrm{nd}}{\overline{T}}_R^j>\delta )$ , $L_{\mathrm{DS}}=0$ ;

14. return $L_{\mathrm{DS}}$ ;

RTDS: Response Time of Dynamic Segment.

First, the upper limit of the DS length, $L_{\mathrm{DS}}^H$ , corresponds to the difference between communication cycle and SS length, that is, $L_{\mathrm{DS}}^H=(T-\mathrm{ns}·S{T}_{\mathrm{slot}})$ . Second, the slot length of each dynamic message is calculated using equation (4), and $L_{\mathrm{DS}}$ increases by a gdMinislot each time until the conditions ${\overline{T}}_R^j\le d{m}_j$ and $L_{\mathrm{DS}}\le L_{\mathrm{DS}}^H$ are no longer satisfied. Finally, if the condition $\sum {\overline{T}}_R^j\le \delta$ is satisfied, then the final $L_{\mathrm{DS}}$ is the current value; otherwise, $L_{\mathrm{DS}}=0$ . The calculation of the average response time of the dynamic message ${\overline{T}}_R^j$ is expressed in Appendix 1.

SAPR sub-algorithm

The pseudocode of the SAPR algorithm is presented in Table 5. For equation (9a), $k_i\ge k_{\rho ,i},(i=1,2,\dots ,n\mathrm{s})$ is a constraint that requires the transmission reliability of the SS to be equal to or greater than the predefined reliability $\rho$ . $K_{\rho }^g=\{k_{\rho ,1},\dots ,k_{\rho ,i},\dots ,k_{\rho ,\mathrm{ns}}\}$ is defined as a set of static slot allocation under the predefined reliability $\rho$ . $k_{\rho ,i}\in K_{\rho }^g$ denotes the number of static slots allocated to the message i. The SAPR algorithm aims to obtain the set $K_{\rho }^g$ that makes $P_{\mathrm{SR}}\ge \rho$ and minimizes $\sum _{i=1}^{\mathrm{ns}}{k}_{\rho ,i}$ .

Table 5.

SAPR algorithm.

1. Input: static message set $W_{\mathrm{st}}$ , communication time $\tau$ , predefined reliability $\rho$ , and communication cycle T;

2. Initialize $K_{\rho }^g=\{1,1,.,1\}$ ;

3. for $i=1$ to ns

4.  Calculate the message transmission reliability $P_{\mathrm{sr}}\left(w_i\right)$ for each static message $w_i$ ;

5.  while $(P_{\mathrm{sr}}{\left(w_i\right)}^{\left(\frac{\tau }{d_i}\right)}\le \rho )$

6.    $k_{\rho ,i}=k_{\rho ,i}+1$ ;

7.   Calculate the message transmission reliability $P_{\mathrm{sr}}\left(w_i\right)$ of static message $w_i$ ;

8.   Update set $K_{\rho }^g$ ;

9.  end while

10. end for

11.  Calculate transmission reliability of static segment $P_{\mathrm{SR}}$ ;

12.  while $(P_{\mathrm{SR}}<\rho )$

13.   Find the static message $w_j$ with a minimum $P_{\mathrm{sr}}\left(w_j\right)$ ;

14.    $k_{\rho ,j}=k_{\rho ,j}+1$ ;

15.   Update set $K_{\rho }^g$ ;

16.   Calculate transmission reliability of static segment $P_{\mathrm{SR}}$ ;

17.  end while

18. return $K_{\rho }^g$ ;

SAPR: Slot Allocation for the Predefined Reliability.

To ensure that each message can be transmitted, initial $K_{\rho }^g$ is set as $\{1,1,\dots ,1\}$ . The definition of $P_{\mathrm{SR}}$ implies that the message transmission reliability of each message, $P_{\mathrm{sr}}(w_i)$ , must be higher than $\rho$ if $P_{\mathrm{SR}}\ge \rho$ . Therefore, the low limit of $k_{\rho ,1},\dots k_{\rho ,i},\dots k_{\rho ,\mathrm{ns}}$ can be calculated. Then, the static message $w_j$ with minimum $P_{\mathrm{sr}}(w_j)$ is determined, and $k_{\rho ,j}=k_{\rho ,j}+1$ is set until $P_{\mathrm{SR}}$ is higher than $\rho$ . The final $K_{\rho }^g$ is the desired result.

Experiments and analysis

Several experiments are performed on an experimental system demonstrated in Figure 5(a) to verify the proposed method in this study. This system consists of a hardware platform and a supervisory program on a PC. On the hardware platform, three FlexRay nodes, namely, $n1$ , $n2$ , and $n3$ , send the FlexRay messages periodically. The supervisory program is developed by Vector CANoe to monitor the messages in the FlexRay bus, as displayed in Figure 5(b). The PC that runs the supervisory program is connected to the FlexRay nodes through Vector VN8910A. Furthermore, the Vector FRstress is used to produce an error message in the experiments considering its high performance in reproducible disturbances on the FlexRay bus. The specific experimental equipment and detailed parameters used in this experiment are listed in Table 6.

Figure 5.

Experiment system: (a) hardware platform and (b) supervisory program.

Table 6.

Experimental equipment.

No.	Equipment name	Type
1	Measurement software	Vector CANoe 8.5
2	FlexRay network interface	VN8910A
3	FlexRay disturbing system	FRstress
4	FlexRay node	MCU: MC9S12XF512Transceiver: TJA1080

The message set, which comes from a real FlexRay network, in all experiments is listed in Table 7. Assume that the predefined reliability $\rho$ is 0.95, and the max response time of DS $\delta$ is 49,000 µs. According to the messages in Table 7, the parameters of the FlexRay network can be calculated using the proposed RBPO algorithm in this study. The results are summarized in Table 8. For the given message set, $\rho$ and $\delta$ , the communication cycle T is selected as 2 ms, and the number of static slots $\mathrm{Nst}=16$ . The $P_{\mathrm{SR}}$ is 0.9999 and is approximately 5.25% higher than $\rho$ . The $\sum {\overline{T}}_R^j$ is 47,940 µs and is approximately 2.2% less than the maximum response time of the DS $\delta$ . Therefore, the parameters obtained from RBPO can satisfy the demand of the FlexRay network design.

Table 7.

Messages in the experiments.

Static/dynamic segment	Node	Message	Length (byte)	Deadline (ms)
Static segment	1	$w_1$	62	2
		$w_2$	58	4
	2	$w_3$	64	2
		$w_4$	60	2
	3	$w_5$	62	4
		$w_6$	60	2
Dynamic segment	1	$m_1$	34	20
		$m_2$	28	16
		$m_3$	16	12
		$m_4$	32	16
	2	$m_5$	36	20
		$m_6$	28	18
		$m_7$	36	14
		$m_8$	22	12
	3	$m_9$	36	14
		$m_{10}$	28	18
		$m_{11}$	16	20
		$m_{12}$	30	16

Table 8.

RBPO results.

T (ms)	Nst	Slot allocation						$L_{\mathrm{DS}}(\mathrm{\mu }\mathrm{s})$	$\sum {\overline{T}}_R^j(\mathrm{\mu }\mathrm{s})$	$P_{\mathrm{SR}}$
		$w_1$	$w_2$	$w_3$	$w_4$	$w_5$	$w_6$
2	16	3	2	3	3	2	3	630	47,940	0.9999

RBPO: Reliability-Based Parameter Optimization.

The following experiments are conducted to verify whether the aforementioned parameters from the RBPO algorithm are optimal. The experiment cannot begin until the FlexRay parameters have been configured into all nodes and the supervisory program in the experimental system.

Comparison of different slot allocations and $N_{\mathrm{st}}$

For the messages in Table 7, 11 groups of slot combinations are selected in this experiment and are listed in Table 9. Four groups are selected for T = 1 ms, whereas seven groups are selected for T = 2 ms. For easy comparison, the results from RBPO in Table 8 are also listed in Table 9. The $P_{\mathrm{SR}}$ for different T and slot allocations is presented in Figure 6, and the corresponding $\sum {\overline{T}}_R^j$ is depicted in Figure 7.

Table 9.

The groups of parameters.

T (ms)	Nst	Static slot allocation
		$w_1$	$w_2$	$w_3$	$w_4$	$w_5$	$w_6$
1	6	1	1	1	1	1	1
	7	1	1	2	1	1	1
	8	2	1	2	1	1	1
	9	2	1	2	2	1	1
2	11	2	2	2	2	1	2
	12	2	2	3	2	1	2
	13	3	2	3	2	1	2
	14	3	2	3	3	1	2
	15	3	2	3	3	1	3
	16	3	2	3	3	2	3
	17	3	3	3	3	2	3

Figure 6.

$P_{\mathrm{SR}}$ for the different number of slots.

Figure 7.

$\sum {\overline{T}}_R^j$ when T = 1 ms and T = 2 ms.

In Figures 6 and 7, the values of $P_{\mathrm{SR}}$ and $\sum {\overline{T}}_R^j$ obtained through the calculation are similar to that obtained by the experiment; and the values of $P_{\mathrm{SR}}$ and $\sum {\overline{T}}_R^j$ increase along with $N_{\mathrm{st}}$ . For T = 1 ms, when N_st = 9, $P_{\mathrm{SR}}$ reaches a maximum, which is equal to 0.9895 in the calculation and 0.9868 in the experiment. For T = 2 ms, when N_st = 17, the $P_{\mathrm{SR}}$ also reaches the maximum, which is equal to 0.9999 in the calculation and 0.9995 in the experiment. The two maximums of $P_{\mathrm{SR}}$ are higher than $\rho$ . However, $\sum {\overline{T}}_R^j$ , which corresponds to each maximum of $P_{\mathrm{SR}}$ , is higher than $\delta$ . Obviously, the groups of parameters of T = 1 ms, N_st = 9 and T = 2 ms, N_st = 17 do not satisfy the network design requirement. Therefore, by comparing $P_{\mathrm{SR}}$ and $\sum {\overline{T}}_R^j$ , only the group of parameters of T = 2 ms and N_st = 16, which comes from RBPO is optimal. This result denotes that the RBPO algorithm can produce improved parameters to satisfy the demand in reliability and real-time capability of the FlexRay network.

Comparison of different slot allocation methods

The methods presented in Li et al. ²⁵ and Tanasa et al. ²⁶ are used to allocate the static slot for the six static messages in Table 7 and further verify the RBPO algorithm. For T = 1 ms and N_st = 8, the allocation solution of the static slot of Li et al. ²⁵ is $\{1,1,3,1,1,1\}$ , and the solution of Tanasa et al. ²⁶ is $\{1,2,1,2,1,1\}$ . When T = 2 ms and N_st = 16, the allocation solution of the static slot of Li et al. ²⁵ is $\{3,3,3,3,1,3\}$ , and the solution of Tanasa et al. ²⁶ is $\{3,3,2,3,3,2\}$ . These slot allocation solutions are configured into the experimental system, and the experiments are performed separately. The results are demonstrated in Figure 8. For the different schemes of slot allocation, regardless of T = 1 and N_st = 8 or T = 2 and N_st = 16, the $P_{\mathrm{SR}}$ is higher in RBPO than in Li et al. ²⁵ and Tanasa et al. ²⁶ This experiment denotes that the parameters obtained by RBPO are better than those obtained by other methods under the same conditions.

Figure 8.

$P_{\mathrm{SR}}$ for different slot allocations.

Figure 9 exhibits the number of static slots calculated using RBPO, the H-1 algorithm in Li et al. ²⁵ for the different message sets. The number of static slots increases with the number of static messages to satisfy the requirement on the reliability and real-time capability of the network. However, the number of static slots is less in RBPO than in H-1, thereby indicating that RBPO can satisfactorily utilize a bandwidth. Figure 10 displays the execution time of RBPO, H-1 algorithm in Li et al., ²⁵ and Method in Tanasa et al. ²⁶ for the different message sets. The execution time of H-1 increases rapidly with the number of static messages. However, the execution time of RBPO rises steadily and is relatively less than the execution time.

Figure 9.

Number of static slots for different message sets.

Figure 10.

Comparison of execution time.

Conclusion

FlexRay has special advantages over traditional vehicular buses, such as CAN (controller area network) and LIN (local interconnection network) in terms of communication speed and transmission determinism. FlexRay is considered the next-generation automotive bus standard and has been applied to real-time and safety-critical systems in vehicles. These systems have stringent requirements for network transmission reliability. Therefore, designing FlexRay must establish a systematic method in the application layer that can ensure a reliable message transmission among ECUs. Although related advancements are observed in the network’s real-time performance, parameter configuration, and reliable transmission, existing methods cannot be used in industrial applications given their lack of comprehensive consideration.

In this study, a model based on the redundant transmission and the probability of bit errors for the static frame is presented to depict the transmission reliability of FlexRay. The design of FlexRay network parameters is formulated as an optimization problem with constraints that consider the network’s transmission reliability and the message’s real-time performance. The RBPO algorithm and its sub-algorithms, namely, RTDS and SAPR, are proposed to approximately solve the network parameter optimization problems. The experimental results indicate that the method proposed in this study can not only satisfy the real-time requirements of messages but also ensure the transmission reliability of FlexRay SS. This result is confirmed by the values of transmission reliability and the response time of the dynamic message for a given message set. The response time of the dynamic message is less than 49,000 µs, whereas the transmission reliability is up to 0.9999, which has increased by over 5%. Furthermore, the total number of allocated static slots is clearly less than those of existing methods. This finding undoubtedly indicates that the proposed method can make better use of the network bandwidth, which is beneficial for practical application in vehicles. In the future, the reliability of a two-channel FlexRay network will be the subject of research and development.