EP3925175A1

EP3925175A1 - Method for routing in time-sensitive networks

Info

Publication number: EP3925175A1
Application number: EP20705338.0A
Authority: EP
Inventors: David Hellmanns
Original assignee: Hirschmann Automation and Control GmbH
Current assignee: Hirschmann Automation and Control GmbH
Priority date: 2019-02-12
Filing date: 2020-02-12
Publication date: 2021-12-22
Also published as: CN113424500A; DE102020103604A1; WO2020165243A1; US20220124020A1; CN113424500B

Abstract

The invention relates to a method for routing in a network. The network consists of a plurality of network nodes. The network may have different interlinks and connections from one network node to the others. An actual topology for the network is thus created. According to the invention, the routing is performed in two phases. Firstly, the number of possible links to the network nodes is reduced in a reduction phase. A reduced topology is thus created, in which network nodes or links to network nodes which are not required for route finding are discarded. In a subsequent routing and time planning phase, an optimised route to a network node in the reduced topology is then calculated.

Description

PROCEDURE FOR ROUTING IN TIME-SENSITIVE NETWORKS

DESCRIPTION

While real-time communication is rather rare in typical IT networks these days, it is an omnipresent topic in a large number of industrial network scenarios, for example for communication between components in a vehicle or machines in production plants. These systems have high real-time requirements, since malfunctions in such systems often lead to high economic damage, e.g. colliding robotic arms on a production line or even at the expense of humans when used for safety applications such as airbags or kill switches. Industrial automation, in particular, is very susceptible to delays and delay variations within communication, as the machines and robots on an assembly line require precise control and synchronization in order to ensure an accurate manufacturing process. Proprietary solutions and dedicated networks are currently used for many of these applications in order to ensure compliance with the specified maximum delays.

Examples of such field buses are CAN, Sercos III, Profibus or EtherCat. Sercos III, Profinet and EtherCat are based on Ethernet, but are incompatible due to proprietary extensions that enable real-time guarantees. Accordingly, communication between devices that are connected via different field buses requires gateways. Gateways lead to communication silos that hinder interoperability. As a result, there is now a trend towards harmonizing the various communication standards and merging critical and non-critical traffic in one network. This trend led to the establishment of the IEEE Time-Sensitive Networking (TSN) Task Group (TG). The TSN TG proposes a family of mechanisms which are collectively referred to as the TSN. These mechanisms define an IEEE 802-compliant Ethernet that can offer real-time guarantees. Ethernet is the de facto communication standard in the IT area. A key mechanism in TSN is IEEE Std. 802.1 Qbv, which enables highly deterministic communication. A class-based time slot method is used therein. "Time Division Multiple Access" (TDMA)] specified for Ethernet. This standard is primarily aimed at expanding switches, but can also be implemented on end hosts.

At each output port, IEEE Std. 802.1 Qbv introduces a timed gate in front of the queue for each traffic class. This gate controls whether the frames in the corresponding queue are released for transmission. Each port has a schedule which defines the opening and closing times for the gates. Although the queues and thus also the gates are class-based, electricity-based control is also possible with appropriate planning. This allows each communication flow between two hosts to be planned separately.

The IEEE standard defines the control mechanism (timed queues), but it does not specify algorithms for calculating these schedules that meet the real-time and bandwidth requirements of the applications. Basically, the configuration of the gates at each switch on the route between the source of the stream and the destination of the stream must be planned accordingly for each real-time stream. In general, calculating such schedules is an NP-hard problem. This application relates to efficient calculation of schedules and routes for TSN. Different approaches based on optimization methods, such as "Satisfiability Modulo Theory" (SMT) and Integer Linear Programming (ILP), as well as heuristics to optimize the runtime to solve the problem, have proven to be useful for calculating schedules. Most of these approaches, however, neglect the possibility of isolating communication flows not only in terms of time through scheduling, but also spatially through routing. Basic time and route planning approaches are known from the prior art. However, if you consider these two problems together, the search space for solutions to the already very complex planning problem is increased even further.

The calculation of time-controlled (TDMA) schedules with specified routes was considered in several approaches, especially for fieldbuses, which today are mainly based on real-time Ethernet technologies. In the publication “An Evaluation of SMT-Based Schedule Synthesis for Time-Triggered Multi-hop Networks” (Wilfried Steiner; 2010) Steiner et al. propose to model the scheduling problem in TTEthernet as a “constraint satisfaction” problem with the help of the “satisfaction modulo theory” (SMT), which can be solved with standard SMT solvers.

In order to ensure that sender applications deliver the messages to be sent to the network in good time, “SMT-based task and network level Static Schedule Generation for Time-Triggered Network Systems” (Craciunas / Oliver, 2016) and “Combined task and network -level scheduling for distributed time-triggered systems ”(Craciunas / Oliver, 2014) also based on SMT, formulations of the common process and network planning problem suggested.

Integer Linear Programming (ILP) is another well-known method to formulate planning problems taking into account optimization goals. In "Profinet IO IRT Message Scheduling" (Hanzalek / Burget / Sucha, 2009), ILP formulations are proposed for optimized planning problems that minimize the calculation time for creating a schedule for Profibus IRT or TSN.

However, SMT and ILP approaches that aim at an exact solution of planning problems suffer from the high complexity of the underlying NP-hard optimization problems. Therefore, several heuristics have been proposed to speed up the schedule computation. For this purpose, a heuristic based on the taboo search was proposed that reduces the runtime of the optimal TSN planning problem.

All of the aforementioned approaches focus exclusively on the temporal isolation of real-time streams, without considering the possibility of isolating streams spatially by routing them along different paths. The planning tool can only find solutions along the edges of given routes, which limits the solution space.

Spatial and temporal isolation of flows is taken into account by common routing and scheduling approaches. An approach is known for expanding software-defined networking (SDN) in order to achieve real-time capability with regard to limited message transit times and distribution times. For this purpose, three systems are known for the temporal separation and spatial separation of real-time streams by routing and planning. Two of the three proposed systems are heuristic and limit the search space by excluding solutions. The third approach uses an ILP model to calculate routes and schedules in one step. The routing part of the ILP model presented is similar to the basic model. Instead of optimizing the ILP model, however, heuristics are proposed that reduce the number of route options and thereby provide valid solutions to neglect. In the present application, a delimitation of the solution space is deliberately omitted.

Furthermore, the approach described can be extended to enable the iterative addition of stream locations. In this extension, edges are removed that connect end hosts that are not involved to the network. This is a very simple approach to reducing the model size, but most parts of the topology that contain invalid solutions are left untouched. In contrast to this approach, in this application we now exclude all edges and nodes that are not part of a loop-free route for a particular stream. To do this, we calculate a dedicated reduced topology for each source-destination node combination, drastically reduced by the problem size.

Furthermore, an approach for joint route and time planning in the form of a 0-1 ILP for mixed critical automotive networks is known. A model which is specially tailored to an application scenario is described. As a result, the proposed approach in the ILP formulation has certain limitations, e.g. the schedule granularity is directly linked to the number of variables. In contrast, a generic model is considered in this application. Furthermore, the present optimization can be used to optimize the aforementioned approach.

ILP models for common routing and scheduling for TSN networks are also known from the prior art. Both approaches present elaborate planning models, which are not the focus of this application, but both did not take into account optimization of the topology in order to reduce the complexity of the ILP. However, since their routing models are very similar to the basic routing model used in this application, the optimization pursued in this application can easily be adapted to the proposed ILPs. It will be in The following shows that the optimized model also has better performance compared to the simpler planning model used.

Finally, analytical approaches are discussed that check compliance with a certain schedule under certain conditions such as deadlines or limited buffer sizes (maximum backlog size for switches). In particular, several extensions of the formal Network Calculus Framework are proposed in the prior art, for example from "Modeling in network calculus a TSN architecture mixing Time-Triggered, Credit Based Shaper and Best-Effort queues" (Daigmorte, Boyer, Zhao; 2018), to model time-controlled planning mechanisms, such as the Timed Gating Mechanism, from TSN as well as other planning algorithms such as the Credit-based Shaper (CBS) from TSN, which is mainly used for audio / video traffic. These analytical approaches are particularly useful for analyzing convergent networks, where the simultaneous execution of different planning mechanisms leads to non-trivial effects. For example, the influence of high-priority time-controlled traffic on low-priority traffic could be analyzed. However, this analysis requires a predetermined schedule as input and therefore does not replace the algorithms for the schedule and route synthesis for the time-controlled traffic, as they are aimed at in this application.

In this application the task is set to propose an optimized approach for the common time and route planning problem. This object is achieved by the features of claim 1.

Instead of solving the entire common time and route planning problem, a preprocessing step is proposed that eliminates impossible solutions before solving the reduced problem with ILP. The preprocessing step significantly reduces the number of conditions and variables of the ILP without excluding possible solutions, ie without affecting the quality of the solution. In summary, it can be said that the following effects are achieved: Introduction of a preprocessing step to significantly reduce the ILP model size without excluding valid solutions and an evaluation of the proposed approach with regard to scalability in relation to the runtime.

Switched Ethernet networks typically work in full duplex mode. As a result, we are assuming full duplex operation, but the transfer of the system model and the proposed optimization to half duplex operation only requires minor adjustments. The network according to the invention is modeled as a directed graph g = {V, £}, where V and £ denote the nodes and edges of the topology. The edges (£) represent the Ethernet connections and each edge e is defined by the tuple of the connected nodes, e = (To, Ti) eV c V jV o * Ti. The use of a directed graph allows the modeling of the full duplex connections, i.e. independent communication in both directions. In addition, hosts are defined as nodes with only one full duplex connection (V ve Hosts: indegree (T) = outdegree (T) = 1) and all other nodes as switches (vv £ Switches: indegree (T) = outdegree (T)> 1 ), this results in V = hosts u switches.

Time-critical control applications, aimed at by IEEE Std 802.1 Qbv, typically run cyclically and model a control loop between sensor, actuator and controller. Unidirectional data streams (source hosts to destination hosts) are modeled. Therefore, the bidirectional communication is modeled as two streams A stream s is defined as a tuple of the source, the destination, the size (number of bytes), the maximum tolerated delay and the cycle time: s = (Tsrc, Tdst, size, c / , c) l V _s , V _d £ hosts, d £ N, size £ [64, MTU \. The set of all streams is also defined. The switches in the present model conform to IEEE Std 802.1 Q and implement in particular the "Enhancements for scheduled traffic". In g, input ports are modeled as incoming edges and output ports as outgoing edges. Although a real switch is implemented both functionalities in one physical port the internal processing of incoming and outgoing frames is strictly separated, which is why the present model does not violate general validity.

In order to further structure the following description of the switch model, we now describe how a frame is handled from its arrival at the input port, through processing and queuing, to its onward transmission at the output port. For the sake of simplicity, the routing process is divided into four phases, namely routing, queuing, transfer selection and transfer.

After the frame arrives at the input port, the switch evaluates the Ethernet header of the frame. Based on the recipient address and the content of the forwarding database, which contains an assignment of destination MAC addresses to output ports, the switch selects the destination output port. The switch provides one or more queues at the output port, since the incoming data rate can be higher than the outgoing data rate of the output port, since frames can be sent from several input ports via one output port. The "Enhancements for scheduled traffic" allow the implementation of up to eight queues in order to handle different types of data traffic separately. The switch assigns a frame to one of the queues by evaluating the "Priority Code Point" (PCP) in the VLAN tag of the frame and making a configurable assignment of PCP values to the flardware queues. In the present model, between A distinction is made between high-priority control frames and best effort frames. Accordingly, a switch is modeled with two logical queues.

For switches with more than two hardware queues, one of them is assigned a logical queue and the others are merged into the second logical queue. This application does not consider the influence of further prioritization or traffic shaping in the second queue. Note that in a single queue scenario with traffic converged, Qbv makes no sense.

The transmission selection logic (TS) decides which queue is processed in the next step. This decision is based on the "Transmission Selection Algorithm" (TSA), which is implemented for each queue. The TS polls the TSA of each queue in descending order to determine if a frame is available for transmission.

Although IEEE Std 802.1 Q specifies multiple TSAs, the present invention models strict priority and considers other TSAs to be out of scope. The TSA with high priority advertises a frame available for transmission if the queue is not empty. As a result, the TS chooses the frame at the top of the non-empty queue with the highest priority. However, this mechanism alone is not able to give hard real-time guarantees with regard to limited latency times or jitter. In the worst case, a high-priority frame is delayed by the transmission time of an MTU-sized best-effort frame that is currently being transmitted.

Therefore, IEEE Std 802.1 Q specifies an additional mechanism called "gating", which enables the processing of queues to be switched on or off for a specific time. This mechanism is implemented by placing a gate after each queue. If the gate of a queue is closed, the TS ignores the queue. This allows the output port can be used on a dedicated basis by one or more queues. Thus, gating enables the temporal separation of high-priority traffic and best effort traffic. The opening and closing times of the gates are configured in the Gate Control List (GCL). Hence the GCL is the implementation of a schedule in which the queue is granted access to the medium. To meet the latency requirements of a stream, the GCLs of all switches passed through must be calculated accordingly. The calculation of all GCLs in a network is therefore a global planning problem.

The GCL is a list of tuples that describe the gate states as a binary vector and the duration of the state. Switches execute GCLs cyclically, ie after the last state, the switch starts processing the GCL from the beginning. The duration of a GCL cycle is defined in the cycle time. If the sum of the durations of all GCL entries is less than the cycle time, the last status is held in order to close the gap. To ensure the synchronous execution of all GCLs (one for each output port) on a switch, the switch maintains a global clock. The switches in a TSN domain synchronize their clocks using the “Precision Time Protocol” (PTP). The processing in the switch described above causes delays in a frame. These delays are formalized as the processing delay d _pr , which relates to the switching process, and the waiting time d _q , which expresses the time the frame spends in the queue of this switch. It is assumed that the processing delay is specific to each switch, but does not change, and that the queuing delay is zero, since the present approach is designed to prevent high priority control frame waiting.

In addition to the aforementioned delays in the switch, a frame experiences further delays on its way from the source host to the destination host, namely transmission delay and propagation delay. The transmission delay d _tr represents the time it takes to modulate the bits of the frame on the cable depending on the link speed and frame size. The connection speed is modeled as a link property and, based on this, the present model is able to take into account different connection speeds in a network. The transmission delay is calculated as follows: d _tr = ^{link speed}

frame size. The signal propagation time characterizes the time that the

Signal needed to propagate in the transmission medium. The signal propagation time therefore depends on a material constant, which describes the signal propagation speed, and is also dependent on the cable length. Typical materials are copper (coaxial cable) and air (glass fiber).

In the present case, the propagation speed and cable length are described as link properties and therefore support different cable lengths and transmission media in this model. The signal propagation time is calculated as follows: d _pg = propagation_speed cablejength. Since the signal propagation speed is link-specific, it can be calculated in a preprocessing step and a constant link-specific value can be used in the present model. The mentioned delay definitions are used to calculate how long a frame occupies a connection and to calculate the arrival time of the frames at the next node.

In order to express the delays discussed in our model, we introduce three binary auxiliary relations and one auxiliary function (cf. equation 1):

W EV: processingjdelayv e processing_delay {V) ve e £: link_speed _e £ link_speed {e) ve e £: propagation_delay _e e propagation_delay {e) The calculation of Gate Control Lists (GCLs) for flow-based planning requires a route for each stream and a time schedule for the edges of this route. Most approaches to calculating real-time communication schedules use a routing algorithm as a preprocessing step to determine the routes for all streams. In these approaches, the actual planning problem is usually modeled as an ILP, SMT, or another optimization problem. Although the solver of the optimization problem searches the search space completely, it is possible that existing solutions cannot be found because the spatial dimension of the problem is not considered. In addition, solving the pure scheduling problem is already NP-hard and accordingly time-consuming. If the given scheduling problem proves unsolvable, the turnaround time is wasted. Finding the cause of not finding a solution is a challenge, because the cause can be varied. For example, it is not possible to differentiate between the case that the network capacity is insufficient to cover the required stream demand and the fact that the "wrong" routes were selected in the preprocessing step. Due to the large number of route combinations available and the complexity of the scheduling problem, a full search across all combinations of routes is not possible.

The excluded solutions problem could be addressed by expanding the optimization problem to solve the routing problem and the scheduling problem together. Approaches for the implementation and evaluation of such optimization problems were presented beforehand, which prove the high complexity. Based on these results, the question arises how the joint calculation of routes and schedules can be optimized. The implementation of heuristics leads back to the initial problem of excluded solutions. Therefore, only optimizations without first eliminating possible solutions are acceptable. For this reason, an approach based on the idea of calculating dedicated topologies for each source-target combination is proposed. These user-defined topologies are subgraphs of the actual network topology, reduced by edges and nodes that are not part of a valid route between source and destination. Since only edges and nodes are excluded from unrealizable routes, no solutions are eliminated, only the search space is reduced.

This section presents the formulation of the common routing and scheduling problem on the basis of the system model presented above (see Section 3). For the sake of readability, the description of the problem of joint route planning and scheduling has been divided into two sub-problems, namely route planning and time planning. Although the calculation of time planning and routes are highly dependent on each other, since time planning always belongs to a route due to the time assignment to the edges of the routes, we describe the ILP conditions for both sub-problems separately.

The routing conditions are displayed.

As already presented, a directed graph is used to represent the network topology for routing purposes. Two auxiliary relations are then defined, namely in_edges and out_edges. These two relationships contain the incoming or outgoing edges for each node.

W eV, v {V ^' , v) e £: {V, V) ein_edges (V)

W EV, V [V, V) ES: {V, V) E out_edges {V) (2)

A binary decision variable x _s , e E {0,1} is introduced for routing, which identifies for each stream-edge combination in (s, e) ES £ whether the stream s the Edge e uses. If x _s , e = 1, then edge e is said to be active for stream s. Otherwise the edge is said to be inactive.

In order to calculate the routes, five basic conditions are used for each stream: First, the source node (V _src ) only sends out information (one-way communication), so it must not have any active incoming edges. Since x _s , e cannot be negative, the restriction does not result in an active incoming edge

Second, the source node must have exactly one active outgoing edge since it is the beginning of the route:

Due to x _s , e £ 0,1}, the restriction can only be met if the following condition is met: x _s , e '= 1 / i ve £ out_edges {V _src ) l {e ^' }: x _s , e = 0.

Third, the destination node must not have any active outbound edges since it is the end of the route:

Fourth, since the route must end on exactly one path at the destination node, we limit the number of active incoming edges to 1:

Finally, after describing the conditions for the source and destination nodes, we need to ensure that the route through the network is contiguous. Therefore, we define that for all nodes of each stream that are neither source nor destination nodes, the number of active inbound edges must be equal to the number of active outbound edges:

The routing conditions presented provide the information as to whether the edge is active for each stream-edge combination. The scheduling constraints must ensure that multiple streams are not scheduled to use the same edge at the same time. Basically, the scheduling constraints enforce TDMA of streams on the edges of the network. For this purpose, two integer variables are introduced for each edge for each stream, which designate the beginning and the end of the assignment of the respective stream on the respective edge: Starts, e, end _s, e ^ [0, sd \. In the present model, the following conditions must be ensured: Firstly, only edges that do not violate the routing conditions may be used. Second, the length of the allocation must be sufficient to carry the stream. The delay definitions described are used to calculate the required allocation. Third, the allocation on successive edges must be consecutive, ie transmission on the next edge must begin immediately after the switch has finished processing the frame. Fourth, multiple streams cannot use an edge at the same time (TDMA). The necessary conditions are presented below.

First, we limit ourselves to the fact that a stream can only allocate time to edges that do not violate the routing conditions. Equation 8 ensures that end _s, e = 0 applies if x _s, e = 0, otherwise end _s, e is only limited by the cycle time. ve £ 8, Vs £ S: end _s, e <cycle_time x _s, e (8)

In addition, an allocation on one edge must be sufficient to transmit the entire content of the stream. Therefore, the condition for the allocation duration takes into account the propagation delay and the transmission delay. ve £ 8, Vs £ S: end _s, e = starts _, e + x _{s, e} transmission_delay {stream_size, link_speed {e))

(9)

If the edge is not active, equation 9 sets starts _, e = end _s, e = 0, otherwise the length of the allocation is set to the duration of the transmission. In addition, we need to ensure that consecutive allocations are made to consecutive streams. In doing so, we take into account the processing delay of the node passed.

Finally, we define a condition to prevent multiple simultaneous allocations on the same edge by ensuring that the allocations do not overlap. In order to express that exactly one of the described assignments has to be chosen, we have to implement an xor.

ILPs generally do not support Boolean operators because they are difficult to express as a linear condition. However, depending on the solver used, so-called indicator conditions can be used to model xor. If the solver does not support indicator conditions, Big M constraints are able to express the xor operation.

For the sake of simplicity, we use Big M constraints here and introduce a new binary variable y _s, s' _, e for each pair of potentially colliding flows (s, s). We also need a constant M, which is always greater than the left side of the equation. However, if the constant chosen is too large, it can lead to numerical problems that invalidate the solution. In our model we therefore set M \ = max {sd, s ^' .d) since the maximum of the deadlines for both streams must be greater than the end of the allocations on all edges of these streams.

In order to avoid overlapping two streams, we implement two conditions that force that stream s is allocated before stream s' or that stream s'is allocated before stream s: K (s, s), e) e {S x S) x £ js F s \

On the right side of the first condition we add y _s, s'e M and on the right side of the second condition we add (1 - y _{s, s} ' e) M. Since y _s, s'e is binary, the solver can either assign y _{s, s} ' e: = 0, which means that stream s is allocated before stream s' or y _{s, s} ' e: = 1 must be satisfied which leads to stream s'being allocated before stream s.

The basic ILP formulation of the routing and scheduling problem presented in this section can already be solved with a standard ILP solver. In general, however, it suffers from scalability problems due to the multitude of conditions and variables. Especially in network topologies with many alternative routes, the joint solution to the scheduling and routing problem significantly increases the search space. Therefore, a method is now proposed to reduce the search space without impairing the quality of the result.

The size of the ILP base model grows sharply with each additional stream, since each stream can potentially use each edge. Therefore, the number of decision variables and conditions increases with each additional stream. Many of these additional conditions and variables restrict edges that are not part of technically feasible routes. Therefore one can reduce the routing and scheduling ILP model without excluding workable solutions. In particular, according to the invention, only collisions of streams at edges that are part of valid routes are taken into account. In the basic model, the effort to avoid overlapping allocations scales quadratically with the number of streams.

The basic idea of this approach is to first determine the number of edges of the original topology in a preprocessing step (topology - Reduction phase). To do this, we calculate a dedicated reduced topology for each source-destination node combination. In the reduction phase it is crucial not to limit the solution space, but only to remove edges that are not part of a practicable solution for the respective source-target node combination. It should be noted that this is the main difference to related approaches which also use a preprocessing step to restrict paths before solving the routing and scheduling problem.

These approaches typically use heuristics to find a number of promising routes, such as choose the k shortest paths, without ensuring that no workable solutions are excluded. Instead, the present invention seeks to exclude precisely those edges that are not part of a practical solution. Our optimization proposal consists of two parts, namely the topology reduction and the actual routing and time planning phase. The topology reduction is carried out as a preprocessing step. In order to map the results of the preprocessing step in the ILP, the ILP model is adapted accordingly.

First, the calculation of the reduced topologies is explained. In this phase, a separate topology is introduced for each combination of source and target. As a result, the ILP does not receive an overall topology as input, but takes an adapted topology into account for each source-destination combination. All loopless routes from the source to the destination are calculated for each source-destination combination.

After the routes have been calculated, a separate topology is calculated for each source-destination combination by discarding all edges in the topology that are not part of a route for this specific source-destination combination. The topology reduction method is presented as pseudocode in Listing 1.

Since all routes are calculated, the solvability is not restricted. In general, between any two nodes up to / V /! Routes exist. However, it can be assumed that real topologies have a much smaller number of paths because the connectivity is much less than with full graphs.

(Listing 1)

In order to take into account the precalculated routes, the conditions of the model according to the invention are adapted as follows: Two auxiliary relations are presented, namely stream_edges and stream_vertices, which contain the edges and nodes of the precalculated routes that represent the reduced topology for each stream (see equation 12). is fi: {(s, edges) £ stream_edges {s) / edges cE} se S: {{s, vertices) £ stream_vertices {s) / vertices cV} (12) Instead of / x _s, e / = / S ^c £ /, \ we reduce the number of decision variables to / x _s, e / = jS x stream_edges {S) l. Furthermore, due to the fact that vs eS: in_edges {V _src ) P stream_edges {s) = 0 and vs eS: out_edges {V _dst ) P stream_edges {s) = 0, one can omit the restrictions on the number of active Zero input edges for the source (Equation 3) and zero the number of active output edges on the target (Equation 5). In Equation 4, Equation 6, and Equation 7, we just need to consider the allowable edges of the corresponding current in Equation 13, Equation 14, and Equation 15.

V (V _S rc '^ dst _< size, d, c ^' ) e S, V _v E stream_vertices (s) \ {V _src , V _dst }:

If only one route exists for a certain source-destination combination, the routing equations can be omitted and all x _s, e set, ie for this source-destination combination to 1 in the planning restrictions, ie no further routing is required from the ILP be carried out when the choice of route is trivial. Finally, the route options are reduced to the route options actually available. Therefore, the model size generally shrinks.

For timing purposes we replace all occurrences of £ with stream_edges {s), V with stream_vertices {s), out_edges {V) with out_edges {V) P stream_edges {s), and in_edges {V) with out_edges {V) P stream_edges { s). In the following, the resulting limitations of the reduced problem are listed: vs {V _src , V _dst , s \ ze, d, c) eS

(16)

Ve e stream_edges {s): end _se <dx _se

Vs eS, Ve e stream_edges {s): end _se = start _se + x _s, e (propagation_delay {e) + transmission_delay {stream_size, link_speed {e))

(17) v {V _S r _C V _dst , \ ze, d, c) ES, W EV \ {V _src , V _dst }: end _se + x _se processing _delay (V)

e E in_edges (e) nstream_edges (s)

e E out_edges (V) nstream_edges (s)

(18)

V {{s, s), e) £ {SS) x (stream_edges {s) P stream_edges {s) / s F s \ end _se <start _{sl e} + y _s, s' _, e M,

Since stream_edges {s) l «/ £ / and lstream_vertices {s) l« / V / apply in most cases, the total number of restrictions is significantly reduced.

In summary, it can be said that the necessary adjustments to the ILP formulation are limited to quantifiers and sum limits. Therefore, the effort for adapting the associated common routing and scheduling approaches is estimated to be low.

The presented optimization on the basis of reduced network topologies for each source-target combination deliberately does not exclude any practical solutions. Nevertheless, reduced topologies can be given not only on a source-target basis, but also on a stream basis, which leads to dedicated reduced topologies for each stream. The network planner can decide on a stream basis how many routing options are to be modeled. Therefore, the complexity of the model can be adjusted during the design phase.

In addition, further preprocessing steps can be implemented. For example, the occupancy rate of different edges or the likelihood of collision of currents can be evaluated. Based on the results of these additional steps, the reduced topologies can be optimized, which leads to optimized models with reduced search spaces.

Further features of the present invention emerge from the accompanying drawings. Show it:

Figure 1: The packet forwarding functions of an IEEE Std 802.1 Q compliant

Switches;

FIG. 2: Transmission selection as specified in IEEE 802.1 Q;

FIG. 3: route determination conditions for stream s; Figure 4: The conditions for route determination do not exclude two special cases if they are used on their own;

FIG. 5: Relationship between start and end of an allocation on successive edges;

Figure 6: Equation 1 1 prevents collisions by allocating either stream s before stream s ’or stream s before stream s’;

FIG. 7: Example of a graph reduction;

FIG. 8: exemplary topology for a factory network;

FIG. 9: exemplary routing options;

FIG. 10: Reduced graph for FIG. 9 (intermediate step);

Figure 1 1: Reduced graph for Figure 9 (result);

FIG. 12: Exemplary streams with start and end time variables;

FIG. 13: Reduced graph for FIG. 12 (intermediate step);

FIG. 14: Reduced graph for FIG. 12 (result);

FIG. 1 shows how a frame is handled from its arrival at the input port via processing and queuing to its onward transmission at the output port. For this purpose, FIG. 1 shows the entire forwarding process. For the sake of simplicity, the routing process is divided into four phases, namely routing, queuing, transfer selection and transfer.

After the frame arrives at the input port, the switch evaluates the Ethernet header of the frame. Based on the recipient address and the content of the forwarding database, which contains an assignment of destination MAC addresses to output ports, the switch selects the destination output port. The switch provides one or more queues at the output port, since the incoming data rate can be higher than the outgoing data rate of the output port, since frames can be sent from several input ports via one output port. The "Enhancements for scheduled traffic" [3] allow the implementation of up to eight queues in order to handle different types of data traffic separately. The switch assigns a frame to one of the queues by evaluating the Priority Code Point (PCP) in the VLAN tag of the frame and making a configurable assignment of PCP values to the flardware queues.

Figure 2 shows the “Transmission Selection Algorithm” (TSA) that is implemented for each queue. The TS polls the TSA of each queue in descending order to determine if a frame is available for transmission. Although IEEE Std 802.1 Q specifies multiple TSAs, this paper models strict priority and considers other TSAs to be out of scope.

The TSA with high priority advertises a frame available for transmission if the queue is not empty. As a result, the TS chooses the frame at the top of the non-empty queue with the highest priority. However, this mechanism alone is not able to give hard real-time guarantees with regard to limited latency times or jitter. In the worst case, a high-priority frame is delayed by the transmission time of an MTU-sized best-effort frame that is currently being transmitted.

Therefore, IEEE Std 802.1 Q specifies an additional mechanism called "gating", which enables the processing of queues to be switched on or off for a specific time. This mechanism is implemented by placing a gate after each queue. If the gate of a queue is closed, the TS ignores the queue. This allows the output port can be used on a dedicated basis by one or more queues. Thus, gating enables the temporal separation of high-priority traffic and best effort traffic.

The opening and closing times of the gates are configured in the Gate Control List (GCL). Hence the GCL is the implementation of a schedule in which the queue is granted access to the medium. To meet the latency requirements of a stream, the GCLs of all switches passed through must be calculated accordingly. The calculation of all GCLs in a network is therefore a global planning problem.

As presented in the system model, a directed graph is used to represent the network topology for routing purposes. For this purpose, two auxiliary relations are then defined, namely in_edges and out_edges. These two relationships contain the incoming edges or outgoing edges for each node (see equation 2).

For the routing according to FIG. 3, a binary decision variable x _s, e ^ 0,1} is introduced which, for each stream-edge combination in (s, e) e S x £, identifies whether the stream s uses the edge e. If x _s, e = 1, we call the edge e active for stream s. Otherwise we call the edge inactive.

To calculate the routes, we use five basic restrictions for each stream: First, the source node (Vsrc) only sends out information (unidirectional communication) and, therefore, it must not have any active incoming edges (equation 3). Since x _s, e cannot be negative, the restriction in equation 3 does not result in an active incoming edge.

Second, the source node must have exactly one active outbound edge since it is the beginning of the route.

Third, the destination node must not have any active outbound edges since it is the end of the route. Fourth, since the route must end exactly on one path at the destination node, the present model can only select one active incoming edge for the destination.

Finally, once the source and destination have been restricted, it is necessary to ensure that the route is connected by a single path through the network. Therefore, it is defined that for each stream all nodes that are neither source nor destination nodes have an equal number of active inbound edges and active outbound edges:

As stated above, both routing loops and isolated loops can occur, as shown in FIG. Routing loops are loops that are directly connected to the actual route, as shown in the figure on the left, while isolated loops, as shown in the figure to the right, are not part of the route.

In our model, as already described, the following conditions must be ensured: Firstly, only edges that have been selected in the routing part can be used. Second, the length of the allocation must be sufficient to carry the power. We use the transmission delay to calculate the required allocation.

Figure 5 shows the transmission of a current. Furthermore, the assignment to consecutive edges must be consecutive, i.e. transmission on the next edge must begin immediately after the switch has finished processing the frame. Finally, several streams may not use an edge at the same time (TDMA).

As mentioned above, a restriction is defined to prevent multiple simultaneous allocations on the same edge by ensuring that the allocations are temporally separated, ie they do not overlap. FIG. 6 shows the two existing non-overlapping allocations for two streams on one edge, namely stream s is assigned before stream s '(left side of FIG. 6) or stream s' is allocated before stream s (right side of FIG. 6). The method of topology reduction is illustrated by way of example in FIG. The original topology is shown on the left-hand side of FIG. 7, while the remaining figures show the results of the reduction for two source-target combinations (once Vsrco- »· Vdsto, top right and Vsrd-» · Vds \ ^, bottom right). In this example, the intersection between the edges of the two reduced topologies is empty and therefore no overlap between the assignments is possible.

However, the preprocessing results can be reused as streams are added or dropped, which are relevant use cases. In this case, the changes to the reduced topologies can be adopted gradually. Therefore, the upfront costs are a good investment as they allow quick recalculation of schedules and routes on the network.

FIG. 8 shows an example of a topology of a possible network for using the present method.

To further optimize the schedule and route synthesis, the network topology is shown as a graph g (V, £) with nodes V and edges £. As an extension of the previous concept, specialized reduced graphs for route and schedule synthesis are proposed. First, the graph reduction for the route synthesis from g to g _{R is} presented and then the reduction steps for the schedule synthesis are discussed.

By reducing the graph, a dedicated routing graph g _{R s is obtained} for each stream s. As a basis for the reduction, we calculate a certain number of routes for each stream. The procedure described is independent of the number of routes. We describe the set of the considered route of the stream & as R _s . We represent a single route as a sequence of the visited nodes, e.g. route 0 for stream &: V _{Ro S} £ v. Furthermore, we denote the set of all nodes that are contained in at least one route of the stream as V _{RQ S} e v. We generate g _{R s} in which we exclude all nodes that do not appear in any route of the stream: Vv e G _{ß, s} : ve V \ (V \ V _{ß, s} ).

The procedure is described below using an example. FIG. 9 shows the original graph including a selection of routing options for a stream D ₀ . The start node of D ₀ is marked in white and the destination node in black. The routing options shown result in a total of eight possible routes (two combinations for each ring traversed).

The reduced graph in FIG. 10 then results from the routing options given in FIG.

This graph is further reduced by converting sequences of nodes with the same node degree degO) to an edge. The degree of knot denotes the number of edges of a knot. A node is inserted at each point where the node degree changes. This then results in the final routing graph g _R , z, ₀ for stream ₀ . The result is shown in Figure 11.

Based on the final routing graph, the ILP model can be greatly reduced because now no decision variable (originally x _se ) is required for every possible edge in the original graph, but only for each edge in the reduced graph.

In the synthesis of a schedule, two factors have a decisive influence on the size of the ILP model:

1 . The number of edges on which the stream must be allocated. For each potential edge of a stream, we add a variable to the model for the start and end time of the transmission.

2. The number of edges on which there is a potential conflict between two streams. One conflict is that two streams have the same edge in the same Use direction. In this case, it must be ensured that the streams are not allocated to the same connection at the same time.

In FIG. 12, the potential edges of two streams are shown for each of which a start (start _se ) and end time variable (end _se ) are added. Since we are calculating a “no-wait schedule”, the start time on the first edge is the only degree of freedom with regard to scheduling. Based on this knowledge, all further start and end times can be calculated depending on the start on the first edge. Accordingly, the number of variables can be significantly reduced.

To avoid conflicts, the original model sets two conditions that prevent two streams (^ ₀ , _± ) from using an edge at the same time. These conditions ensure that either stream D ₀ before stream or before D _{0 is} processed. In the original model, the number of conditions is already optimized by only considering a potential conflict between two streams on an edge as possible if both streams have at least one route that uses this edge. FIG. 13 shows the result of this optimization. Only the edges that use both streams in the same direction remain.

It is noticeable that the edges on which a conflict can occur form sequences of several consecutive edges. Due to the “no-wait” property of the schedule, streams cannot overtake each other once the order has been determined on an edge. This means that it is not possible to plan before D ₀ for successive edges and D ₀ before on the next edge in the sequence applies. As a result, sequences of successive edges can be viewed as a conflict domain and the decision as to which stream is scheduled first needs to be made only once for each conflict domain. Figure 14 shows the resulting situation. Until now, potential conflicts have only been considered due to edge use. If you look at the temporal course of the streams, you can optimize the model even further. A certain period of time passes for each edge and intermediate node that a stream passes. On the basis of this time span, it is possible to calculate when a stream can arrive at an edge at the earliest. For each stream it is also known at what point in time the stream must arrive at its destination at the latest. From this you can deduce when a stream must pass an edge at the latest. So there is a specific time window for each stream on each edge. We can use this knowledge in two ways: 1. Collisions between two streams only need to be considered if the time windows overlap on an edge used by both streams. 2. The time window can be used to restrict the solution space by limiting the definition range of the stream's start time variable accordingly. To do this, we restrict the definition range of the variables start _se and end _se accordingly.

In summary, it can be said that the present optimized model clearly outperforms the base model in non-trivial scenarios in general. The preprocessing time increases with more complex topology, but the total runtime is still reduced by up to a factor of 100. In addition, the reduced topologies of preprocessing can be reused for incremental changes to the network, which enables cost-effective reconfiguration of the network.

Claims

EXPECTATIONS

1. Procedure for routing and scheduling in a network,

wherein the network consists of a plurality of network nodes

and the network has an actual topology,

characterized,

that initially in a reduction phase the number of possible links to the

Network node is reduced

and thus a reduced topology is calculated,

then, in a routing and time planning phase, an optimization of the routing and scheduling is calculated in the reduced topology.

2. The method according to claim 1, characterized in that the reduced topology has fewer network nodes than the actual topology.

3. The method according to any one of claims 1 or 2, characterized in that in the reduction phase the space of possible solutions for routing is not limited, but only links or network nodes that do not belong to the solution space are removed.

4. The method according to any one of claims 1 to 3, characterized in that a separate topology is introduced in the reduction phase for each combination of source and destination and a route from a source to the destination or network node is calculated for each topology.

5. The method according to claim 4, characterized in that all links which are not part of the calculated route are discarded.

6. The method according to any one of claims 1 to 5, characterized in that the calculation of the routes is carried out by “integer linear programming” (ILP).

7. The method according to any one of claims 1 to 6, characterized in that all transmission times of the possible routes are calculated to calculate the optimized route and then a time-optimized route is selected.

8. The method according to any one of claims 1 to 6, characterized in that all routes of the possible routes are calculated to calculate the optimized route and then a route-optimized route is selected.

9. The method according to any one of claims 1 to 8, characterized in that the occupancy rate of the links used is taken into account in the reduction phase.

10. The method according to any one of claims 1 to 9, characterized in that the collision probability of the links used is taken into account in the reduction phase.

1 1. The method according to any one of claims 1 to 10, characterized in that the method is carried out by a network participant at a network node.

12. The method according to any one of claims 1 to 1 1, characterized in that the method is to be used on Ethernet-based networks.

13. Network with several network participants,

with multiple network nodes and an actual topology, characterized in that for routing between two

Network subscribers the method for routing in a network according to one of claims 1 to 12 is carried out.

14. Network according to claim 13, characterized in that the network is a TDMA-based network or a CAN bus or SERCOS III or a Profibus or Ethercat.