CN115834511A - Gating scheduling method for periodic messages of each priority in time-sensitive network - Google Patents
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Abstract
The invention discloses a gate control scheduling method of periodic messages of each priority in a time-sensitive network, which comprises the steps of reading messages to be scheduled, extracting a sending port, a receiving port, a period, a priority and a length, determining a passing link, calculating a least common multiple, then sequencing, verifying the ith message according to sending time slots temp (i) and temp (i) (p), assigning values to a message two-dimensional scheduling array element value launchslot (i) (p), solving the scheduling time of conflict-free and low-delay forwarding of all messages under the condition of meeting constraint conditions under the condition of giving the periodic messages, further solving a proper gate control scheduling list, and realizing the conflict-free and low-delay forwarding scheduling of the messages. Compared with the existing gating scheduling method, the method simplifies the constraint strategy during scheduling distribution, thereby reducing the calculation workload, reducing the time complexity and simultaneously ensuring the real-time property and the low-delay characteristic of the scheduled high-priority message.
Description
Technical Field
The invention belongs to the technical field of time-sensitive networks, and particularly relates to a gating scheduling method for periodic messages of various priorities in a time-sensitive network.
Background
A Time Sensitive Network (TSN) developed by Audio Video Bridging (AVB) is used as a bottom layer protocol architecture, and has the advantages of low Time delay, low jitter, high reliability and the like on the basis of real-Time Ethernet. The characteristics enable the time-sensitive network to realize the deterministic end-to-end transmission of data and meet the end-to-end performance requirements of key data streams in the industrial network.
The time sensitive network is defined by a series of standards related to a data link layer, including a series of standards such as IEEE802.1AS time synchronization, IEEE802.1Qbv gating scheduling, IEEE802.1Qbu frame preemption, IEEE802.1Qcc network configuration and the like, and the standards are mainly used for solving the problems of time synchronization, traffic scheduling, network configuration and the like in the TSN.
Time Aware Shaping (TAS) is proposed in the IEEE802.1Qbv protocol, which is an algorithm based on the Time division multiplexing principle that divides a network communication system into transmission periods that repeat continuously according to a certain length. Within a period of time, the system can allocate different time slice resources to a priority service type, especially time-sensitive service. The basic purpose of time-aware shaping is to ensure that time-sensitive traffic (high priority frames) does not increase transmission delay because the transmission port is occupied by low priority frames. Each output port controls the transmit permission of the corresponding priority through a gated List (GCL: gate Control List). In the GCL table, O represents that the gate state is open, and C represents that the gate state is closed, so that whether the data frames in each queue are transmitted or not is controlled.
In terms of time-sensitive network gating scheduling studies, foreign scholars describe how to determine the formal constraints of a valid gating list and use integer linear programming to determine a feasible solution for the transmission properties of time-aware shaping. On the basis, other scholars provide a joint configuration method aiming at the transmission characteristics of a time-sensitive network and combining with a 5G network architecture, the method can realize end-to-end scheduling optimization on a bridge network formed by taking 5G as a bridge, and a gating list configuration scheme meeting the end-to-end QoS requirement is obtained through a proper constraint strategy. Although the constraint strategies are many, the repeated constraints among a plurality of constraint strategies are more, the workload of calculation is greatly increased, and the definition of jitter is violated in the design of jitter constraint, so that the constraint strategies are unreasonable in the aspect of constraint strategies.
Disclosure of Invention
The invention aims to overcome the defects of the prior art, and provides a gate control scheduling method of periodic messages of each priority in a Time Sensitive Network (TSN) on the basis of a gate control scheduling mechanism of a traditional Time Aware Shaping (TAS) algorithm.
In order to achieve the above object, the method for gating and scheduling periodic messages of each priority in a time-sensitive network according to the present invention comprises the following steps:
(1) Reading each message to be scheduled, extracting a sending port, a receiving port, a period, a priority and a length of each message, and obtaining the ith message T to be scheduled i Can be expressed as:
T i ={Source(i),destination(i),period(i),priority(i),length(i)}
wherein, the sending port, the receiving port, the period, the priority and the message length of the ith message are sequentially arranged from left to right.
Then, determining a passing link according to the network topological graph;
(2) Calculating the minimum common multiple LCM of the periods of all the messages, and taking the minimum common multiple LCM as a matrix period;
(3) Sequencing all messages to be scheduled in the following mode:
a) Sorting the messages from small to large according to the size of the message period;
b) If the periods are equal, sequencing according to whether the transmission link of the message passes through the cascade link between the exchangers or not, and sequencing according to the priority of the cascade link between the exchangers;
c) If all the messages pass through the cascade link between the exchangers, sequencing the messages from high to low according to the priority of the messages;
d) If the priority is equal, sorting the messages according to the length of the messages from large to small
All the messages to be scheduled after sequencing are placed into a message array tsnUnset, and the total message number is recorded as tNum;
setting a message two-dimensional scheduling array launchslot, wherein the value of launchslot (i) (p) is the scheduling time slot of the p-th period of the ith message, and the initial values are all-1, p belongs to [0, LCM/period (i) -1];
(4) Sequentially traversing each message in the message array tsnUnset and allocating scheduling time slots for the messages
4.1 Generating a sending time slot to be verified according to the LCM (least common multiple), the period of the message and the message length, wherein the sending time slot temp (i) corresponding to the ith message is an integer in [0, period (i) -t (i) ], the initial value is 0, t (i) is the transmission duration of the ith message, and the transmission duration comprises link transmission time and scheduling time;
4.2 Verifying a sending time slot temp (i) corresponding to the ith message, if a scheduling constraint condition is met, setting an element value launchslot (i) (p) of the corresponding message in the launchslot from-1 to temp (i) + p × period (i), simultaneously removing the ith message from a message array tsnUnset, if the message is from a set undoSet, removing the message from the set undoSet, and entering a step 4.6);
if the constraint condition is not satisfied, the message j which conflicts with the ith message is shown to exist, the sizes of the priority (i) of the conflicted ith message and the priority (j) of the message j are firstly judged, if the priority (j) is smaller than the priority (i), the message j is put into the aggregate event, and if the priority (j) is more than or equal to the priority (i), the message j is not put into the aggregate event; then, judging whether the sending time slot temp (i) reaches the upper limit period (i) -t (i), if not, adding 1 to the sending time slot temp (i), and returning to the step 4.1), if so, judging whether the undoSet is empty, if not, entering the step 4.3), and if so, entering the step 4.4);
4.3 Step 4), traversing the set undoSet, and executing the operation of the step 4.1) -4.2) on each message;
4.4 Generating a sending time slot to be verified for each period of the message according to the minimum common multiple LCM, the period (i) of the ith message and the message length (i), and marking as temp (i) (p); wherein, a sending time slot temp (i) (p) corresponding to the p-th period of the ith message is an integer in [0+ p × period (i), period (i) -t (i) + p × period (i) ], the initial is an integer at the leftmost side of the interval, period (i) is the period of the ith message, t (i) is the transmission duration of the ith message, including the link transmission duration and the scheduling duration, and p ∈ [0, lcm/period (i) -1];
4.5 Sequentially verifying a sending time slot temp (i) (p) of each period of the ith message, and if a scheduling constraint condition is met, setting an element value launchslot (i) (p) to temp (i) (p) and simultaneously removing the ith message from a message array tsnUnset; if not, adding 1 to temp (i) (p) and returning to step 4.4);
4.6 Judging whether the array tsnUnset is empty, if so, indicating that all messages are successfully distributed, obtaining a conflict-free sent message two-dimensional scheduling array number launchslot, and entering the step (5), otherwise, returning to the step 4.1) to continue to distribute scheduling slots for uncompleted messages;
(5) Constructing a link time slot number axis graph with the horizontal axis as a time slot for all links according to the message two-dimensional scheduling array launchslot, and then obtaining a feasible gating queue scheduling scheme of an output port according to specific message scheduling time slot allocation information in the link time slot number axis graph of the link corresponding to the output port of the switch;
wherein the scheduling constraint is
a) And conflict-free constraint: the same link can be occupied by only one message at most in the same time slot, if different messages i and j passing through the same link L exist, the link L is the mth link of the message i from the sending end to the receiving end in sequence, and is the nth link of the message j from the sending end to the receiving end in sequence, and if the message i and the message j do not conflict, the following inequalities are satisfied for any p and q:
launchslot(i)(p)+m×t(i)<launchslot(j)(q)+(n-1)×t(j)
or
launchslot(i)(p)+(m-1)×t(i)>launchslot(j)(q)+n×t(j)
Wherein p and q are respectively the numbers of the transmission periods of the messages i and j in a matrix period, which represent the p-th transmission period of the message i and the q-th transmission period of the message j, and p belongs to [0, LCM/period (i) -1], q belongs to [0, LCM/period (j) -1];
b) And path constraint: if message i needs to continuously pass through link L 1 And a link L 2 And in time slot S x Over a link L 1 Must be in time slot S x + d (i) via link L 2 D (i) is the scheduling duration of the message i;
c) End-to-end constraint: the initial time slot of the message i passing through the link must be within the maximum time slot number, namely: launchslot (i) (p) < LCM, and launchslot (i) (p) > =0, p ∈ [0, LCM/period (i) -1].
The invention aims to realize the following steps:
the invention discloses a gate control scheduling method of periodic messages of each priority in a time-sensitive network, which comprises the steps of reading a message to be scheduled, extracting a sending port, a receiving port, a period, a priority and a length, determining a passing link, calculating a least common multiple, then sequencing, verifying the ith message according to sending time slots temp (i) and temp (i) (p), assigning values to a message two-dimensional scheduling array element value launchslot (i) (p), solving the scheduling time of conflict-free and low-delay forwarding when all messages meet constraint conditions under the condition of giving the periodic message, further solving a proper gate control scheduling list, and realizing the conflict-free and low-delay forwarding scheduling of the message. Compared with the existing gating scheduling method, the method simplifies the constraint strategy during scheduling distribution, thereby reducing the calculation workload, reducing the time complexity and simultaneously ensuring the real-time property and the low-delay characteristic of the scheduled high-priority message.
Drawings
FIG. 1 is a flowchart of an embodiment of a method for gated scheduling of periodic messages of various priorities in a time-sensitive network according to the present invention;
FIG. 2 is a network topology diagram of an embodiment of a time sensitive network;
FIG. 3 is a graph of the number of link slots after message 1, message 2, and message 3 have been allocated;
FIG. 4 is a graph of the number of link slots completed for message 4;
FIG. 5 is a graph of the number of link slots completed for message 5;
fig. 6 is a graph of the number of link slots completed for message 6.
Detailed Description
Specific embodiments of the present invention are described below in conjunction with the accompanying drawings so that those skilled in the art can better understand the present invention. It is to be expressly noted that in the following description, a detailed description of known functions and designs will be omitted when it may obscure the subject matter of the present invention.
Fig. 1 is a flowchart of a method for scheduling gating of periodic messages of each priority in a time-sensitive network according to an embodiment of the present invention.
In this embodiment, as shown in fig. 1, a method for gating and scheduling periodic messages of each priority in a time-sensitive network according to the present invention includes the following steps:
step S1: extracting the sending port, the receiving port, the period, the priority and the length, and determining the passing link
Reading each message to be scheduled, extracting a sending port, a receiving port, a period, a priority and a length of each message, and obtaining the ith message T to be scheduled i Can be expressed as:
T i ={Source(i),destination(i),period(i),priority(i),length(i)}
wherein, the sending port, the receiving port, the period, the priority and the message length of the ith message are sequentially arranged from left to right.
Then, determining a passing link according to the network topological graph;
step S2: calculating the least common multiple of the periods of all messages
Calculating the LCM (least common multiple) of the periods of all the messages, and taking the LCM as a matrix period;
and step S3: sequencing all messages to be scheduled
The ordering is as follows:
a) Sorting the messages from small to large according to the size of the message period;
b) If the periods are equal, sequencing according to whether the transmission link of the message passes through the cascade link between the exchangers or not, and sequencing according to the priority of the cascade link between the exchangers;
c) If all the messages pass through the cascade link between the exchangers, sequencing the messages from high to low according to the priority of the messages;
d) If the priority is equal, sorting the messages according to the length of the messages from large to small
All the messages to be scheduled after sequencing are placed into a message array tsnUnset, and the total message number is recorded as tNum;
setting a message two-dimensional scheduling array launchslot, wherein the value of launchslot (i) (p) is the scheduling time slot of the p-th period of the ith message, and the initial values are all-1, p belongs to [0, LCM/period (i) -1];
and step S4: traversing each message in the message array tsnUnset in turn, and allocating scheduling time slot for each message
Step S4.1: generating a sending time slot to be verified according to the LCM, the period of the message and the message length, wherein the sending time slot temp (i) corresponding to the ith message is an integer in [0, period (i) -t (i) ], the initial value is 0, t (i) is the transmission duration of the ith message, and the transmission duration comprises link transmission time and scheduling time;
step S4.2: verifying a sending time slot temp (i) corresponding to the ith message, if a scheduling constraint condition is met, setting an element value launchslot (i) (p) of the corresponding message in the launchslot from-1 to temp (i) + p × period (i), simultaneously removing the ith message from a message array tsnUnset, if the message is from a set undoSet, removing the message from the set undoSet, and entering step S4.6);
if the constraint condition is not satisfied, the message j which conflicts with the ith message is shown to exist, the sizes of the priority (i) of the conflicted ith message and the priority (j) of the message j are firstly judged, if the priority (j) is smaller than the priority (i), the message j is put into the aggregate event, and if the priority (j) is more than or equal to the priority (i), the message j is not put into the aggregate event; then, judging whether the sending time slot temp (i) reaches the upper limit period (i) -t (i), if not, adding 1 to the sending time slot temp (i), and returning to the step S4.1, if so, judging whether the undoSet is empty, if not, entering the step S4.3, and if not, entering the step S4.4;
step S4.3: traversing the set undoSet, and executing the operations of the steps S4.1-S4.2 on each message;
step S4.4: generating a sending time slot to be verified for each period of the message according to the least common multiple LCM, the period (i) of the ith message and the message length (i), and recording the sending time slot as temp (i) (p); wherein, a sending time slot temp (i) (p) corresponding to the p-th period of the ith message is an integer in [0+ p × period (i), period (i) -t (i) + p × period (i) ], the initial is an integer at the leftmost side of the interval, period (i) is the period of the ith message, t (i) is the transmission duration of the ith message, including the link transmission duration and the scheduling duration, and p ∈ [0, lcm/period (i) -1];
step S4.5: sequentially verifying a sending time slot temp (i) (p) of each period of the ith message, if a scheduling constraint condition is met, setting an element value launchslot (i) (p) to temp (i) (p), and simultaneously removing the ith message from a message array tsnUnset; if not, adding 1 to temp (i) (p), and returning to step S4.4;
step S4.6: judging whether the array tsnUnset is empty, if so, indicating that all messages are successfully distributed, obtaining a conflict-free sent message two-dimensional scheduling array number launchslot, entering the step S5, and otherwise, returning to the step S4.1 to continuously distribute scheduling time slots for uncompleted messages;
step S5: constructing a link time slot number axis graph to obtain a gating queue scheduling scheme
Constructing a link time slot number axis graph with a horizontal axis as a time slot for all links according to the message two-dimensional scheduling array launchslot, and then obtaining a feasible gating queue scheduling scheme of an output port according to specific message scheduling time slot allocation information in the link time slot number axis graph of the link corresponding to the output port of the switch;
wherein the scheduling constraint is
a) And conflict-free constraint: the same link in the same time slot can be occupied by only one message at most, if different messages i and j passing through the same link L exist, the link L is the mth link of the message i from the sending end to the receiving end in sequence and is the nth link of the message j from the sending end to the receiving end in sequence, and if the message i and the message j are not in conflict, the following inequalities are satisfied for any p and q:
launchslot(i)(p)+m×t(i)<launchslot(j)(q)+(n-1)×t(j)
or
launchslot(i)(p)+(m-1)×t(i)>launchslot(j)(q)+n×t(j)
Wherein p and q are respectively the numbers of the transmission periods of the messages i and j in a matrix period, which represent the p-th transmission period of the message i and the q-th transmission period of the message j, and p belongs to [0, LCM/period (i) -1], q belongs to [0, LCM/period (j) -1];
b) And path constraint: if message i needs to continuously pass through link L 1 And a link L 2 And in time slot S x Over a link L 1 Must be in time slot S x + d (i) through link L 2 D (i) is the scheduling duration of the message i;
c) End-to-end constraint: the initial time slot of the message i passing through the link must be within the maximum time slot number, namely: launchslot (i) (p) < LCM, and launchslot (i) (p) > =0, p ∈ [0, LCM/period (i) -1].
Examples
Fig. 2 is a network topology diagram of an embodiment of a time sensitive network. As shown in fig. 2, there are four terminals of ABCD and two switches SW1 and SW2; suppose that links from ABCD up to SW1 or SW2 are labeled 1, 2, 3, 4, links from SW1 or SW2 down to ABCD are labeled 5, 6, 7, 8, links from SW1 to SW2 are labeled 9, links from SW2 to SW1 are labeled 10, and 6 output ports of switches SW1, SW2 are labeled in the figure. Assuming that the normalized unit of the link transmission rate is 1, and the normalized unit of the switch scheduling delay is 5.
There are 6 messages as follows:
TABLE 1
[1] Obtaining the minimum common multiple LCM =1200 of the period according to the above 6 messages;
[2] sequencing the messages according to the step (3), and putting the sequenced messages into tsnUnSet as follows:
tsnUnset={1,2,3,4,5,6};
[3] allocating scheduling time slots for the messages according to the steps (4.1) and (4.2), wherein after the messages 1, 2 and 3 are allocated, a link time slot number axis diagram is shown in fig. 3;
[4] continuing to allocate the scheduling time slot for the message 4, executing the step (4.2) to find that the scheduling time slot allocated for the message 4 cannot meet the constraint condition, and entering the step (4.4) (4.5) to complete the link time slot number axis diagram of the message 4, as shown in fig. 4;
[5] continuing to allocate time slots for the message 5, after the step (4.1) and the step (4.2) are executed, finding that the scheduling time slots allocated for the message 5 cannot meet the constraint condition, the message 4 conflicts with the message 5, the priority of the message 5 is smaller than that of the message 5, adding the message into the undoSet, and performing the step (4.3) to reallocate the scheduling time slots for the message in the undoSet, so that the time slot allocation of the message 5 and the time slot reallocation of the message 4 are completed, and after the completion, the steps are shown in fig. 5;
[6] continuing to allocate the scheduling time slot for the message 6, executing the scheduling time slot allocated for the message 6 in the steps (4.1) (4.2), and entering the step (4.6) to complete the time slot allocation for all the messages, as shown in fig. 6;
[7] obtaining a gating scheduling policy of 6 output ports of the switch according to the time slot allocation state of the relevant link, for example, for a link 8 corresponding to an output port (4) of SW2, obtaining a feasible gating scheduling policy according to the time slot allocation information of the link 8 is as follows:
TABLE 2
On the basis of a gating scheduling mechanism of the traditional TAS method, the invention further researches a gating list GCL scheduling generation algorithm aiming at periodic messages; compared with the existing gating scheduling algorithm, the method simplifies the constraint strategy during scheduling distribution, thereby reducing the calculation workload, reducing the time complexity, and simultaneously ensuring the real-time property and the low-delay characteristic of the scheduled high-priority message. But is limited in that the gated scheduling list cannot be dynamically generated according to message changes.
Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, and various changes may be made apparent to those skilled in the art as long as they are within the spirit and scope of the present invention as defined and defined by the appended claims, and all matters of the invention which utilize the inventive concepts are protected.
Claims (1)
1. A gate control scheduling method for each priority periodic message in a time sensitive network is characterized by comprising the following steps:
(1) Reading each message to be scheduled, extracting a sending port, a receiving port, a period, a priority and a length of each message, and obtaining the ith message T to be scheduled i Can be expressed as:
T i ={Source(i),destination(i),period(i),priority(i),length(i)}
the sending port, the receiving port, the period, the priority and the message length of the ith message are sequentially arranged from left to right.
Then, determining a passing link according to the network topological graph;
(2) Calculating the minimum common multiple LCM of the periods of all the messages, and taking the minimum common multiple LCM as a matrix period;
(3) Sequencing all messages to be scheduled in the following mode:
a) Sorting the messages from small to large according to the size of the message period;
b) If the periods are equal, sequencing according to whether the transmission link of the message passes through the cascade link between the exchangers or not, and sequencing according to the priority of the cascade link between the exchangers;
c) If the messages pass through the inter-switch cascade link, sequencing the messages from high to low according to the priority of the messages;
d) If the priority is equal, sorting the messages according to the length of the messages from large to small
All the messages to be scheduled after sequencing are placed into a message array tsnUnset, and the total message number is recorded as tNum;
setting a message two-dimensional scheduling array launchslot, wherein the value of launchslot (i) (p) is the scheduling time slot of the p-th period of the ith message, and the initial values are all-1, p belongs to [0, LCM/period (i) -1];
(4) Sequentially traversing each message in the message array tsnUnset and allocating scheduling time slots for the messages
4.1 Generating a sending time slot to be verified according to the LCM (least common multiple), the period of the message and the message length, wherein the sending time slot temp (i) corresponding to the ith message is an integer in [0, period (i) -t (i) ], the initial value is 0, t (i) is the transmission duration of the ith message, and the transmission duration comprises link transmission time and scheduling time;
4.2 Verifying a sending time slot temp (i) corresponding to the ith message, if a scheduling constraint condition is met, setting an element value launchslot (i) (p) of the corresponding message in the launchslot from-1 to temp (i) + p × period (i), simultaneously removing the ith message from a message array tsnUnset, if the message is from a set undoSet, removing the message from the set undoSet, and entering a step 4.6);
if the constraint condition is not satisfied, the message j which conflicts with the ith message is shown to exist, the sizes of the priority (i) of the conflicted ith message and the priority (j) of the message j are firstly judged, if the priority (j) is smaller than the priority (i), the message j is put into the aggregate event, and if the priority (j) is more than or equal to the priority (i), the message j is not put into the aggregate event; then, judging whether the sending time slot temp (i) reaches the upper limit period (i) -t (i), if not, adding 1 to the sending time slot temp (i), and returning to the step 4.1), if so, judging whether the undoSet is empty, if not, entering the step 4.3), and if so, entering the step 4.4);
4.3 Traversing the set undoSet, and executing the operations of the steps 4.1) -4.2) on each message;
4.4 Generating a sending time slot to be verified for each period of the message according to the minimum common multiple LCM, the period (i) of the ith message and the message length (i), and recording the sending time slot as temp (i) (p); wherein, a sending time slot temp (i) (p) corresponding to the p-th period of the ith message is an integer in [0+ p × period (i), period (i) -t (i) + p × period (i) ], the initial is an integer at the leftmost side of the interval, period (i) is the period of the ith message, t (i) is the transmission duration of the ith message, including the link transmission duration and the scheduling duration, and p ∈ [0, lcm/period (i) -1];
4.5 Sequentially verifying a sending time slot temp (i) (p) of each period of the ith message, and if a scheduling constraint condition is met, setting an element value launchslot (i) (p) to temp (i) (p) and simultaneously removing the ith message from a message array tsnUnset; if not, adding 1 to temp (i) (p), and returning to the step 4.4);
4.6 Judging whether the array tsnUnset is empty, if so, indicating that all messages are successfully distributed, obtaining a conflict-free sent message two-dimensional scheduling array number launchslot, and entering the step (5), otherwise, returning to the step 4.1) to continue to distribute scheduling slots for uncompleted messages;
(5) Constructing a link time slot number axis graph with the horizontal axis as a time slot for all links according to the message two-dimensional scheduling array launchslot, and then obtaining a feasible gating queue scheduling scheme of an output port according to specific message scheduling time slot allocation information in the link time slot number axis graph of the link corresponding to the output port of the switch;
wherein the scheduling constraint is
a) And conflict-free constraint: the same link in the same time slot can be occupied by only one message at most, if different messages i and j passing through the same link L exist, the link L is the mth link of the message i from the sending end to the receiving end in sequence and is the nth link of the message j from the sending end to the receiving end in sequence, and if the message i and the message j are not in conflict, the following inequalities are satisfied for any p and q:
launchslot(i)(p)+m×t(i)<launchslot(j)(q)+(n-1)×t(j)
or
launchslot(i)(p)+(m-1)×t(i)>launchslot(j)(q)+n×t(j)
Wherein p and q are respectively the numbers of the transmission periods of the messages i and j in a matrix period, which represent the p-th transmission period of the message i and the q-th transmission period of the message j, and p belongs to [0, LCM/period (i) -1], q belongs to [0, LCM/period (j) -1];
b) And path constraint: if message i needs to continuously pass through link L 1 And a link L 2 And in time slot S x Over a link L 1 Must be in time slot S x + d (i) through link L 2 D (i) is the scheduling duration of the message i;
c) End-to-end constraint: the initial time slot of the message i passing through the link must be within the maximum time slot number, namely: launchslot (i) (p) < LCM, and launchslot (i) (p) > =0, p ∈ [0, LCM/period (i) -1].
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