CN112565014A - Satellite network end-to-end delay upper bound acquisition method based on network calculus - Google Patents

Satellite network end-to-end delay upper bound acquisition method based on network calculus Download PDF

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CN112565014A
CN112565014A CN202011405235.0A CN202011405235A CN112565014A CN 112565014 A CN112565014 A CN 112565014A CN 202011405235 A CN202011405235 A CN 202011405235A CN 112565014 A CN112565014 A CN 112565014A
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魏德宾
杨力
王旭
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Dalian University
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Abstract

The invention discloses a method for acquiring an upper bound of end-to-end delay of a satellite network based on network calculation, which comprises the following steps: acquiring link time delay; obtaining time delay between nodes by utilizing network calculation; obtaining an end-to-end delay upper bound according to the link delay and the delay among the nodes; according to the method, the propagation delay is obtained by calculating the inter-satellite distance, the arrival curve and the service curve of the node are set, and the satellite network method is combined, so that the end-to-end delay upper bound of the satellite network is obtained, and support can be provided for network QoS control.

Description

Satellite network end-to-end delay upper bound acquisition method based on network calculus
Technical Field
The invention relates to the field of analysis of end-to-end delay upper bound of a satellite network, in particular to a method for acquiring the end-to-end delay upper bound of the satellite network based on network calculation.
Background
In recent years, satellite networks have been widely used due to their characteristics of large transmission capacity, long communication distance, no influence from terrain and natural disasters, etc., and have become a beneficial complement to terrestrial communication and also an important means for realizing global seamless coverage. However, the satellite network brings larger delay compared with the terrestrial network, and the end-to-end delay of the network is one of the most important parameters of the Quality of Service (QoS), and the accuracy of the boundary analysis directly affects the guarantee level of the QoS of the network.
At present, the delay performance analysis of the network mainly includes methods such as queuing theory and network calculus. The network performance analysis using the queuing theory method requires more accurate traffic and service methods, which are difficult to obtain for the current increasingly complex network morphology and traffic flow characteristics. The network calculation adopts an upper bound to describe the arrival process of the service flow and adopts a lower bound to describe the service process, thereby obtaining the QoS performance bound of the service flow and enabling the analysis method to be more flexible. However, in the satellite network, since the link propagation delay changes periodically and the change cannot be ignored, if the conventional network analysis method is directly applied to the satellite network, the propagation delay is uniformly valued, and the challenge of calculation accuracy is inevitably faced. In addition, in order to obtain an end-to-end delay upper bound, the traditional delay bound calculation excessively amplifies queuing delay, so that the difference between the calculated delay bound and the actual delay is large, and the performance of a QoS control algorithm based on network calculation is influenced. Therefore, how to analyze and accurately solve the end-to-end delay upper bound of the satellite network by using the network calculus theory becomes an important concern.
Disclosure of Invention
In view of the fact that the existing time delay upper bound analysis method cannot accurately solve the problem of end-to-end time delay upper bound of the satellite network, the application provides a method for acquiring the end-to-end time delay upper bound of the satellite network based on network calculation so as to guarantee that support can be provided for network QoS control.
In order to achieve the purpose, the technical scheme of the application is as follows: the method for acquiring the upper bound of the end-to-end delay of the satellite network based on network calculation comprises the following steps:
acquiring link time delay;
obtaining time delay between nodes by utilizing network calculation;
and obtaining an end-to-end delay upper bound according to the link delay and the delay between the nodes.
Further, the obtaining of the link delay specifically includes: let R be the radius of the earth, hA,hBThe orbit heights of the satellite a and the satellite B,
Figure BDA0002818367640000021
the latitude and longitude of the satellite A and the satellite B are respectively the satellite points; the inter-satellite link length dBAExpressed as:
Figure BDA0002818367640000022
wherein
Figure BDA0002818367640000023
Obtaining the link time delay D according to the inter-satellite link length and the light speed clComprises the following steps:
Figure BDA0002818367640000024
further, the obtaining of the time delay between the nodes by using network operation specifically includes:
when a traffic flow a (t) arrives at a node, the traffic flow a is limited by a token bucket with a node parameter of (r, b), namely the arrival curve α (t) of the node is restricted by rt + b, b is burst traffic, and r is a long-term average rate of a data flow;
for the traffic flow a (t), the service curve provided by the nodes in the path is:
Figure BDA0002818367640000025
wherein C represents a service rate provided by the node, and T represents a service delay of the data packet at the node; the delay parameter is considered to be the packet processing delay, so the delay between network nodes is expressed as:
T＝L/C (2)
where L represents the maximum packet length.
Further, if there are n service flows, assume service flow ai(t), i ═ 1,2, …, n assigned weightsIs omegaiIs then assigned to traffic flow aiService rate C of (t)iIs composed of
Figure BDA0002818367640000031
Using C in the above formulaiThe curve obtained by substituting C in the formula (1) is a certain service flow Ai(t) traffic service curve.
Further, assume a traffic flow ai(t) passing through the node p, the arrival curve of the node is alpha, the service curve is beta, the time delay D of the service flow passing through the nodepIs composed of
Figure BDA0002818367640000032
Wherein, WtThe peak rate of the link from the previous node to the current node; t isiRepresents traffic flow ai(t) service delay at node p; biBurst traffic for a certain node, riIs the long-term average rate of a certain node;
from a joint solution of the arrival curve and the service curve
Figure BDA0002818367640000033
Then substituting the arrival curve alpha (t) and the formulas (1) - (3) into the formula to obtain the upper bound D of the single-node time delaypComprises the following steps:
Figure BDA0002818367640000034
the rate of the service flow reaches the peak rate W of the link bandwidthtResulting in a rapid aggregation of a large amount of traffic at the node, and in queuing of a large amount of traffic due to the limited processing capacity of the node, resulting in a maximum delay for that period, i.e. when W is the time of daytt＝rit+biThen, obtain
Figure BDA0002818367640000041
Time delay DpReaches the maximum value, so:
Figure BDA0002818367640000042
further, in the satellite network, the end-to-end delay includes a variable delay and a fixed delay, where the variable delay includes a queuing delay and a link propagation delay of a system buffer at a node; the fixed delay comprises a transmission delay within the node, i.e. the time required for the node to get data from the node to the transmitter when transmitting the data.
Further, assume a traffic flow ai(t) sequentially passes through m nodes, and the arrival curves in the nodes sequentially pass through alphaiI is 1,2, …, m, the service curve of the system is β in turniI is 1,2, …, m, the propagation delay between two adjacent nodes is in turn
Figure BDA0002818367640000046
The transmission time delay of the intermediate node is as follows in sequence:
Figure BDA0002818367640000047
the end-to-end delay upper bound D1→mComprises the following steps:
Figure BDA0002818367640000043
1) when m is 1, the time delay upper bound D is increased by the single nodepOr equation (5) to obtain an end-to-end delay upper bound D1(ii) a When m is 2, deducing the time delay of the 1 st node by the horizontal deviation
Figure BDA0002818367640000044
After passing through the 1 st node, the output stream will be affected by the propagation delay of the link when passing through the link, so the arrival curve of the output stream when arriving at the 2 nd node
Figure BDA0002818367640000048
Bring it to curve a2Substituting the formula (t) and the formula (1) into a horizontal deviation inference formula to solve and obtain the time delay of the node as follows:
Figure BDA0002818367640000045
so the end-to-end delay between the two nodes 1 and 2 is:
Figure BDA0002818367640000051
2) when m is k-1, the upper bound of the end-to-end delay is:
Figure BDA0002818367640000052
3) when m is k, the arrival curve of the k-th node is
Figure BDA0002818367640000053
Delay upper bound D of single nodepIt is found that the time delay of the kth node is:
Figure BDA0002818367640000054
end-to-end delay D from node 1 to node k1→kTime delay D equal to the first k-1 nodes1→k-1And the time delay D of the kth nodekTo sum, i.e.
Figure BDA0002818367640000055
Wherein the content of the first and second substances,
Figure BDA0002818367640000056
is the sum of the propagation delay on the link and the transmission delay of the intermediate node; transmission delay D of intermediate nodefIs Df＝sNiWhere the constant s is the transmission delay of a node, NiIs the number of path hops.
Compared with the existing method, the method has the advantages that: according to the method, the propagation delay is obtained by calculating the inter-satellite distance, the arrival curve and the service curve of the node are set, and the satellite network method is combined, so that the end-to-end delay upper bound of the satellite network is obtained. By comparison, the upper bound of the end-to-end delay of the satellite network obtained by the invention is closer to a simulation value than that of the traditional method, and the invention can provide support for network QoS control.
Drawings
FIG. 1 is a schematic diagram of inter-satellite link length;
FIG. 2 is a diagram of an end-to-end network model;
FIG. 3 is an Iridium constellation topology;
FIG. 4 is a graph of end-to-end delay versus path node count;
FIG. 5 is a graph of end-to-end delay versus service rate;
FIG. 6 is a graph of end-to-end delay versus weight;
fig. 7 is a graph of end-to-end delay versus burst size.
Detailed Description
The invention is described in further detail below with reference to the following figures and specific examples: the present application is further described by taking this as an example.
Example 1
The embodiments of the present invention are implemented based on the technical solutions of the present invention, and the present invention provides detailed embodiments and specific operation processes, but the scope of the present invention is not limited to the following embodiments.
The embodiment provides a method for acquiring an upper bound of an end-to-end delay of a satellite network based on network calculation, which comprises the following steps:
firstly, acquiring link time delay;
specifically, since the inter-satellite link is an important component of the satellite network, it can realize the connection of all network nodes without depending on ground equipment, and the satellite is combined into a whole. Let R be the radius of the earth, hA,hBThe orbit heights of the satellite a and the satellite B,
Figure BDA0002818367640000061
the latitude and longitude of the satellite A and the satellite B are respectively acquired from the ephemeris; the inter-satellite link length dBAExpressed as:
Figure BDA0002818367640000071
wherein
Figure BDA0002818367640000072
Obtaining the link time delay D according to the inter-satellite link length and the light speed clComprises the following steps:
Figure BDA0002818367640000073
secondly, acquiring time delay among nodes by utilizing network calculation;
specifically, m-2 intermediate nodes exist between a node 1 and a node m in a satellite network, when a traffic flow a (t) arrives at a node, the traffic flow a is limited by a token bucket with a parameter (r, b) of the node, that is, the traffic flow a is constrained by an arrival curve α (t) ═ rt + b of the node, b is burst traffic, and r is a long-term average rate of a data flow;
for the traffic flow a (t), each node passing through provides a certain service capability for the traffic flow; therefore, for any network node, no matter what queue scheduling algorithm is adopted, the node can be assumed to provide a speed-delay service curve for the data flow as service guarantee for the data flow; therefore, the service curve provided by the nodes in the path is as follows:
Figure BDA0002818367640000074
wherein C represents a service rate provided by the node, and T represents a service delay of the data packet at the node; the delay parameter can be considered as packet processing delay, so the delay between network nodes is expressed as:
T＝L/C (2)
where L represents the maximum packet length.
And thirdly, obtaining an end-to-end delay upper bound according to the link delay and the time delay between the nodes.
In particular, since in a satellite network there will be a plurality of traffic streams ai(t) arrive at one node at the same time. Assuming that the traffic flows are independent of each other and share the link bandwidth W, the bandwidth allocation is performed according to the weight allocated to each traffic flow so that the traffic flows can all obtain the corresponding service. If there are n traffic flows, assume traffic flow Ai(t), i is 1,2, …, n is assigned a weight ωiIs then assigned to traffic flow aiService rate C of (t)iIs composed of
Figure BDA0002818367640000081
Using C in the above formulaiThe curve obtained by substituting C in the formula (1) is a certain service flow Ai(t) traffic service curve.
Suppose a traffic flow ai(t) passing through the node p, the arrival curve of the node is alpha, the service curve is beta, the time delay D of the service flow passing through the nodepIs composed of
Figure BDA0002818367640000082
Wherein, WtThe peak rate of the link from the previous node to the current node; t isiRepresents traffic flow ai(t) service delay at node p; biBurst traffic for a certain node, riIs the long-term average rate of a certain node;
from a joint solution of the arrival curve and the service curve
Figure BDA0002818367640000083
Then substituting the arrival curve alpha (t) and the formulas (1) - (3) into the formula to obtain the upper bound D of the single-node time delaypComprises the following steps:
Figure BDA0002818367640000084
the traditional single-node queuing delay is bounded by
Figure BDA0002818367640000085
Because we consider the average rate to be lower than the serving rate of the node, i.e., ri≤Ci. Therefore, the above formula is amplified by
Figure BDA0002818367640000086
Thus, the excessively amplified queuing delay causes a large difference between a calculation delay boundary and an actual delay, and the performance of a QoS control algorithm based on network calculation is influenced. The rate of the service flow reaches the peak rate W of the link bandwidthtResulting in a rapid aggregation of a large amount of traffic at the node, and in queuing of a large amount of traffic due to the limited processing capacity of the node, resulting in a maximum delay for that period, i.e. when W is the time of daytt＝rit+biThen, obtain
Figure BDA0002818367640000091
Time delay DpReaches the maximum value, so:
Figure BDA0002818367640000092
in a satellite network, end-to-end time delay comprises variable time delay and fixed time delay, wherein the variable time delay comprises queuing time delay and link propagation time delay of a system cache at a node; the fixed delay comprises a transmission delay within the node, i.e. the time required for the node to get data from the node to the transmitter when transmitting the data.
Suppose a traffic flow ai(t) passing through m nodes in sequence, the arrival curves in the nodes being according toIs next to alphaiI is 1,2, …, m, the service curve of the system is β in turniI is 1,2, …, m, the propagation delay between two adjacent nodes is in turn
Figure BDA0002818367640000093
The transmission time delay of the intermediate node is as follows in sequence:
Figure BDA0002818367640000094
the end-to-end delay upper bound D1→mComprises the following steps:
Figure BDA0002818367640000095
1) when m is 1, the time delay upper bound D is increased by the single nodepOr equation (5) to obtain an end-to-end delay upper bound D1(ii) a When m is 2, deducing the time delay of the 1 st node by the horizontal deviation
Figure BDA0002818367640000096
After passing through the 1 st node, the output stream will be affected by the propagation delay of the link when passing through the link, so the arrival curve of the output stream when arriving at the 2 nd node
Figure BDA0002818367640000098
Bring it to curve a2Substituting the formula (t) and the formula (1) into a horizontal deviation inference formula to solve and obtain the time delay of the node as follows:
Figure BDA0002818367640000097
so the end-to-end delay between the two nodes 1 and 2 is:
Figure BDA0002818367640000101
2) when m is k-1, the upper bound of the end-to-end delay is:
Figure BDA0002818367640000102
3) when m is k, the arrival curve of the k-th node is
Figure BDA0002818367640000103
Delay upper bound D of single nodepIt is found that the time delay of the kth node is:
Figure BDA0002818367640000104
end-to-end delay D from node 1 to node k1→kTime delay D equal to the first k-1 nodes1→k-1And the time delay D of the kth nodekTo sum, i.e.
Figure BDA0002818367640000105
Wherein the content of the first and second substances,
Figure BDA0002818367640000106
is the sum of the propagation delay on the link and the transmission delay of the intermediate node; transmission delay D of intermediate nodefIs Df＝sNiWhere the constant s is the transmission delay of a node, NiIs the number of path hops.
In order to verify the effectiveness and feasibility of the satellite network end-to-end time delay upper bound acquisition method based on network calculation, the Iridium constellation is used as a network model and compared with the method provided by the application and a traditional time delay method by adopting a token bucket. The ISL (inter Satellite Link) link bandwidth between satellites is 500Mb/s, the long-term average rate of data stream is 80Mb/s, the burst size of the data stream is 200kbits, the service rate of the system is 100Mb/s, the transmission time delay of two adjacent nodes is set to be 0.2ms, the average size of packets is 1000bits, and the simulation time is set to be 1000 s.
1. Relationship between number of path nodes and end-to-end delay
As can be seen from fig. 4, when the number of end-to-end nodes of the satellite network increases, both the theoretical delay and the simulation delay increase, and the end-to-end delay based on the token bucket is higher than the theoretical value of the method provided by the present application. This is because: firstly, the end-to-end time delay upper bound analysis method based on the satellite network considers the characteristic that the propagation time delay of the satellite network node changes along with the change of the satellite network node along with the time. Secondly, the time delay of the link at the peak rate is used as the upper bound of the queuing time delay of the link, and the end-to-end time delay upper bound of the satellite network is more accurately calculated. In addition, as the number of nodes in the path increases, the delay obtained by simulation is closer to the upper bound of the theoretical delay of the method provided by the application, and the result reflects that when the number of nodes on the link is large, the network algorithm can reflect the real network delay performance.
2. Service rate versus end-to-end delay
In fig. 5, the number of nodes in the end-to-end path is set to 7. It can be seen from the figure that when the service rate value is smaller, the delay difference between the simulation value and the theoretical value is larger, which is caused by the network congestion due to the overload of the link, and thus the delay difference between the simulation value and the theoretical value is larger, and as the service rate increases, the network condition is better, the delay difference between the simulation value and the theoretical value gradually decreases, and particularly after the service rate reaches 400Mb/s, the delay difference between the simulation value and the theoretical value is smaller, and is closer to the theoretical value obtained by the method provided by the present application.
3. Weight to end-to-end delay relationship
When the number of nodes in the end-to-end path is 7, it can be seen from fig. 6 that both the theoretical delay and the simulation delay decrease with the increase of the traffic weight value, and the trend of the decrease becomes flatter and flatter. This is because as the traffic weight value increases, the service rate of the node also increases, resulting in a decrease in delay as the traffic weight value increases. However, when the weight value is less than 0.5, the delay decreases faster, and when the weight value is greater than 0.5, the delay tends to be flat. This is because the network tends to be stable with the service of the node, so that the corresponding data stream gets the corresponding service, resulting in the delay tending to be flat. The network end-to-end delay simulation value is closer to the upper bound of the delay theoretical value obtained by the method provided by the application, so that the satellite network performance can be better reflected by the satellite network delay upper bound obtained by network calculation derivation.
4. Relationship between burst size and end-to-end delay
When the number of nodes in the end-to-end path is 7, it can be seen from fig. 7 that as the burst size increases, the end-to-end simulation delay value also increases. At the initial stage of simulation, the increase speed of the end-to-end simulation delay value is too fast, and when a certain burst value is reached, the end-to-end delay tends to be smooth and close to a theoretical value. This is because the network is not stable in the early stage of simulation, and the burst size increases at this time, which results in a faster delay growth speed, and after the network is relatively stable, the delay growth is slow as the burst size increases and the load balancing capability exists between nodes.
Simulation analysis is carried out by using different indexes, and the satellite network end-to-end delay upper bound acquisition method based on network calculation provided by the invention is closer to a simulation value than the traditional method, and can provide support for network QoS control.
The above description is only for the purpose of creating a preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can substitute or change the technical solution and the inventive concept of the present invention within the technical scope of the present invention.

Claims (7)

1. The method for acquiring the upper bound of the end-to-end delay of the satellite network based on network calculation is characterized by comprising the following steps:
acquiring link time delay;
obtaining time delay between nodes by utilizing network calculation;
and obtaining an end-to-end delay upper bound according to the link delay and the delay between the nodes.
2. The network calculus-based satellite network terminal of claim 1The method for acquiring the upper bound of the arrival-end delay is characterized in that the method for acquiring the link delay specifically comprises the following steps: let R be the radius of the earth, hA,hBThe orbit heights of the satellite a and the satellite B,
Figure FDA0002818367630000011
the latitude and longitude of the satellite A and the satellite B are respectively the satellite points; the inter-satellite link length dBAExpressed as:
Figure FDA0002818367630000012
wherein
Figure FDA0002818367630000013
Obtaining the link time delay D according to the inter-satellite link length and the light speed clComprises the following steps:
Figure FDA0002818367630000014
3. the method according to claim 1, wherein the obtaining the time delay between the nodes by using the network algorithm specifically comprises:
when a traffic flow a (t) arrives at a node, the traffic flow a is limited by a token bucket with a node parameter of (r, b), namely the arrival curve α (t) of the node is restricted by rt + b, b is burst traffic, and r is a long-term average rate of a data flow;
for the traffic flow a (t), the service curve provided by the nodes in the path is:
Figure FDA0002818367630000015
wherein C represents a service rate provided by the node, and T represents a service delay of the data packet at the node; the delay parameter is considered to be the packet processing delay, so the delay between network nodes is expressed as:
T＝L/C (2)
where L represents the maximum packet length.
4. The method of claim 1, wherein if there are n traffic flows, it is assumed that traffic flow a is an upper bound of end-to-end delay of the satellite networki(t), i is 1,2, …, n is assigned a weight ωiIs then assigned to traffic flow aiService rate C of (t)iIs composed of
Figure FDA0002818367630000021
Using C in the above formulaiThe curve obtained by substituting C in the formula (1) is a certain service flow Ai(t) traffic service curve.
5. The network calculus based satellite network end-to-end delay upper bound acquisition method of claim 1, wherein a service flow a is assumedi(t) passing through the node p, the arrival curve of the node is alpha, the service curve is beta, the time delay D of the service flow passing through the nodepIs composed of
Figure FDA0002818367630000022
Wherein, WtThe peak rate of the link from the previous node to the current node; t isiRepresents traffic flow ai(t) service delay at node p; biBurst traffic for a certain node, riIs the long-term average rate of a certain node;
from a joint solution of the arrival curve and the service curve
Figure FDA0002818367630000023
Then substituting the arrival curve alpha (t) and the formulas (1) - (3) into the formula to obtain the upper bound D of the single-node time delaypComprises the following steps:
Figure FDA0002818367630000024
the rate of the service flow reaches the peak rate W of the link bandwidthtResulting in a rapid aggregation of a large amount of traffic at the node, and in queuing of a large amount of traffic due to the limited processing capacity of the node, resulting in a maximum delay for that period, i.e. when W is the time of daytt＝rit+biThen, obtain
Figure FDA0002818367630000031
Time delay DpReaches the maximum value, so:
Figure FDA0002818367630000032
6. the network calculus based satellite network end-to-end delay upper bound acquisition method of claim 1, wherein in the satellite network, the end-to-end delay comprises a variable delay and a fixed delay, and the variable delay comprises a queuing delay and a link propagation delay of a system buffer at a node; the fixed delay comprises a transmission delay within the node, i.e. the time required for the node to get data from the node to the transmitter when transmitting the data.
7. The network calculus based satellite network end-to-end delay upper bound acquisition method of claim 6, wherein a service flow A is assumedi(t) sequentially passes through m nodes, and the arrival curves in the nodes sequentially pass through alphaiI is 1,2, …, m, the service curve of the system is β in turniI is 1,2, …, m, the propagation delay between two adjacent nodes is in turn
Figure FDA0002818367630000033
The transmission time delay of the intermediate node is as follows in sequence:
Figure FDA0002818367630000034
the end-to-end delay upper bound D1→mComprises the following steps:
Figure FDA0002818367630000035
1) when m is 1, the time delay upper bound D is increased by the single nodepOr equation (5) to obtain an end-to-end delay upper bound D1(ii) a When m is 2, deducing the time delay of the 1 st node by the horizontal deviation
Figure FDA0002818367630000036
After passing through the 1 st node, the output stream will be affected by the propagation delay of the link when passing through the link, so the arrival curve of the output stream when arriving at the 2 nd node
Figure FDA0002818367630000037
Bring it to curve a2Substituting the formula (t) and the formula (1) into a horizontal deviation inference formula to solve and obtain the time delay of the node as follows:
Figure FDA0002818367630000038
so the end-to-end delay between the two nodes 1 and 2 is:
Figure FDA0002818367630000041
2) when m is k-1, the upper bound of the end-to-end delay is:
Figure FDA0002818367630000042
3) when m is k, the arrival curve of the k-th node is
Figure FDA0002818367630000043
Delay upper bound D of single nodepIt is found that the time delay of the kth node is:
Figure FDA0002818367630000044
end-to-end delay D from node 1 to node k1→kTime delay D equal to the first k-1 nodes1→k-1And the time delay D of the kth nodekTo sum, i.e.
Figure FDA0002818367630000045
Wherein the content of the first and second substances,
Figure FDA0002818367630000046
is the sum of the propagation delay on the link and the transmission delay of the intermediate node; transmission delay D of intermediate nodefIs Df＝sNiWhere the constant s is the transmission delay of a node, NiIs the number of path hops.
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