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low. The EF PHB requires a sufficiently large number of output ports to provide low delay, low loss, and low jitter.
EF PHBs can be implemented if the output ports bandwidth is sufficiently large, combined with small buffer sizes and other network resources dedicated to EF packets, to allow the routers service rate for EF packets on an output port to exceed the arrival rate λ of packets at that port.
This means that packets with PHB EF are considered with a pre-allocated amount of output bandwidth and a priority that ensures minimum loss, minimum delay and minimum jitter before being put into operation.
PHB EF is suitable for channel simulation, leased line simulation, and real-time services such as voice, video without compromising on high loss, delay and jitter values.
Figure 2.10 Example of EF installation
Figure 2.10 shows an example of an EF PHB implementation. This is a simple priority queue scheduling technique. At the edges of the DS domain, EF packet traffic is prioritized according to the values agreed upon by the SLA. The EF queue in the figure needs to output packets at a rate higher than the packet arrival rate λ. To provide an EF PHB over an end-to-end DS domain, bandwidth at the output ports of the core routers needs to be allocated in advance to ensure the requirement μ > λ. This can be done by a pre-configured provisioning process. In the figure, EF packets are placed in the priority queue (the upper queue). With such a length, the queue can operate with μ > λ.
Since EF was primarily used for real-time services such as voice and video, and since real-time services use UDP instead of TCP, RED is generally
not suitable for EF queues because applications using UDP will not respond to random packet drop and RED will strip unnecessary packets.
2.2.4.2 Assured Forwarding (AF) PHB
PHB AF is defined by RFC 2597. The purpose of PHB AF is to deliver packets reliably and therefore delay and jitter are considered less important than packet loss. PHB AF is suitable for non-real-time services such as applications using TCP. PHB AF first defines four classes: AF1, AF2, AF3, AF4. For each of these AF classes, packets are then classified into three subclasses with three distinct priority levels.
Table 2.8 shows the four AF classes and 12 AF subclasses and the DSCP values for the 12 AF subclasses defined by RFC 2597. RFC 2597 also allows for more than three separate priority levels to be added for internal use. However, these separate priority levels will only have internal significance.
PHB Class
PHB Subclass
Package type
DSCP
AF4
AF41
Short
100010
AF42
Medium
100100
AF43
High
100110
AF3
AF31
Short
011010
AF32
Medium
011100
AF33
High
011110
AF2
AF21
Short
010010
AF22
Medium
010100
AF23
High
010110
AF1
AF11
Short
001010
AF12
Medium
001100
AF13
High
001110
Table 2.8 AF DSCPs
The AF PHB ensures that packets are forwarded with a high probability of delivery to the destination within the bounds of the rate agreed upon in an SLA. If AF traffic at an ingress port exceeds the pre-priority rate, which is considered non-compliant or “out of profile”, the excess packets will not be delivered to the destination with the same probability as the packets belonging to the defined traffic or “in profile” packets. When there is network congestion, the out of profile packets are dropped before the in profile packets are dropped.
When service levels are defined using AF classes, different quantity and quality between AF classes can be realized by allocating different amounts of bandwidth and buffer space to the four AF classes. Unlike
EF, most AF traffic is non-real-time traffic using TCP, and the RED queue management strategy is an AQM (Adaptive Queue Management) strategy suitable for use in AF PHBs. The four AF PHB layers can be implemented as four separate queues. The output port bandwidth is divided into four AF queues. For each AF queue, packets are marked with three “colors” corresponding to three separate priority levels.
In addition to the 32 DSCP 1 groups defined in Table 2.8, 21 DSCPs have been standardized as follows: one for PHB EF, 12 for PHB AF, and 8 for CSCP. There are 11 DSCP 1 groups still available for other standards.
2.2.5.Example of Differentiated Services
We will look at an example of the Differentiated Service model and mechanism of operation. The architecture of Differentiated Service consists of two basic sets of functions:
Edge functions: include packet classification and traffic conditioning. At the inbound edge of the network, incoming packets are marked. In particular, the DS field in the packet header is set to a certain value. For example, in Figure 2.12, packets sent from H1 to H3 are marked at R1, while packets from H2 to H4 are marked at R2. The labels on the received packets identify the service class to which they belong. Different traffic classes receive different services in the core network. The RFC definition uses the term behavior aggregate rather than the term traffic class. After being marked, a packet can be forwarded immediately into the network, delayed for a period of time before being forwarded, or dropped. We will see that there are many factors that affect how a packet is marked, and whether it is forwarded immediately, delayed, or dropped.
Figure 2.12 DiffServ Example
Core functionality: When a DS-marked packet arrives at a Diffservcapable router, the packet is forwarded to the next router based on
Per-hop behavior is associated with packet classes. Per-hop behavior affects router buffers and the bandwidth shared between competing classes. An important principle of the Differentiated Service architecture is that a routers per-hop behavior is based only on the packets marking or the class to which it belongs. Therefore, if packets sent from H1 to H3 as shown in the figure receive the same marking as packets from H2 to H4, then the network routers treat the packets exactly the same, regardless of whether the packet originated from H1 or H2. For example, R3 does not distinguish between packets from h1 and H2 when forwarding packets to R4. Therefore, the Differentiated Service architecture avoids the need to maintain router state about separate source-destination pairs, which is important for network scalability.
Chapter Conclusion
Chapter 2 has presented and clarified two main models of deploying and installing quality of service in IP networks. While the traditional best-effort model has many disadvantages, later models such as IntServ and DiffServ have partly solved the problems that best-effort could not solve. IntServ follows the direction of ensuring quality of service for each separate flow, it is built similar to the circuit switching model with the use of the RSVP resource reservation protocol. IntSer is suitable for services that require fixed bandwidth that is not shared such as VoIP services, multicast TV services. However, IntSer has disadvantages such as using a lot of network resources, low scalability and lack of flexibility. DiffServ was born with the idea of solving the disadvantages of the IntServ model.
DiffServ follows the direction of ensuring quality based on the principle of hop-by-hop behavior based on the priority of marked packets. The policy for different types of traffic is decided by the administrator and can be changed according to reality, so it is very flexible. DiffServ makes better use of network resources, avoiding idle bandwidth and processing capacity on routers. In addition, the DifServ model can be deployed on many independent domains, so the ability to expand the network becomes easy.
Chapter 3: METHODS TO ENSURE QoS FOR MULTIMEDIA COMMUNICATIONS
In packet-switched networks, different packet flows often have to share the transmission medium all the way to the destination station. To ensure the fair and efficient allocation of bandwidth to flows, appropriate serving mechanisms are required at network nodes, especially at gateways or routers, where many different data flows often pass through. The scheduler is responsible for serving packets of the selected flow and deciding which packet will be served next. Here, a flow is understood as a set of packets belonging to the same priority class, or originating from the same source, or having the same source and destination addresses, etc.
In normal state when there is no congestion, packets will be sent as soon as they are delivered. In case of congestion, if QoS assurance methods are not applied, prolonged congestion can cause packet drops, affecting service quality. In some cases, congestion is prolonged and widespread in the network, which can easily lead to the network being frozen, or many packets being dropped, seriously affecting service quality.
Therefore, in this chapter, in sections 3.2 and 3.3, we introduce some typical network traffic load monitoring techniques to predict and prevent congestion before it occurs through the measure of dropping (removing) packets early when there are signs of impending congestion.
3.1. DropTail method
DropTail is a simple, traditional queue management method based on FIFO mechanism. All incoming packets are placed in the queue, when the queue is full, the later packets are dropped.
Due to its simplicity and ease of implementation, DropTail has been used for many years on Internet router systems. However, this algorithm has the following disadvantages:
− Cannot avoid the phenomenon of “Lock out”: Occurs when 1 or several traffic streams monopolize the queue, making packets of other connections unable to pass through the router. This phenomenon greatly affects reliable transmission protocols such as TCP. According to the anti-congestion algorithm, when locked out, the TCP connection stream will reduce the window size and reduce the packet transmission speed exponentially.
− Can cause Global Synchronization: This is the result of a severe “Lock out” phenomenon. Some neighboring routers have their queues monopolized by a number of connections, causing a series of other TCP connections to be unable to pass through and simultaneously reducing the transmission speed. After those monopolized connections are temporarily suspended,
Once the queue is cleared, it takes a considerable amount of time for TCP connections to return to their original speed.
− Full Queue phenomenon: Data transmitted on the Internet often has an explosion, packets arriving at the router are often in clusters rather than in turn. Therefore, the operating mechanism of DropTail makes the queue easily full for a long period of time, leading to the average delay time of large packets. To avoid this phenomenon, with DropTail, the only way is to increase the routers buffer, this method is very expensive and ineffective.
− No QoS guarantee: With the DropTail mechanism, there is no way to prioritize important packets to be transmitted through the router earlier when all are in the queue. Meanwhile, with multimedia communication, ensuring connection and stable speed is extremely important and the DropTail algorithm cannot satisfy.
The problem of choosing the buffer size of the routers in the network is to “absorb” short bursts of traffic without causing too much queuing delay. This is necessary in bursty data transmission. The queue size determines the size of the packet bursts (traffic spikes) that we want to be able to transmit without being dropped at the routers.
In IP-based application networks, packet dropping is an important mechanism for indirectly reporting congestion to end stations. A solution that prevents router queues from filling up while reducing the packet drop rate is called dynamic queue management.
3.2. Random elimination method – RED
3.2.1 Overview
RED (Random Early Detection of congestion; Random Early Drop) is one of the first AQM algorithms proposed in 1993 by Sally Floyd and Van Jacobson, two scientists at the Lawrence Berkeley Laboratory of the University of California, USA. Due to its outstanding advantages compared to previous queue management algorithms, RED has been widely installed and deployed on the Internet.
The most fundamental point of their work is that the most effective place to detect congestion and react to it is at the gateway or router.
Source entities (senders) can also do this by estimating end-to-end delay, throughput variability, or the rate of packet retransmissions due to drop. However, the sender and receiver view of a particular connection cannot tell which gateways on the network are congested, and cannot distinguish between propagation delay and queuing delay. Only the gateway has a true view of the state of the queue, the link share of the connections passing through it at any given time, and the quality of service requirements of the
traffic flows. The RED gateway monitors the average queue length, which detects early signs of impending congestion (average queue length exceeding a predetermined threshold) and reacts appropriately in one of two ways:
− Drop incoming packets with a certain probability, to indirectly inform the source of congestion, the source needs to reduce the transmission rate to keep the queue from filling up, maintaining the ability to absorb incoming traffic spikes.
− Mark “congestion” with a certain probability in the ECN field in the header of TCP packets to notify the source (the receiving entity will copy this bit into the acknowledgement packet).
Figure 3. 1 RED algorithm
The main goal of RED is to avoid congestion by keeping the average queue size within a sufficiently small and stable region, which also means keeping the queuing delay sufficiently small and stable. Achieving this goal also helps: avoid global synchronization, not resist bursty traffic flows (i.e. flows with low average throughput but high volatility), and maintain an upper bound on the average queue size even in the absence of cooperation from transport layer protocols.
To achieve the above goals, RED gateways must do the following:
− The first is to detect congestion early and react appropriately to keep the average queue size small enough to keep the network operating in the low latency, high throughput region, while still allowing the queue size to fluctuate within a certain range to absorb short-term fluctuations. As discussed above, the gateway is the most appropriate place to detect congestion and is also the most appropriate place to decide which specific connection to report congestion to.
− The second thing is to notify the source of congestion. This is done by marking and notifying the source to reduce traffic. Normally the RED gateway will randomly drop packets. However, if congestion
If congestion is detected before the queue is full, it should be combined with packet marking to signal congestion. The RED gateway has two options: drop or mark; where marking is done by marking the ECN field of the packet with a certain probability, to signal the source to reduce the traffic entering the network.
− An important goal that RED gateways need to achieve is to avoid global synchronization and not to resist traffic flows that have a sudden characteristic. Global synchronization occurs when all connections simultaneously reduce their transmission window size, leading to a severe drop in throughput at the same time. On the other hand, Drop Tail or Random Drop strategies are very sensitive to sudden flows; that is, the gateway queue will often overflow when packets from these flows arrive. To avoid these two phenomena, gateways can use special algorithms to detect congestion and decide which connections will be notified of congestion at the gateway. The RED gateway randomly selects incoming packets to mark; with this method, the probability of marking a packet from a particular connection is proportional to the connections shared bandwidth at the gateway.
− Another goal is to control the average queue size even without cooperation from the source entities. This can be done by dropping packets when the average size exceeds an upper threshold (instead of marking it). This approach is necessary in cases where most connections have transmission times that are less than the round-trip time, or where the source entities are not able to reduce traffic in response to marking or dropping packets (such as UDP flows).
3.2.2 Algorithm
This section describes the algorithm for RED gateways. RED gateways calculate the average queue size using a low-pass filter. This average queue size is compared with two thresholds: minth and maxth. When the average queue size is less than the lower threshold, no incoming packets are marked or dropped; when the average queue size is greater than the upper threshold, all incoming packets are dropped. When the average queue size is between minth and maxth, each incoming packet is marked or dropped with a probability pa, where pa is a function of the average queue size avg; the probability of marking or dropping a packet for a particular connection is proportional to the bandwidth share of that connection at the gateway. The general algorithm for a RED gateway is described as follows: [5]
For each packet arrival
Caculate the average queue size avg If minth ≤ avg < maxth
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Qos Assurance Methods for Multimedia Communications
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zt2a3ge
zc2o3n4t5e6n7ts
low. The EF PHB requires a sufficiently large number of output ports to provide low delay, low loss, and low jitter.
EF PHBs can be implemented if the output port's bandwidth is sufficiently large, combined with small buffer sizes and other network resources dedicated to EF packets, to allow the router's service rate for EF packets on an output port to exceed the arrival rate λ of packets at that port.
This means that packets with PHB EF are considered with a pre-allocated amount of output bandwidth and a priority that ensures minimum loss, minimum delay and minimum jitter before being put into operation.
PHB EF is suitable for channel simulation, leased line simulation, and real-time services such as voice, video without compromising on high loss, delay and jitter values.
Figure 2.10 Example of EF installation
Figure 2.10 shows an example of an EF PHB implementation. This is a simple priority queue scheduling technique. At the edges of the DS domain, EF packet traffic is prioritized according to the values agreed upon by the SLA. The EF queue in the figure needs to output packets at a rate higher than the packet arrival rate λ. To provide an EF PHB over an end-to-end DS domain, bandwidth at the output ports of the core routers needs to be allocated in advance to ensure the requirement μ > λ. This can be done by a pre-configured provisioning process. In the figure, EF packets are placed in the priority queue (the upper queue). With such a length, the queue can operate with μ > λ.
Since EF was primarily used for real-time services such as voice and video, and since real-time services use UDP instead of TCP, RED is generally
not suitable for EF queues because applications using UDP will not respond to random packet drop and RED will strip unnecessary packets.
2.2.4.2 Assured Forwarding (AF) PHB
PHB AF is defined by RFC 2597. The purpose of PHB AF is to deliver packets reliably and therefore delay and jitter are considered less important than packet loss. PHB AF is suitable for non-real-time services such as applications using TCP. PHB AF first defines four classes: AF1, AF2, AF3, AF4. For each of these AF classes, packets are then classified into three subclasses with three distinct priority levels.
Table 2.8 shows the four AF classes and 12 AF subclasses and the DSCP values for the 12 AF subclasses defined by RFC 2597. RFC 2597 also allows for more than three separate priority levels to be added for internal use. However, these separate priority levels will only have internal significance.
PHB Class
PHB Subclass
Package type
DSCP
AF4
AF41
Short
100010
AF42
Medium
100100
AF43
High
100110
AF3
AF31
Short
011010
AF32
Medium
011100
AF33
High
011110
AF2
AF21
Short
010010
AF22
Medium
010100
AF23
High
010110
AF1
AF11
Short
001010
AF12
Medium
001100
AF13
High
001110
Table 2.8 AF DSCPs
The AF PHB ensures that packets are forwarded with a high probability of delivery to the destination within the bounds of the rate agreed upon in an SLA. If AF traffic at an ingress port exceeds the pre-priority rate, which is considered non-compliant or “out of profile”, the excess packets will not be delivered to the destination with the same probability as the packets belonging to the defined traffic or “in profile” packets. When there is network congestion, the out of profile packets are dropped before the in profile packets are dropped.
When service levels are defined using AF classes, different quantity and quality between AF classes can be realized by allocating different amounts of bandwidth and buffer space to the four AF classes. Unlike
EF, most AF traffic is non-real-time traffic using TCP, and the RED queue management strategy is an AQM (Adaptive Queue Management) strategy suitable for use in AF PHBs. The four AF PHB layers can be implemented as four separate queues. The output port bandwidth is divided into four AF queues. For each AF queue, packets are marked with three “colors” corresponding to three separate priority levels.
In addition to the 32 DSCP 1 groups defined in Table 2.8, 21 DSCPs have been standardized as follows: one for PHB EF, 12 for PHB AF, and 8 for CSCP. There are 11 DSCP 1 groups still available for other standards.
2.2.5.Example of Differentiated Services
We will look at an example of the Differentiated Service model and mechanism of operation. The architecture of Differentiated Service consists of two basic sets of functions:
Edge functions: include packet classification and traffic conditioning. At the inbound edge of the network, incoming packets are marked. In particular, the DS field in the packet header is set to a certain value. For example, in Figure 2.12, packets sent from H1 to H3 are marked at R1, while packets from H2 to H4 are marked at R2. The labels on the received packets identify the service class to which they belong. Different traffic classes receive different services in the core network. The RFC definition uses the term behavior aggregate rather than the term traffic class. After being marked, a packet can be forwarded immediately into the network, delayed for a period of time before being forwarded, or dropped. We will see that there are many factors that affect how a packet is marked, and whether it is forwarded immediately, delayed, or dropped.
Figure 2.12 DiffServ Example
Core functionality: When a DS-marked packet arrives at a Diffservcapable router, the packet is forwarded to the next router based on
Per-hop behavior is associated with packet classes. Per-hop behavior affects router buffers and the bandwidth shared between competing classes. An important principle of the Differentiated Service architecture is that a router's per-hop behavior is based only on the packet's marking or the class to which it belongs. Therefore, if packets sent from H1 to H3 as shown in the figure receive the same marking as packets from H2 to H4, then the network routers treat the packets exactly the same, regardless of whether the packet originated from H1 or H2. For example, R3 does not distinguish between packets from h1 and H2 when forwarding packets to R4. Therefore, the Differentiated Service architecture avoids the need to maintain router state about separate source-destination pairs, which is important for network scalability.
Chapter Conclusion
Chapter 2 has presented and clarified two main models of deploying and installing quality of service in IP networks. While the traditional best-effort model has many disadvantages, later models such as IntServ and DiffServ have partly solved the problems that best-effort could not solve. IntServ follows the direction of ensuring quality of service for each separate flow, it is built similar to the circuit switching model with the use of the RSVP resource reservation protocol. IntSer is suitable for services that require fixed bandwidth that is not shared such as VoIP services, multicast TV services. However, IntSer has disadvantages such as using a lot of network resources, low scalability and lack of flexibility. DiffServ was born with the idea of solving the disadvantages of the IntServ model.
DiffServ follows the direction of ensuring quality based on the principle of hop-by-hop behavior based on the priority of marked packets. The policy for different types of traffic is decided by the administrator and can be changed according to reality, so it is very flexible. DiffServ makes better use of network resources, avoiding idle bandwidth and processing capacity on routers. In addition, the DifServ model can be deployed on many independent domains, so the ability to expand the network becomes easy.
Chapter 3: METHODS TO ENSURE QoS FOR MULTIMEDIA COMMUNICATIONS
In packet-switched networks, different packet flows often have to share the transmission medium all the way to the destination station. To ensure the fair and efficient allocation of bandwidth to flows, appropriate serving mechanisms are required at network nodes, especially at gateways or routers, where many different data flows often pass through. The scheduler is responsible for serving packets of the selected flow and deciding which packet will be served next. Here, a flow is understood as a set of packets belonging to the same priority class, or originating from the same source, or having the same source and destination addresses, etc.
In normal state when there is no congestion, packets will be sent as soon as they are delivered. In case of congestion, if QoS assurance methods are not applied, prolonged congestion can cause packet drops, affecting service quality. In some cases, congestion is prolonged and widespread in the network, which can easily lead to the network being "frozen", or many packets being dropped, seriously affecting service quality.
Therefore, in this chapter, in sections 3.2 and 3.3, we introduce some typical network traffic load monitoring techniques to predict and prevent congestion before it occurs through the measure of dropping (removing) packets early when there are signs of impending congestion.
3.1. DropTail method
DropTail is a simple, traditional queue management method based on FIFO mechanism. All incoming packets are placed in the queue, when the queue is full, the later packets are dropped.
Due to its simplicity and ease of implementation, DropTail has been used for many years on Internet router systems. However, this algorithm has the following disadvantages:
− Cannot avoid the phenomenon of “Lock out”: Occurs when 1 or several traffic streams monopolize the queue, making packets of other connections unable to pass through the router. This phenomenon greatly affects reliable transmission protocols such as TCP. According to the anti-congestion algorithm, when locked out, the TCP connection stream will reduce the window size and reduce the packet transmission speed exponentially.
− Can cause Global Synchronization: This is the result of a severe “Lock out” phenomenon. Some neighboring routers have their queues monopolized by a number of connections, causing a series of other TCP connections to be unable to pass through and simultaneously reducing the transmission speed. After those monopolized connections are temporarily suspended,
Once the queue is cleared, it takes a considerable amount of time for TCP connections to return to their original speed.
− Full Queue phenomenon: Data transmitted on the Internet often has an explosion, packets arriving at the router are often in clusters rather than in turn. Therefore, the operating mechanism of DropTail makes the queue easily full for a long period of time, leading to the average delay time of large packets. To avoid this phenomenon, with DropTail, the only way is to increase the router's buffer, this method is very expensive and ineffective.
− No QoS guarantee: With the DropTail mechanism, there is no way to prioritize important packets to be transmitted through the router earlier when all are in the queue. Meanwhile, with multimedia communication, ensuring connection and stable speed is extremely important and the DropTail algorithm cannot satisfy.
The problem of choosing the buffer size of the routers in the network is to “absorb” short bursts of traffic without causing too much queuing delay. This is necessary in bursty data transmission. The queue size determines the size of the packet bursts (traffic spikes) that we want to be able to transmit without being dropped at the routers.
In IP-based application networks, packet dropping is an important mechanism for indirectly reporting congestion to end stations. A solution that prevents router queues from filling up while reducing the packet drop rate is called dynamic queue management.
3.2. Random elimination method – RED
3.2.1 Overview
RED (Random Early Detection of congestion; Random Early Drop) is one of the first AQM algorithms proposed in 1993 by Sally Floyd and Van Jacobson, two scientists at the Lawrence Berkeley Laboratory of the University of California, USA. Due to its outstanding advantages compared to previous queue management algorithms, RED has been widely installed and deployed on the Internet.
The most fundamental point of their work is that the most effective place to detect congestion and react to it is at the gateway or router.
Source entities (senders) can also do this by estimating end-to-end delay, throughput variability, or the rate of packet retransmissions due to drop. However, the sender and receiver view of a particular connection cannot tell which gateways on the network are congested, and cannot distinguish between propagation delay and queuing delay. Only the gateway has a true view of the state of the queue, the link share of the connections passing through it at any given time, and the quality of service requirements of the
traffic flows. The RED gateway monitors the average queue length, which detects early signs of impending congestion (average queue length exceeding a predetermined threshold) and reacts appropriately in one of two ways:
− Drop incoming packets with a certain probability, to indirectly inform the source of congestion, the source needs to reduce the transmission rate to keep the queue from filling up, maintaining the ability to absorb incoming traffic spikes.
− Mark “congestion” with a certain probability in the ECN field in the header of TCP packets to notify the source (the receiving entity will copy this bit into the acknowledgement packet).
Figure 3. 1 RED algorithm
The main goal of RED is to avoid congestion by keeping the average queue size within a sufficiently small and stable region, which also means keeping the queuing delay sufficiently small and stable. Achieving this goal also helps: avoid global synchronization, not resist bursty traffic flows (i.e. flows with low average throughput but high volatility), and maintain an upper bound on the average queue size even in the absence of cooperation from transport layer protocols.
To achieve the above goals, RED gateways must do the following:
− The first is to detect congestion early and react appropriately to keep the average queue size small enough to keep the network operating in the low latency, high throughput region, while still allowing the queue size to fluctuate within a certain range to absorb short-term fluctuations. As discussed above, the gateway is the most appropriate place to detect congestion and is also the most appropriate place to decide which specific connection to report congestion to.
− The second thing is to notify the source of congestion. This is done by marking and notifying the source to reduce traffic. Normally the RED gateway will randomly drop packets. However, if congestion
If congestion is detected before the queue is full, it should be combined with packet marking to signal congestion. The RED gateway has two options: drop or mark; where marking is done by marking the ECN field of the packet with a certain probability, to signal the source to reduce the traffic entering the network.
− An important goal that RED gateways need to achieve is to avoid global synchronization and not to resist traffic flows that have a sudden characteristic. Global synchronization occurs when all connections simultaneously reduce their transmission window size, leading to a severe drop in throughput at the same time. On the other hand, Drop Tail or Random Drop strategies are very sensitive to sudden flows; that is, the gateway queue will often overflow when packets from these flows arrive. To avoid these two phenomena, gateways can use special algorithms to detect congestion and decide which connections will be notified of congestion at the gateway. The RED gateway randomly selects incoming packets to mark; with this method, the probability of marking a packet from a particular connection is proportional to the connection's shared bandwidth at the gateway.
− Another goal is to control the average queue size even without cooperation from the source entities. This can be done by dropping packets when the average size exceeds an upper threshold (instead of marking it). This approach is necessary in cases where most connections have transmission times that are less than the round-trip time, or where the source entities are not able to reduce traffic in response to marking or dropping packets (such as UDP flows).
3.2.2 Algorithm
This section describes the algorithm for RED gateways. RED gateways calculate the average queue size using a low-pass filter. This average queue size is compared with two thresholds: minth and maxth. When the average queue size is less than the lower threshold, no incoming packets are marked or dropped; when the average queue size is greater than the upper threshold, all incoming packets are dropped. When the average queue size is between minth and maxth, each incoming packet is marked or dropped with a probability pa, where pa is a function of the average queue size avg; the probability of marking or dropping a packet for a particular connection is proportional to the bandwidth share of that connection at the gateway. The general algorithm for a RED gateway is described as follows: [5]
For each packet arrival
Caculate the average queue size avg If minth ≤ avg < maxth
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Practice database programming with VB.net - 39 -
Java programming Web design profession - Dalat College of Technology - 8 -
Description of the Mlp Neural Network Training Algorithm Using Backpropagation Learning with Overshoot Step. Algorithm for Calculating Overshoot Step
LE MINH HOANG
Special lecture
Hanoi Pedagogical University, 1999-2002
Thanks
I would like to express my gratitude to the teachers who taught me wholeheartedly during the difficult years when I first started learning computer science and programming. Their understanding and enthusiasm not only provided me with valuable knowledge but also set a good example for me to follow when I stood on the podium as a teacher.
This document is written based on documents collected from many different sources, by the efforts of many generations of teachers and students who have taught and studied at the Mathematics-Information Technology High School, Hanoi National University of Education, and I am just the one who compiled it. Through this, I would like to thank my colleagues who have read and contributed valuable comments, and thank the students - the people who directly created this book.
Due to time constraints, some topics have been available but have not been edited and included in the document. Readers can refer to the reference section for more information. We look forward to receiving your comments and suggestions to complete this book.
Tokyo, April 28, 2003
Le Minh Hoang
i
INDEX
PART 1. LISTING PROBLEM 1
§1. REVIEW OF SOME KNOWLEDGE OF COMBINATIONAL ALGEBRA 2
1.1. IPEDIATED RECONCILIATION 2
1.2. NON-ITCHED CONFORMITY 2
1.3. PERMISSION 2
1.4. COMPOSITION 3
§2. GENERATION METHOD 4
2.1. GENERATE BINARY SEQUENCES OF LENGTH N 5
2.2. LISTING K-ELEMENT SUBSTITUTES 6
2.3. LIST THE PERMISSIONS 8
§3. BACKWARDING ALGORITHM 12
3.1. LIST BINARY SEQUENCES OF LENGTH N 12
3.2. LISTING K-ELEMENT SUBSTITUTES 13
3.3. LIST OF NON-REPEATING COMBINATIONS K 15
3.4. ANALYSIS PROBLEM 16
3.5. 18-PAIR PROBLEM
§4. 24-BRANCH TECHNIQUE
4.1. OPTIMISATION PROBLEM 24
4.2. THE COMBINATION EXPLOSION 24
4.3. TECHNICAL MODEL OF NEAR BRANCH 24
4.4. TOURIST PROBLEM 25
4.5. ABC SERIES 28
PART 2. DATA STRUCTURES AND ALGORITHMS 33
§1. BASIC STEPS WHEN SOLVING COMPUTER TECHNOLOGY PROBLEMS 34
1.1. DETERMINING PROBLEM 34
1.2. FIND THE DATA STRUCTURE TO REPRESENT PROBLEM 34
1.3. FIND ALGORITHM 35
1.4. PROGRAMMING 37
1.5. TESTING 37
1.6. PROGRAM OPTIMIZATION 38
§2. ANALYSIS OF ALGORITHM EXECUTION TIME 40
2.1. COMPUTATIONAL COMPLEXITY OF THE ALGORITHM 40
2.2. DETERMINING THE COMPUTATIONAL COMPLEXITY OF THE ALGORITHM 40
2.3. COMPUTATIONAL COMPLEXITY WITH INPUT DATA STATUS 43
2.4. COST OF IMPLEMENTING ALGORITHM 43
§3. RECURRENCE AND RECURRENT ALGORITHM 45
3.1. CONCEPT OF RECURRENCE 45
3.2. RECURRENT ALGORITHM 45
3.3. EXAMPLE OF RECURRENT ALGORITHM 46
3.4. EFFECT OF RECURRENCE 50
§4. DATA STRUCTURE REPRESENTING LIST 52
4.1. CONCEPT OF LIST 52
4.2. REPRESENTING LISTS IN COMPUTERS 52
§5. STACKS AND QUEUES 58
5.1. STACK 58
5.2. QUEUE 60
§6. TREE 64
6.1. DEFINITIONS 64
6.2. BINARY TREE 65
6.3. BINARY TREE REPRESENTATION 67
6.4. BINARY TREE TRANSFORMATION 69
6.5. K_PHAN 70
6.6. GENERAL TREE 71
§7. PREFIX, INTEGRATED AND SUBFIX NOTATION 74
7.1. EXPRESSION IN THE FORM OF BINARY TREES 74
7.2. NOTATIONS FOR THE SAME EXPRESSION 74
7.3. HOW TO CALCULATE THE VALUE OF EXPRESSION 75
7.4. CONVERTING FROM INTEGRATED TO SUFFIX 78
7.5. BUILDING A BINARY TREE TO REPRESENT THE EXPRESSION 80
§8. SORTING 82
8.1. SORTING PROBLEM 82
8.2. SELECTIONSORT ALGORITHM 84
8.3. BUBBLESORT ALGORITHM 85
8.4. INSERT SORT ALGORITHM 85
8.5. SHELLSORT 87
8.6. QUICKSORT SORTING ALGORITHM 88
8.7. HEAPSORT ALGORITHM 92
8.8. SORTING BY DISTRIBUTION COUNTING 95
8.9. STABILITY OF SORTING ALGORITHM 96
8.10. RADIXSORT ALGORITHM 97
8.11. MERGESORT ALGORITHM 102
8.12. SETTINGS 105
8.13. REVIEW, COMMENT. 112
§9. SEARCHING 116
9.1. SEARCH PROBLEM 116
9.2. SEQUENTIAL SEARCH 116
9.3. BINARY SEARCH 116
9.4. BINARY SEARCH TREE (BST) 117
9.5. HASH 122
9.6. NUMBER KEY WITH SEARCH PROBLEM 122
9.7. DIGITAL SEARCH TREE (DST) 123
9.8. RADIX SEARCH TREE (RST) 126
9.9. FINAL REMARKS 131
PART 3. PLANNING ACTIVITIES 133
§1. RETRIEVAL FORMULA 134
1.1. EXAMPLE 134
1.2. FIRST IMPROVEMENT 135
1.3. SECOND IMPROVEMENT 137
1.4. RECURRENT INSTALLATION 137
§2. METHODS OF OPERATION PLANNING 139
2.1. PLANNING PROBLEM 139
2.2. ACTIVITY PLANNING METHOD 139
§3. SOME DYNAMIC PLANNING PROBLEMS 143
3.1. LONGEST INCREASING MONOTONE SUBSEQUENCE 143
3.2. THE BAG PROBLEM 148
3.3. STRING TRANSFORMATION 150
3.4. SUB-SEQUENCES WHOSE SUM IS DIVIDABLE BY K 154
3.5. COMBINATIONAL MULTIPLICATION OF MATRIX SERIES 159
3.6. PRACTICE EXERCISES 163
PART 4. ALGORITHM ON GRAPHS 169
§1. BASIC CONCEPTS 170
1.1. DEFINITION OF GRAPH 170
1.2. CONCEPTS 171
§2. GRAPHIC PRESENTATION ON COMPUTER 173
2.1. ADJACENT MATRIX (ADJECTIVE MATRIX) 173
2.2. LIST OF EDGES 174
2.3. LIST OF ADJACENTS 175
2.4. COMMENTS 176
§3. GRAPH SEARCH ALGORITHMS 177
3.1. PROBLEM 177
3.2. DEPTH FIRST SEARCH ALGORITHM 178
3.3. BREADTH FIRST SEARCH ALGORITHM 184
3.4. COMPUTATIONAL COMPLEXITY OF BFS AND DFS 189
§4. CONNECTIVITY OF GRAPH 190
4.1. DEFINITIONS 190
4.2. CONNECTEDNESS IN UNDIRECTED GRAPHS 191
4.3. FULL GRAPH AND WARSHALL ALGORITHM 191
4.4. STRONGLY INTERCONNECTED COMPONENTS 195
§5. SOME APPLICATIONS OF GRAPH SEARCH ALGORITHMS 205
5.1. BUILDING A SPANNING TREE OF GRAPH 205
5.2. SET OF BASIC CYCLES OF GRAPH 208
5.3. GRAPH DIRECTION AND DEMAND LISTING PROBLEM 208
5.4. MATCH LIST 214
§6. EULER CYCLES, EULER PATHS, EULER GRAPHS 218
6.1. PROBLEM 7 BRIDGES 218
6.2. DEFINITIONS 218
6.3. THEOREM 218
6.4. FLEURY'S ALGORITHM FOR FINDING EULER CYCLES 219
6.5. SETTINGS 220
6.6. BETTER ALGORITHM 222
§7. HAMILTON CYCLE, HAMILTON PATH, HAMILTON GRAPHS 225
7.1. DEFINITIONS 225
7.2. THEOREM 225
7.3. SETTINGS 226
§8. SHORTEST PATH PROBLEM 230
8.1. WEIGHTED GRAPH 230
8.2. SHORTEST PATH PROBLEM 230
8.3. CASE OF GRAPHS WITHOUT NEGATIVE CYCLES - FORD BELLMAN'S ALGORITHM 232
8.4. CASE OF NON-NEGATIVE WEIGHTS ON ARCS - DIJKSTRA'S ALGORITHM 234
8.5. DIJKSTRA'S ALGORITHM AND HEAP STRUCTURE 237
8.6. CASE OF GRAPH WITHOUT CYCLES - TOPOLOGICAL ORDER 240
8.7. SHORTEST PATH BETWEEN ANY PAIR OF PERCEPTS - FLOYD'S ALGORITHM. 242
8.8. COMMENTS 245
§9. MINIMUM SPANNING TREE PROBLEM 247
9.1. MINIMUM SPANNING TREE PROBLEM 247
9.2. KRUSKAL'S ALGORITHM (JOSEPH KRUSKAL - 1956) 247
9.3. PRIM'S ALGORITHM (ROBERT PRIM - 1957) 252
§10. MAXIMUM FLOW PROBLEM ON NETWORK 256
10.1. PROBLEM 256
10.2. CUTTING, FLOW INCREASE, FORD - FULKERSON THEOREM 256
10.3. SETTINGS 258
10.4. FORD - FULKERSON ALGORITHM (LRFORD & DRFULKERSON - 1962) 262
§11. PROBLEM OF FINDING MAXIMUM MATCHING SET ON A BI-SIDED GRAPH 266
11.1. BIPARTITE GRAPH 266
11.2. UNWEIGHTED PAIRING PROBLEMS AND CONCEPTS 266
11.3. OPEN PATH ALGORITHM 267
11.4. SETTINGS 268
§12. PROBLEM OF FINDING MAXIMUM SET WITH MINIMUM WEIGHT ON A BI-SIDED GRAPH - HUNGARIAN ALGORITHM 273
12.1. ASSIGNMENT PROBLEM 273
12.2. ANALYSIS 273
12.3. ALGORITHM 274
12.4. SETTINGS 278
12.5. PROBLEM OF FINDING MAXIMUM MATCHING SET WITH MAXIMUM WEIGHT ON A BI-SIDED GRAPHS 284
12.6. UPGRADE 284
§13. PROBLEM OF FINDING MAXIMUM COMPONENTS ON GRAPH 290
13.1. CONCEPTS 290
13.2. EDMONDS ALGORITHM (1965) 291
13.3. LAWLER METHOD (1973) 293
13.4. SETTINGS 295
13.5. COMPUTATIONAL COMPLEXITY 299
FURTHER READING 301
PICTURE
Figure 1: Backtracking search tree in binary sequence enumeration problem 13
Figure 2: Arrange 8 queens on an 8x8 chessboard 19
Figure 3: The diagonal NE-SW has index 10 and the diagonal NE-SW has index 0 19
Figure 4: Algorithm flowchart 36
Figure 5: Hanoi Tower 49
Figure 6: Node structure of a singly linked list 53
Figure 7: Singly linked list 53
Figure 8: Node structure of doubly linked list 55
Figure 9: Doubly linked list 55
Figure 10: One-way circular join list 55
Figure 11: Bidirectional circular join list 56
Figure 12: Using a circular list to describe Queue 61
Figure 13: Moving the train car. 63
Figure 14: Moving the train (2) 63
Figure 15: Tree 64
Figure 16: Levels of nodes on the tree 65
Figure 17: Expression tree 65
Figure 18: Degenerate binary tree types 66
Figure 19: Complete binary tree and full binary tree 66
Figure 20: Numbering the nodes of a complete binary tree for representation by an array of 67
Figure 21: Disadvantages of the tree representation method using arrays 68
Figure 22: Node structure of binary tree 68
Figure 23: Tree representation using 69-link structure
Figure 24: Numbering the nodes of a 3_part tree to represent it with an array of 71
Figure 25: Representing a general tree using an array of 72
Figure 26: Node structure of the general tree 73
Figure 27: Expression in the form of a binary tree 74
Figure 28: Inner loop of QuickSort 89
Figure 29: State before recursive call 90
Figure 30: Heap 92
Figure 31: Pile up 93
Figure 32: Invert the value of k 1 for k n and consider the remainder 93
Figure 33: Stack the remaining parts and then invert k 1 to k n-194
Figure 34: Numbering the 97 bits
Figure 35: Merge sort algorithm 102
Figure 36: Setting up sorting algorithms with large data 114
Figure 37: Binary search tree 118
Figure 38: Deleting a leaf node in the tree BST 119
Figure 39. Delete a node with only one child branch on a BST 120 tree