106
-Take any point M(x 0 ;y 0 ) not on (d)
If ax 0 + by 0 +c < 0 then the half-plane (excluding the edge (d) containing point M is the solution domain of the inequality ax +by +c < 0 .
If ax + by +c > 0 then the half-plane (excluding the edge (d)) not containing point M is the solution domain of the inequality ax + by +c > 0.
Note that teachers should guide students when to practice solutions and take the entire shore (d). Example 1: determine the domain of solutions of the equation 3x + y 
0
Teacher: Draw a straight line with equation (d): 3x + y =0. Students: Students do it.
Teacher: Choose a point belonging to one of the two half-planes. Student: For example, point M(1;1)
Teacher: Substitute into the equation of line (d) and see if that point belongs to the solution domain of the equation?
HS: realize that M(1;1) is not a solution of the given equation. GV: Determine the domain of the solution of the equation.
HS: So the solution region we need to find is the half-plane with edge (d) that does not contain point M as shown in the figure.
Teacher guides students to do activity 1 H 1 (Textbook) Activity 2.
2System of first-degree equations with two unknowns Example 2:
3 x y 3 0
2 x 3 y 6 0
2 x y 4 0
(I)
The teacher guides students to follow these steps:
+ Draw straight lines with equations in system (I)
+ Please indicate the domain of solutions of each equation in system (I)
+ Show the domain of the system. Do H 2 in the textbook.
Teacher: Draw the lines y-3x=0, x-2y+5=0, 5x+2y+10=0. Students: Do it under the teacher's guidance.
Teacher: Determine the domain of solutions of each equation in the system.
Students: do it themselves under the guidance of the teacher, ask a student to practice. Teacher: Determine the domain of the system.
HS: Take the intersection of the three regions above.
Like the equation, the system of equations, the system of first-order quadratic equations with two unknowns is a mathematical content with many practical applications, especially in the field of solving economic problems. Let's continue to study the following part:
Activity 3:
3. Some applications to economic problems. The teacher presents the problem according to the textbook.
Analyze the problem to find the solution.
This is an economic problem, we pay attention to raw materials of type I and type II. Pay attention to the amount of money, extract substance A and substance B. Analyze the data and conditions of the problem.
Teacher: If we use x tons of type I raw materials and y tons of type II raw materials, how many kilograms of substance A and substance B can we extract?
HS: under the teacher's suggestion
Each ton of type I raw material can extract 20kg of substance A and 0.6kg of substance B.
Each ton of type II raw material can extract 10kg of substance A and 1.5kg of substance B.
Then how much can be extracted from x tons of type I raw materials and y tons of type II raw materials?
We have: (20x+10y) kg of substance A (o,6x+1,5y) kg of substance B
Teacher: People plan to extract at least 140 kg of substance A and 9 kg of substance B from two types of raw materials. Then both types I and II extract substances A and B, which will satisfy what?
HS: 20x+10y 
140
0.6x+1.5y 
9
Teacher: Please express the amount of money to buy raw materials of type I and type II? Student: T(x;y) = 4x+3y
Teacher: How many tons of each type of raw material should be used to minimize costs?
0 | x | 10 |
0 | y | 9 |
2 x | y | 14 |
2 x | 5 years | 30 |
Maybe you are interested!
-
Practical Application, Problems, Limitations and Causes -
![Qos Assurance Methods for Multimedia Communications
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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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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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Termination of labor contracts in the 2012 Labor Code and practical application in enterprises in Vietnam - 5 -
Division of common property of spouses according to Vietnamese law - Practical application and improvement direction - 16 -
Practical Application of Inspection and Examination Measures; Handling of Import Tax Obligations Violations and Compulsory Compensation for Damages
HS: The problem becomes finding numbers x and y that satisfy the equation
(II)
So that T(x;y) = 4x+3y has the smallest value.
Teacher: To solve the above problem, find the solution of the equation system (II)?
HS: Present the solution after learning the steps to determine the domain of solutions of a first-degree quadratic equation with two variables.
Teacher: Prepare the drawing, color to highlight the area of quadrilateral ABCD and calculate the points A, B, C, D as the intersection of the corresponding lines in system (II).
- Choose any point in the quadrilateral ABCD and prove that the quadrilateral ABCD is the solution.
HS: Prove and present on the board.
Teacher: In all points in the domain of solution of system (II), find point (x;y) so that T(x;y) has the smallest value.
HS: under the teacher's suggestion
Because we only consider T(x;y) = 4x+3y with (x;y) satisfying system (II), we only consider the line
straight (d m ): 4x+3y = T
Passes through at least 1 point of quadrilateral ABCD
y
4 x T
3 3
Notice that this family of lines is parallel to the line y=
As T increases
4 x
3
Draw that line parallel to the top, then the smallest value of T is reached at the top A (5;4). We find T=32 corresponding to T(5;4).
So: To minimize raw material costs, it is necessary to use 5 tons of type I raw materials and 4 tons of type II raw materials. Then the total cost is 32 million VND.
Teacher prepares drawing board with figure 4.7 in textbook
14
x=10
2x+y=14
9
D
C
6
A
4
B 2x+5y=30
2
O
5
7
10
15
x
y=9
Reinforcement:
+ The general form of a first-degree inequality with two unknowns x,y is ax + by 
0 (1)
(ax+by
+ The set of points whose coordinates are solutions to inequality (1) is called its solution domain.
_ Rules for practicing the geometric representation of the solution domain of an inequality (1) Step 1. On the Cartesian coordinate plane perpendicular to oxy, draw the line ax +
by = c (d)
Step 2. Take a point M 0 (x 0 ,y 0 ) d (we usually take the origin 0)
+ Step 3. Calculate ax 0 + by 0 and compare ax 0 + by 0 with c.
+ Step 4. Conclusion
If ax 0 + by 0 < c then the half-plane with edge d containing point M 0 is the solution domain of ax +by 
c.
If ax 0 +by 0 > c then the half-plane with edge d not containing M 0 is the solution domain of ax + by 
c
+ To solve a system of first-degree inequalities with two variables, we solve the inequalities in turn, then take the intersection of the solution sets.
Consolidation exercises
A factory produces two types of products, denoted I and II. One ton of product I makes a profit of 2 million VND, one ton of product II makes a profit of 1.6 million VND. To produce 1 ton of product I, machine M1 must be used for 3 hours and machine M2 for 1 hour. To produce 1 ton of product II, machine M1 must be used for 1 hour and machine M2 for 1 hour. One machine cannot be used to produce two types of products at the same time. Machine M1 works no more than 6 hours a day, machine M2 works no more than 4 hours a day. Plan the production so that the total profit is the highest.
Analysis of suggested answers:
Let x, y be the tons of products of type I, II produced in one day.
Because machine M 1 only works no more than 6 hours in a day and machine M 2 only works no more than 4 hours in a day.
Total interest L = 2x + 1.6y. So we have the following problem: Find real numbers x and y that satisfy the system:
x
y
3 x
x
0
0
y 6
y
4
So that L = 2x + 1.6y is a maximum.
Thus, the enterprise will earn maximum profit when producing 1 ton of product I and 3 tons of product II per day. At that time, the profit achieved is L = 6.8 million VND.
Consolidation: -Students need to grasp the concept of inequality and system of first-degree inequalities with two variables.
- Grasp the concept of the solution set of an inequality and a system of first-degree inequalities with two variables and represent that solution set on the coordinate plane.
- Understand and know how to relate to practical problems, especially extreme value problems. Homework from lessons 42 to 48 (pp.132-136).
Guide students to study at home.
You need to pay attention to study carefully at home how to determine the domain of solutions of quadratic inequality and redo the exercises taught today.
Study and refer to documents with instructions on how to solve economic problems and do similar exercises.
3.3.2. Proposed opinions and evaluation of experimental results analysis.
The practice results show that about 100% of students in class 10A 10 understand the lesson, of which 90% absorb and practice solving math problems quickly during class.
In the remaining classes, about 70% to 80% of students grasp the lesson and practice solving math problems. In class 10A12 (basic C), only about 50% to 60% grasp the lesson.
Students have grasped the steps to solve problems using general methods to solve practical problems, initially knowing how to apply them to solving problems and linking mathematics with practice.
Most students are very interested in teaching mathematics in a practical way, the lessons are lively and do not feel boring, rigid and dry.
Colleagues' opinions.
The lesson is carefully prepared, with exercises for students to solve and approach problems in the lesson. Agree with the spirit of teaching closely linked to practice.
The practical reinforcement problems are too long and difficult for students, more suitable textbooks and problems are needed.
Often have difficulty in communicating ideas about the lesson plan.
My opinion.
Through the experiment of teaching grade 10 through the above prepared curriculum and testing and evaluating the results in those classes, I can make some comments as follows:
- Students are very interested in learning and absorb the knowledge given quite quickly. They are able to apply that knowledge to solve and do exercises, as well as similar or more difficult types of math.
- Teachers can organize activities during class to help students develop their thinking process and initially know how to cooperate to solve math problems leading to good results.
GENERAL CONCLUSION
Through the content presented above, under the guidance of teacher Nguyen Ngoc Uy and the comments and criticisms of colleagues, it can be seen that the thesis has achieved the following results:
Contribution of the topic.
About theory :
The thesis has clarified the importance of mathematics, the role of mathematics in practical life, in science and technology and in other sciences.
- Highlight the application and use of mathematics in teaching mathematics in high schools, specifically advanced algebra 10. Propose a general method for solving math problems in practical applications associated with the knowledge learned in mathematics.
- Through the learned parts, we should build a connection between mathematics and practice in teaching and learning activities through concepts, theorems, and teaching exercises.
In practice :
- Prepare some specific lesson plans in the spirit of application, thereby clarifying and analyzing the content of mathematics with practice and the practical origin of mathematics that interact with each other.
- Experimentally teach the above problems to students at the school where I work, propose feasible directions to effectively link math teaching with real life. Thereby, there are comments on the advantages and disadvantages of implementation.
Limitations of the topic:
Only practical problems have been proposed to be linked to each part of the advanced algebra 10 curriculum. However, the exercise system is still not rich, and there is no complete and scientific pedagogical experiment.