traditional method and gives better results than the channel borrowing algorithms considered in section 1.4 above.
1.6. Conclusion
In this chapter, the thesis has reviewed the overview of cellular mobile networks, basic concepts, channel allocation as well as compared the channel allocation methods FCA, DCA, HCA and examined their effectiveness. In particular, the thesis has considered channel borrowing/locking algorithms to improve the capacity of cellular mobile networks due to limited network resources, thereby improving capacity, service quality and increasing the load balancing ability of the entire system. The content of this chapter is the basis for reviewing and proposing new channel borrowing and locking methods that will be reviewed in the following chapters of the thesis.
Chapter 2. DYNAMIC CHANNEL BORROWING AND LOCK BASED ON FUZZY LOGIC CONTROLLER AND NEURAL NETWORK
In chapter 2, the thesis will examine the channel borrowing, locking and dynamic load balancing algorithms based on the fuzzy logic controller FDCBS and the fuzzy neural network NFDCBS proposed by author Yao-Tien Wang [47][48]. The limitations of these algorithms are evaluated, and some improvements to the NFDCBS algorithm are proposed. Then, chapter 2 also points out the limitations of the channel borrowing method based on the fuzzy logic controller, the traditional neuro-fuzzy controller, and proposes a new channel borrowing and locking method based on the fuzzy neural network controller using subsethood measurement.
2.1. Introduction
In traditional channel locking and borrowing methods, threshold values are often used to determine the cell load status [5][6][7][30]. However, determining the appropriate cell load threshold value is extremely difficult and time-consuming. On the other hand, using thresholds to separate cell load statuses can easily cause a ping-pong effect [7][30]. Because when the cell load fluctuates around the threshold, it will cause the system to become unstable and transmit unnecessary messages at a high level. This affects the quality of the entire system. On the other hand, the number of incoming calls and the call execution time are uncertain and unpredictable. This poses an urgent need for a more suitable and effective forecasting mechanism. Most of the recently proposed methods use intelligent computational tools, in which neural networks, fuzzy logic, genetic algorithms, and swarm theory are the main ones. The use of intelligent computational methods, or the combination of these methods with traditional channel borrowing and locking methods, has significantly improved the capacity and quality of cellular mobile systems. Among them, the algorithms proposed by Yao-Tien Wang [47][48] are of particular interest because of their efficiency.
Yao-Tien Wang developed the FDCBS channel borrowing algorithm [47] based on the fuzzy logic controller. The FDCBS algorithm allows to overcome the limitations of traditional methods and predict the load status of the cell. FDCBS shows better adaptability and error tolerance than other algorithms. At the same time, it also allows to reduce the probability of channel blocking, the probability of dropped calls, the complexity of message transmission and the channel reception delay. However, like many other algorithms, FDCBS also reveals many disadvantages such as FDCBS strongly depends on expert knowledge, it is difficult to cover all cases that occur when the problem is complex, and the approximation ability is limited due to the nature of the design of the fuzzy control rule set. In [48], Yao-Tien Wang overcame that by proposing the dynamic channel borrowing controller NFDCBS. NFDCBS uses fuzzy neural networks with training data sets to generate automatic rule sets, so it is less dependent on domain expert knowledge. The following thesis will examine these algorithms of Yao-Tien Wang and point out their limitations. The thesis also proposes some improvements to these algorithms to increase capacity and improve the quality of cellular mobile network systems.
2.2. FDCBS and NFDCBS channel borrowing algorithms
2.2.1. Cellular mobile network system model
The cellular mobile system model assumed by FDCBS is as follows: the system consists of a number of hexagonal cells, each served by a base station (BS). The base station and the mobile station (MS) communicate with each other via a radio link. Each cell is assigned a fixed number of CH channels and that set of channels will be reused in cells that are at least far enough away from it to avoid interference. A group of consecutive cells using distinct channels forms a Compact pattern of radius R . Consider a cell c , the interfering neighbors of c are defined by IN(c)={c'| dist(c,c')
<D min }, where D min is the minimum distance between co-channel cells determined by the formula D min =3(3R) 1/2 . If Ni is the number of cells in loop i , then for hexagonal cells Ni =1 if i=0, Ni = 6i if i>1 .
Perform diversity of all cells in the network into some distinct subsets G 0 , G 1 , ...G k-1 such that any two cells in the same subset are at least D min apart . Similarly, for the channel set assigned to a cellular mobile network, perform diversity of all channels into K distinct subsets P 0 , P 1 ,....,P k-1 . The channels in P i (i=1,2,..,k-1) are called elementary channels for the cells in G i and are arranged in a definite order. A channel i is chosen to be used (U i ) or allowed (V i ) depending on whether it is assigned to an MS or not. An allowed channel of c is interfered with if it is used by cells in IN(c).
2.1.3. Fuzzy logic dynamic channel borrowing controller FDCBS
For convenience, a cell C i is a primary cell of a CH channel if and only if CH is the primary channel of cell C i . Thus, cells in G i are primary cells of channels in P i and are secondary cells of channels in P j ( j i ). The set of cells covered by a set of BSs is shown in Figure 2.1.
Cell group
Cell
Channel cell
Interference neighboring cell
Figure 2.1: Cellular network with hexagonal cells
2.2.2. Fuzzy logic based channel borrowing controller
The fuzzy logic channel borrowing controller consists of 2 parts: fuzzy logic controller, consisting of 4 main blocks: Fuzzification block, fuzzy rule base block, fuzzy inference block and defuzzification block;
Fuzzy logic controller (FLC)
4
1
3
Fuzzy block
Fuzzy rule base
Defuzzification block
2
5
7
6
Move
multi-channel
8
9
12
10
11
Cellular Loading Decision Making
Agreement with related cell cells
Inference engine
Process control
Traffic Load | 7 | Provide cell loading status or not | |
2 | Number of channels allowed | 8 | Find target cells |
3 | Fuzzy variable | 9 | Impact output after defuzzification |
4 | Fuzzy output vector | 10 | Lend channels |
5 | Cell loading status | 11 | Borrow channels |
6 | Target cells found? | 12 | Number of channels allowed |
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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 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 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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On a new method of controlling the borrowing and locking of cellular mobile network frequency channels - 18 -
Compare Annual Expenditures for Education Based on Purchasing Power Parity -
Comparison of Activity-Based Costing and Traditional Costing -
Applying Project-Based Learning to Organize Study Tours to the Hoa Lu Ancient Capital Cultural Heritage
Fig.2.2: Fuzzy logic based channel borrowing controller
and FDCBS consists of three blocks that implement three phases: the cell load state decision phase, the cell-related negotiation phase, and the multi-channel migration phase. All three phases are designed by applying fuzzy logic control to them. The cell load decision phase specifies the amount of cell-related information as well as the rules for extracting information to make cell load reallocation decisions. The purpose of this phase is to obtain enough information to make appropriate decisions when the cell load is “very hot”, “hot”, “medium”, “cold” and “very cold”. The cell-related negotiation phase allows the current cell to perform the negotiation exchange, select cells from which to move channels or to which cells when performing load reallocation. The multi-channel migration phase maintains the management of channel migration from one cell to another.
2.2.3. Cell loading state decision phase
In order to estimate the load state in the cellular network and determine the most suitable place to perform load-sharing channel switching in the system, FDCBS proposes a method to approximate the cell load state based on a fuzzy logic controller to make a decision on load redistribution in the cellular mobile network. Specifically, FDCBS allows to construct the membership functions of different allowed channels, the traffic load membership function and the central value for language labels through the FCM (Fuzzy C-means) clustering algorithms that are suitable for the data characteristics of different cells.
Unlike many algorithms [29][30][31][55] that only use the allowed channel number parameter as the sole load index for the BS in the cellular system, FDCBS uses both the channel number parameter and many other parameters that also affect the system load such as incoming call rate, call execution time... And to have the accuracy in assessing the cell load status, FDCBS also uses the cell traffic load parameter as the input variable of the fuzzy logic controller (FLC). FLC allows the integration of knowledge and experience of field experts in designing a set of fuzzy control rules. From there, FLC controls processes whose input-output relationship is described by a set of fuzzy control rules with linguistic variables instead of having to perform calculations on a model.
complex system model. A basic FLC consists of four main blocks: the fuzzifier, the fuzzy rule base, the inference engine, and the defuzzifier. If the output of the defuzzifier is not a control action to the system, it is a fuzzy logic decision-making system. The fuzzifier is responsible for converting the measured data into appropriate linguistic values. The fuzzy rule base stores the empirical knowledge of the process operator by the domain expert. The inference engine is the core of the FLC and it is capable of simulating human decision-making, by performing approximate reasoning to achieve a desired control strategy. The defuzzifier is used to make a decision or a non-fuzzy control action in the real world.
2.2.3.1. Fuzzy block
Fuzzification is the process of mapping a set of crisp values into component fuzzy sets. A membership function of a fuzzy set A is defined as u A which has the form:
u A : X 0.1
whereas the support of a fuzzy set A is a clear set of all x U
The fuzzy membership function u x (x)>0 and is defined as:
Supp ( A ) x U | u A ( x ) 0
(2.1)
so that the value
(2.2)
In other words: A fuzzy set A defined on a countable or finite space can be written as:
n
A a i/ x i
i 1
(2.3)
When X is an interval of real numbers, the fuzzy set A is written as:
A A ( x ) / x
x
(2.4)
The most basic operations of fuzzy set theory are complement, intersection and fuzzy union operations defined by Zadeh [56]:
- Complement: A ( x ) 1 u A ( x )
with
x X
(2.5)
- Intersection: A B ( x ) min u A( x ), u B( x )
with
x X
(2.6)
- Union: A B ( x ) m ax u A( x ), u B( x ) with
x X
(2.7)
The fuzzy membership functions of the input signal are the number of channels that allow AC to be determined.
within range
x a 0,a 6in equations (2.8) to (2.12) and of the input signal is
traffic load
y b 0,b 2
in equation (2.13) to b(2.15) with the membership function of the form
The triangle (other forms may be used) is defined as follows:
1 when x a 1
VC ( a x ) / ( a a ) when a x a
(2.8)
1 2 1 1 2
0
when x a 2
0 when x a 1 or x a 3
( a x ) / ( a a ) when a x a
C
1 2 1 1 2
(2.9)
( a
x ) / ( a a ) when a x a
1
0
3 3 2 2 3
when x a 2
when x a 2 or x a 4
( x a ) / ( a
a )
when a
x a
M
2 3 2 2 3
(2.10)
( a
x ) / ( a a ) when a x a
1
0
4 4 3 3 4
when x a 3
when x a 3 or x a 5
( x a ) / ( a
a )
when a
x a
H
3 4 3 3 4
(2.11)
( a
x ) / ( a a ) when a x a
1
5 5 4 4 5
when x a 4
0 when x a 5
VH ( x a ) / ( a a ) when a x a
(2.12)
4 5 4 4 5
1
when x a 5
0 when y b 1
L ( y b ) / ( b b ) when b y b
(2.13)
0 1 0 0 1
1
when y b 1