Currency-Based Audit Sampling Technique

Note: The selected sample must be within the overall format limit, not smaller or larger than the set format limit. If any element on the route exceeds the format limit, we ignore that element and select the next element.

For example: An auditor needs to select a sample of 4 elements from a population of 7000 elements. Using a Random Number Table, select through the following steps:

Step 1: Build a coding system by numbering from 0001 to 7000

Step 2: Build the relationship between the audit object and the Random Number Table. We see that the audit object consists of 4 digits, so we have a 4/5 relationship. The auditor decides to choose the first 4 digits of the random number table.

Step 3: Choose a route: the auditor decides to choose a route down the column, and the starting point is row (1), column (1) in the Random Number Table.

Step 4: Format the whole and choose the starting point.

Overall format: (1;7000)

The starting point is based on the factors given in B1,2,3 based on the random number table, we have the starting point: 1048.

We see that the starting point is within the overall format limits, so we choose the following elements:

Element 1: 1048 (selected because it is within the format limit (1;7000) Element 2: 2236 (selected)

Element 3: 2413 (selected)

Element 4: 4216 (selected)

So we choose 4 sample elements: - Payment voucher number 1048

- Payment voucher number 2236

- Payment voucher number 2413

- Payment voucher number 4216

Note: During the process of applying the random number table, there may be elements appearing more than once. In this case, we have two solutions as follows:

*)First, the auditor can apply non-replacement sampling (sampling without replacement) which means not accepting that element to appear in the sample again (or an element that does not appear a second time in the sample) and will ignore that element to select the next element. At this time, the number of sample elements remains the same or unchanged and the reliability of the sample increases.

*)Second, the auditor applies sampling with replacement (sampling with replacement) which means that an element can appear many times in the sample. At this time, that element is considered to be selected into the sample again (more than once) and thus the number of sample elements is reduced and the reliability of the selected sample is also reduced.

Both of the above solutions are acceptable in audit sampling with appropriate statistical formulas, however in most cases non-replacement sampling is more widely applied.

-Technique 2: Randomly select samples according to computer program

To ease the work and save time, auditing firms have hired or built computer programs that can provide a series of random numbers of a population as required by the audit.

Nowadays, these specialized programs are very diverse, but in general, they still respect the first two steps of random sampling according to the Random Number Table: building a coding system for the population's objects with numbers and establishing a relationship between the Random Number Table and the coded objects.

However, the biggest difference between random sampling and computer-based sampling is:

+ Random sampling: the samples selected are random numbers in the Random Number Table.

+ Computer-generated sampling: random numbers are not taken from the BSNN but are generated by the computer.

Now:

+The program input needs to have:

*) The smallest and largest numbers of the serial numbers of the audit object such as the total of invoices, documents, and goods catalogs.

*)The sample size to be selected and possibly a random number as a starting point, sampling program.

+ Output: List of random numbers in order of selection or in ascending order or both (selection sample).

For example, when using this computer program for random sampling, this auditor enters the following information into the computer:

*)Lower limit of the population: 0001

*)Overall upper limit: 7000

*)Number of elements to select: 100

*)Print order: small to large

- Technique 3: Random sampling by distance (systematic sampling)

Systematic sampling is a method of selecting elements in the population that are evenly spaced (sampling interval).

The principle of this method is that from a randomly chosen starting point, elements will be selected that are a fixed distance apart (equal distance).

This fixed interval is calculated by dividing the number of elements in the population by the number of elements in the sample.

Calculation formula:

Fixed distance

Number of elements in the population

=

Number of elements in the sample

Example 1 : There are 5000 payment vouchers in total, so a sample of 100 payment vouchers needs to be selected by systematic sampling.

We calculate the fixed distance = 5000/100 = 50 Suppose we choose 5 invoice samples from number 4242 to 4342 Fixed distance = (4342 - 4242) / 5 = 20

To select the next sample unit when we know the first sample unit, we choose as follows:

Let the sample interval be k.

The first sample unit is m 1 (or the starting point) The smallest sample unit x 1

Thus the first sample unit m 1 lies in the range: x 1  m 1  x 1 + k

According to the above example, the first sample unit or starting point lies in the range: 1  m 1  1 + 50 (with k = 50)

 1  m 1  51

Suppose we choose the starting point m 1 = 30

To determine the next sample unit, we calculate according to the following formula: m i = m i-1 + k

Also according to the above example we have:

Element 2: m 2 = m 1 + k = 30 + 50 = 80 Element 3: m 3 = m 2 + k = 80 + 50 = 130

......

Element 100: m 100 = m 99 + k= m 99 + 50 = m 1 + 99k = 30 + 99*50= 4980

Note: The first sample unit is selected randomly so that each initial population unit has an equal chance of being selected. However, after the first sample unit is selected, each subsequent unit does not have an equal chance of being selected for the sample.

In the above example we only choose one starting point, so what if we choose multiple starting points?

Now even if multiple starting points are selected, all of these starting points are selected between 1 and 51:

1  m i  51

With i running from 1 to n, where n is the number of starting points.

Suppose we choose two starting points: m 1 = 20 and m 1' = 42

Similarly, when we choose multiple starting points, we must pay attention to choosing the starting point m 1 from the smallest element x 1 to that element plus the sample distance k (x 1 + k)

But the question here is how many starting points do we choose for each starting point?

sample element

For example, if we choose n starting points, the number of elements to be selected at each starting point, denoted by N, is calculated according to the following formula:

N = Number of elements in the sample

Number of starting points (n)

When multiple starting points are selected, the number of sample elements corresponding to each starting point will change, resulting in the fixed distance also changing.

Now the fixed distance is redefined as follows:

Fixed distance

Number of elements in the population

=

Number of elements to select at each starting point N

According to the above example, we choose two starting points. Now the number of elements to choose at each starting point:

N = 100 / 2 = 50 elements

Fixed distance k = 5000 / 50 = 100

For starting point 1 : m 1 = 20 (element 1)

Element 2: m 2 = m 1 + k = 20 + 100 = 120 Element 3: m 3 = m 2 + k = 120 + 100 = 220

.......

Element 50: m 50 = m 49 + k = m 1 + 49k

For starting point 2 : m 1 = 42 (element 1)

Element 2: m 2 = m 1 + k = 42 + 100 = 142 Element 3: m 3 = m 2 + k = 142 + 100 = 242

.......

Element 50: m 50 = m 49 + k

Example 2: The auditor selects a sample of 200 payment vouchers from a total of 10,000 payment vouchers. The auditor needs to select 5 starting points:

Number of elements to be selected at each starting point = 200/5 = 40 elements At each starting point we select 40 elements

Fixed distance = 10,000 / 40 = 250

Thus, the 5 starting points lie between the 1st and 251st payment slips (x 1 = 1  m i  x 1 + k = 251 with i = 1.5).

Suppose the 5 starting points are: 25, 87, 115, 159, 221.

At starting point 1 : m 1 = 25

m 2 = 25+250 = 275

........

m 40 = m 39 + 250

At starting point 2 : m1 = 87

m 2 = 87 + 250 = 337

......

m 40 = m 39 + 250

At starting point 3: m 1 = 115

m 2 = 115 + 250 = 365

......

m 40 = m 39 + 250

At starting point 4: m 1 = 159

m 2 = 159 + 250 = 409

......

m 40 = m 39 + 250

At starting point 5: m 1 = 221

m 2 = 221 + 250 = 471

......

m 40 = m 39 + 250

Note: To overcome the situation where the accountant can know the starting point in advance and know the elements that the auditor will check, the auditor needs to choose multiple starting points.

The sample selected by this method must be representative and satisfy the requirements.

bridge:

+ The elements of the sample selected to be representative of the population must have

similar characteristics

+ The elements of the sample must be arranged in a systematic sequence.

+ Do not leave any element in the whole missing.

2/Select non-statistical samples

In contrast, in non-statistical sampling, the auditor cannot quantify sampling risk. Therefore, the auditor may determine a larger sample size than necessary or, conversely, accept a higher sampling risk than is acceptable.

At the same time, the auditor cannot infer the population results from the sample results using mathematical formulas. Instead, the auditor relies on his professional judgment to evaluate the population results from the sample test results.

Thus, non-statistical sampling cannot give results with higher reliability than statistical sampling. However, due to the advantages of low cost and simplicity, non-statistical sampling is still widely used in modern auditing, especially for tests on relatively small populations.

Non-statistical sampling techniques

In non-statistical sampling, these techniques are commonly applied to select samples including:

-Technique 1: Select samples by "block"

+Concept: It is a sampling method in which the auditor selects sample elements including continuous elements in the population as determined by the auditor (sample elements are selected according to each series of elements of each period, of a series of numbers or a series of letters).

For example: + Check all cash disbursement transactions arising in the first quarter of year N.

+Or select a sample of payment vouchers from number 217 to 985, select a sample from payment voucher number 525 to payment voucher number 765.

+Or select a sample of receivables for all customers whose names start with the letters H, L (representativeness is not guaranteed).

+ Select multiple blocks: select a sample including all payment vouchers in March and August to check payment transactions during the year.

Here we can have 3 ways of sampling according to block selection technique as follows:

+ Method 1 : Continuously take 30 receipts of January or February or March in the first quarter of year N for auditing. At this time, we choose a block of 30 elements.

The auditor decided to select 30 receipts from January because the auditor determined that in January there was a new accountant who was not familiar with the work, so errors were likely to occur in January. In February and March, because the accountant was familiar with the work, errors were less likely to occur or there were no errors. Therefore, we continuously selected 30 receipts from January to audit.

+ Method 2 : Continuously take 10 receipts of January, 10 receipts of February, 10 receipts of March to audit. In this way, we choose 3 blocks, each block has 10 elements.

+ Method 3 : Continuously take 5 receipts at the beginning of January and 5 receipts at the end of January; 5 receipts at the beginning of February and 5 receipts at the end of February; 5 receipts at the beginning of March and 5 receipts at the end of March. Using this method, we choose 6 blocks, each block has 5 elements.

Comment: The larger the number of selection blocks, the more representative the sample elements can be of the whole because they are evenly distributed in the whole .

In determining the specific sample the auditor needs to pay special attention to the circumstances.

like:

+ Personnel changes

+ Change accounting system and business policies

+ Seasonality of business...

-Technique 2: Select samples based on professional judgment

In many cases, especially when there are smaller sample sizes or a larger number of situations

In unusual situations, judgmental sampling provides a good chance of representative samples.

This method is applied when the auditor has a firm grasp of the characteristics of the audit subject's business situation.

In practice, auditors can use two sampling methods: random sampling and judgmental sampling.

+ Method 1: Selecting a "random" sample : This is done by the auditor looking through the population and selecting elements, without paying attention to their size, origin, or different characteristics, in an attempt to select an unbiased sample (also known as random selection).

However, this unbiased nature is difficult to ensure because depending on each auditor, some elements are given priority over others.

For example: Some auditors prefer to choose transactions in January, some auditors prefer transactions in February, etc.

+ Method 2: Selecting samples based on professional judgment : These are methods that use the auditor's professional judgment to select sample elements. Auditors often consider the following factors to increase the representativeness of the sample when selecting elements for testing:

*)If there are multiple types of transactions within the scope of the audit, each type of transaction is included in the selection sample.

*)If there are multiple people responsible for a business during the period, the form must include each person's business.

*)Items or transactions with larger amounts will be given more priority.

For example, we can use this method in the following cases:

**) Changes in financial and accounting policies and regulations

**) Change of accounting personnel

**) Newly arising transactions or transactions that have committed violations in previous audit periods are also sampled according to the auditor's assessment or judgment.

The method of selecting samples based on the auditor's judgment has the advantage of saving time and costs for auditing, and the implementation method is also simpler than random selection methods. However, the disadvantage of this method is that there is a high audit risk if the auditor does not grasp the characteristics of the audit client as well as the auditor's qualifications and experience are limited.

-Audit sampling techniques by currency unit.

Monetary sampling is a sampling method based on the monetary amount of elements in the population.

This sampling technique is commonly used for basic tests. Its most prominent feature is that the sample unit is converted from physical units (items, invoices, assets, etc.) to monetary units such as VND, USD, etc. In this case, the total is the cumulative amount of the audited object and the sample unit is each specific monetary unit.

Thus, when using the random sampling method by currency unit, an item, asset, or transaction with a large amount of money is more likely to be selected than a corresponding object with a smaller scale. This helps the auditor select elements with large amounts of money (elements with higher materiality than other elements of the same nature but with small amounts of money) while still ensuring the random nature of the selected sample. However, if the items tend to understate their value, the application of the sampling method by currency unit is no longer appropriate.

Monetary unit sampling also uses common random sampling techniques: random number tables, random number generators, or systematic sampling methods.

4.2.4.3. Audit sampling techniques by currency unit

1/Select statistical model

-Technique 1: Using Random Number Table

The auditor wants to select 5 Payables from a total of 10 Payables to audit. The route is in the column from top to bottom, starting point: Row 5, Column 2 does not accept duplicates and selects the number with the smaller gap.

STT

Supplier	Amount
1	INDOVINA Bank	3,946
2	P&G Bank	17,284

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• Qos Assurance Methods for Multimedia Communications zt2i3t4l5ee zt2a3gs zt2a3ge zc2o3n4t5e6n7ts low. The EF PHB requires a sufficiently large number of output ports to provide low delay, low loss, and low jitter. EF PHBs can be implemented if the output port's bandwidth is sufficiently large, combined with small buffer sizes and other network resources dedicated to EF packets, to allow the router's service rate for EF packets on an output port to exceed the arrival rate λ of packets at that port. This means that packets with PHB EF are considered with a pre-allocated amount of output bandwidth and a priority that ensures minimum loss, minimum delay and minimum jitter before being put into operation. PHB EF is suitable for channel simulation, leased line simulation, and real-time services such as voice, video without compromising on high loss, delay and jitter values. Figure 2.10 Example of EF installation Figure 2.10 shows an example of an EF PHB implementation. This is a simple priority queue scheduling technique. At the edges of the DS domain, EF packet traffic is prioritized according to the values ​​agreed upon by the SLA. The EF queue in the figure needs to output packets at a rate higher than the packet arrival rate λ. To provide an EF PHB over an end-to-end DS domain, bandwidth at the output ports of the core routers needs to be allocated in advance to ensure the requirement μ > λ. This can be done by a pre-configured provisioning process. In the figure, EF packets are placed in the priority queue (the upper queue). With such a length, the queue can operate with μ > λ. Since EF was primarily used for real-time services such as voice and video, and since real-time services use UDP instead of TCP, RED is generally not suitable for EF queues because applications using UDP will not respond to random packet drop and RED will strip unnecessary packets. 2.2.4.2 Assured Forwarding (AF) PHB PHB AF is defined by RFC 2597. The purpose of PHB AF is to deliver packets reliably and therefore delay and jitter are considered less important than packet loss. PHB AF is suitable for non-real-time services such as applications using TCP. PHB AF first defines four classes: AF1, AF2, AF3, AF4. For each of these AF classes, packets are then classified into three subclasses with three distinct priority levels. Table 2.8 shows the four AF classes and 12 AF subclasses and the DSCP values ​​for the 12 AF subclasses defined by RFC 2597. RFC 2597 also allows for more than three separate priority levels to be added for internal use. However, these separate priority levels will only have internal significance. PHB Class PHB Subclass Package type DSCP AF4 AF41 Short 100010 AF42 Medium 100100 AF43 High 100110 AF3 AF31 Short 011010 AF32 Medium 011100 AF33 High 011110 AF2 AF21 Short 010010 AF22 Medium 010100 AF23 High 010110 AF1 AF11 Short 001010 AF12 Medium 001100 AF13 High 001110 Table 2.8 AF DSCPs The AF PHB ensures that packets are forwarded with a high probability of delivery to the destination within the bounds of the rate agreed upon in an SLA. If AF traffic at an ingress port exceeds the pre-priority rate, which is considered non-compliant or “out of profile”, the excess packets will not be delivered to the destination with the same probability as the packets belonging to the defined traffic or “in profile” packets. When there is network congestion, the out of profile packets are dropped before the in profile packets are dropped. When service levels are defined using AF classes, different quantity and quality between AF classes can be realized by allocating different amounts of bandwidth and buffer space to the four AF classes. Unlike EF, most AF traffic is non-real-time traffic using TCP, and the RED queue management strategy is an AQM (Adaptive Queue Management) strategy suitable for use in AF PHBs. The four AF PHB layers can be implemented as four separate queues. The output port bandwidth is divided into four AF queues. For each AF queue, packets are marked with three “colors” corresponding to three separate priority levels. In addition to the 32 DSCP 1 groups defined in Table 2.8, 21 DSCPs have been standardized as follows: one for PHB EF, 12 for PHB AF, and 8 for CSCP. There are 11 DSCP 1 groups still available for other standards. 2.2.5.Example of Differentiated Services We will look at an example of the Differentiated Service model and mechanism of operation. The architecture of Differentiated Service consists of two basic sets of functions: Edge functions: include packet classification and traffic conditioning. At the inbound edge of the network, incoming packets are marked. In particular, the DS field in the packet header is set to a certain value. For example, in Figure 2.12, packets sent from H1 to H3 are marked at R1, while packets from H2 to H4 are marked at R2. The labels on the received packets identify the service class to which they belong. Different traffic classes receive different services in the core network. The RFC definition uses the term behavior aggregate rather than the term traffic class. After being marked, a packet can be forwarded immediately into the network, delayed for a period of time before being forwarded, or dropped. We will see that there are many factors that affect how a packet is marked, and whether it is forwarded immediately, delayed, or dropped. Figure 2.12 DiffServ Example Core functionality: When a DS-marked packet arrives at a Diffservcapable router, the packet is forwarded to the next router based on Per-hop behavior is associated with packet classes. Per-hop behavior affects router buffers and the bandwidth shared between competing classes. An important principle of the Differentiated Service architecture is that a router's per-hop behavior is based only on the packet's marking or the class to which it belongs. Therefore, if packets sent from H1 to H3 as shown in the figure receive the same marking as packets from H2 to H4, then the network routers treat the packets exactly the same, regardless of whether the packet originated from H1 or H2. For example, R3 does not distinguish between packets from h1 and H2 when forwarding packets to R4. Therefore, the Differentiated Service architecture avoids the need to maintain router state about separate source-destination pairs, which is important for network scalability. Chapter Conclusion Chapter 2 has presented and clarified two main models of deploying and installing quality of service in IP networks. While the traditional best-effort model has many disadvantages, later models such as IntServ and DiffServ have partly solved the problems that best-effort could not solve. IntServ follows the direction of ensuring quality of service for each separate flow, it is built similar to the circuit switching model with the use of the RSVP resource reservation protocol. IntSer is suitable for services that require fixed bandwidth that is not shared such as VoIP services, multicast TV services. However, IntSer has disadvantages such as using a lot of network resources, low scalability and lack of flexibility. DiffServ was born with the idea of ​​solving the disadvantages of the IntServ model. DiffServ follows the direction of ensuring quality based on the principle of hop-by-hop behavior based on the priority of marked packets. The policy for different types of traffic is decided by the administrator and can be changed according to reality, so it is very flexible. DiffServ makes better use of network resources, avoiding idle bandwidth and processing capacity on routers. In addition, the DifServ model can be deployed on many independent domains, so the ability to expand the network becomes easy. Chapter 3: METHODS TO ENSURE QoS FOR MULTIMEDIA COMMUNICATIONS In packet-switched networks, different packet flows often have to share the transmission medium all the way to the destination station. To ensure the fair and efficient allocation of bandwidth to flows, appropriate serving mechanisms are required at network nodes, especially at gateways or routers, where many different data flows often pass through. The scheduler is responsible for serving packets of the selected flow and deciding which packet will be served next. Here, a flow is understood as a set of packets belonging to the same priority class, or originating from the same source, or having the same source and destination addresses, etc. In normal state when there is no congestion, packets will be sent as soon as they are delivered. In case of congestion, if QoS assurance methods are not applied, prolonged congestion can cause packet drops, affecting service quality. In some cases, congestion is prolonged and widespread in the network, which can easily lead to the network being "frozen", or many packets being dropped, seriously affecting service quality. Therefore, in this chapter, in sections 3.2 and 3.3, we introduce some typical network traffic load monitoring techniques to predict and prevent congestion before it occurs through the measure of dropping (removing) packets early when there are signs of impending congestion. 3.1. DropTail method DropTail is a simple, traditional queue management method based on FIFO mechanism. All incoming packets are placed in the queue, when the queue is full, the later packets are dropped. Due to its simplicity and ease of implementation, DropTail has been used for many years on Internet router systems. However, this algorithm has the following disadvantages: − Cannot avoid the phenomenon of “Lock out”: Occurs when 1 or several traffic streams monopolize the queue, making packets of other connections unable to pass through the router. This phenomenon greatly affects reliable transmission protocols such as TCP. According to the anti-congestion algorithm, when locked out, the TCP connection stream will reduce the window size and reduce the packet transmission speed exponentially. − Can cause Global Synchronization: This is the result of a severe “Lock out” phenomenon. Some neighboring routers have their queues monopolized by a number of connections, causing a series of other TCP connections to be unable to pass through and simultaneously reducing the transmission speed. After those monopolized connections are temporarily suspended, Once the queue is cleared, it takes a considerable amount of time for TCP connections to return to their original speed. − Full Queue phenomenon: Data transmitted on the Internet often has an explosion, packets arriving at the router are often in clusters rather than in turn. Therefore, the operating mechanism of DropTail makes the queue easily full for a long period of time, leading to the average delay time of large packets. To avoid this phenomenon, with DropTail, the only way is to increase the router's buffer, this method is very expensive and ineffective. − No QoS guarantee: With the DropTail mechanism, there is no way to prioritize important packets to be transmitted through the router earlier when all are in the queue. Meanwhile, with multimedia communication, ensuring connection and stable speed is extremely important and the DropTail algorithm cannot satisfy. The problem of choosing the buffer size of the routers in the network is to “absorb” short bursts of traffic without causing too much queuing delay. This is necessary in bursty data transmission. The queue size determines the size of the packet bursts (traffic spikes) that we want to be able to transmit without being dropped at the routers. In IP-based application networks, packet dropping is an important mechanism for indirectly reporting congestion to end stations. A solution that prevents router queues from filling up while reducing the packet drop rate is called dynamic queue management. 3.2. Random elimination method – RED 3.2.1 Overview RED (Random Early Detection of congestion; Random Early Drop) is one of the first AQM algorithms proposed in 1993 by Sally Floyd and Van Jacobson, two scientists at the Lawrence Berkeley Laboratory of the University of California, USA. Due to its outstanding advantages compared to previous queue management algorithms, RED has been widely installed and deployed on the Internet. The most fundamental point of their work is that the most effective place to detect congestion and react to it is at the gateway or router. Source entities (senders) can also do this by estimating end-to-end delay, throughput variability, or the rate of packet retransmissions due to drop. However, the sender and receiver view of a particular connection cannot tell which gateways on the network are congested, and cannot distinguish between propagation delay and queuing delay. Only the gateway has a true view of the state of the queue, the link share of the connections passing through it at any given time, and the quality of service requirements of the traffic flows. 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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 div.maincontent .s1 { color: black; font-family:"Times New Roman", serif; font-style: normal; font-weight: normal; text-decoration: none; font-size: 15pt; } div.maincontent .s2 { color: black; font-family:"Times New Roman", serif; font-style: normal; font-weight: bold; text-decoration: none; font-size: 15pt; } div.maincontent .p { color: black; font-family:"Times New Roman", serif; font-style: normal; font-weight: normal; text-decoration: none; font-size: 14pt; margin:0pt; } div.maincontent p { color: black; font-family:"Times New Roman", serif; font-style: normal; font-weight: normal; text-decoration: none; font-size: 14pt; margin:0pt; } div.maincontent .s3 { color: black; font-family:"Times New Roman", serif; font-style: normal; font-weight: bold; text-decoration: none; font-size: 14pt; } div.maincontent .s4 { color: black; font-family:"Times New Roman", serif; font-style: normal; font-weight: normal; text-decoration: none; font-size: 14pt; } div.maincontent .s5 { color: black; font-family:"Times New Roman", serif; font-style: italic; font-weight: normal; text-decoration: none; font-size: 14pt; } div.maincontent .s6 { color: black; font-family:"Times New Roman", serif; font-style: italic; font-weight: bold; text-decoration: none; font-size: 14pt; } div.maincontent .s7 { color: black; font-family:Wingdings; font-style: normal; font-weight: normal; text-decoration: none; font-size: 14pt; } div.maincontent .s8 { color: black; font-family:Arial, sans-serif; font-style: italic; font-weight: bold; text-decoration: none; font-size: 15pt; } div.maincontent .s9 { color: black; font-family:"Times New Roman", serif; font-style: normal; font-weight: bold; text-decoration: none; font-size: 14pt; } div.maincontent .s10 { color: black; font-family:"Times New Roman", serif; font-style: normal; font-weight: normal; text-decoration: none; font-size: 9pt; vertical-align: 6pt; } div.maincontent .s11 { color: black; font-family:"Times New Roman", serif; font-style: normal; font-weight: normal; text-decoration: none; font-size: 13pt; } div.maincontent .s12 { color: black; font-family:"Times New Roman", serif; font-style: normal; font-weight: normal; text-decoration: none; font-size: 10pt; } div.maincontent .s13 { color: black; font-family:"Times New Roman", serif; font-style: normal; font-weight: normal; text-d
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