The impact of noise and Transmission Window on the efficiency of Go-Back-N

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ON THE EFFICIENCY OF GO-BACK-N

The impact of noise and Transmission Window on the efficiency of Go-Back-N

Ken Sund

Bachelor Thesis, 15 hp/credits

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Abstract

Reliable data transfer is one of the more important issues contained within computer networking. In order for data transfer to be reliable there need to exist protocols and mechanisms to combat the potential problems that could occur, such as corrupted data or loss of data. One of these protocols is Go-Back-N which is one the more fundamental protocols[8, Chapter 3]. The reason for loss of data or data corruption could for example be a consequence of a noisy channel. For this reason this study has focused on the impact noise will have on the overall transmission efficiency and if the transmission window (which is a component in Go-Back-N) could be used to mitigate the potential loss in efficiency. The results that were gathered using a Go-Back-N emulator showcased that the major loss in efficiency occured when noise (or packet error ratio) moved towards 4% packet corruption. There were also major differences between different transmission speeds. Higher transmission speeds were more prone towards major decreases in efficiency compared to lower transmission speeds, and the reason is because a higher transmission speed requires a larger transmission window (more allowed data at any given time) which causes a drop in efficiency. It could also be shown that, given the proposed theoretical models, that selecting the required transmission window relied heavily on the delay-bandwidth and that deviating from it caused drops in efficiency.

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Acknowledgements

I would like to give my thanks and utmost appreciation to my friends and parents for allowing me to ramble on about networking, reliable data transfer and other subjects they would much rather ignore. I would also extend my appreciation to my supervisor for giving me valuable advice during the entire process.

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1 Introduction

1.1 Background

Whenever data is transfered from one point to another there is a risk that something goes wrong. The potential risks are that, for example, data can either be lost or the data can be corrupted during transmission.

Reliability in data transfer has been an integral part of telecommunications for a long time.

Kahn and Cerf were two of the main engineers that designed the protocol Transmission Con- trol Protocol back in the mid- to late 1970’s which is now the most common protocols and a core component of TCP/IP[2][3]. These types of protocols are not only designed and implemented for conventional networking but also for specific networking/telecommunication environments. One of those environments is for example deep space or satellite communication [13][4]

In order to mitigate some of the problems associated with data transfer certain protocols have been implemented, namely Automatic-Repeat-ReQuest (ARQ) protocols[8, Chapter 3]. Each protocol is designed to handle lost or corrupted data in their own way.

On of these protocols is called Go-Back-N, which is a so called sliding window protocol, allowing more data to be transfered at any given time, called pipelining, before the sender requires a confirmation that data has successfully been processed by the receiver[8, Chapter 3]. Each protocol has its own advantages and disadvantages. Rehman[12] mentions for example that Go-Back-N has a higher throughput than the protocol Stop-and-Wait and a lower complexity than Selective Repeat, which is another sliding window protocol.

If the underlying channel becomes more unreliable it will increase the risk of packet loss and data corruption. Whenever the probability of data corruption increases it will also increase the delays and transmission time, which is the case for Go-Back-N[12][11].

1.2 Purpose

On this basis this work will test and analyze one of the fundamental protocols, Go-Back- N, in order to understand the impact packet loss has on transmission efficiency and how the transmission window mitigates the potential loss of transmission efficiency. This will done by gathering data using a Go-Back-N emulator that allows adjusting parameters such as Packet Loss Ratio and Transmission window size, aswell as certain delays. The data that has been gathered will be analysed in terms of overall transmission efficiency. The result will then be discussed with reference to the theoretical model for computing transmission efficiency (See section 3.2.1).

1.2.1 Research Questions

• How does packet error ratio impact throughput efficiency for Go-Back-N?

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• Can Transmission Window Size mitigate potential loss of throughput efficiency?

1.3 Hypothesis

Given previous research[6][12][11] (See section 2) the expected results are as follows. It was shown for different variations of Go-Back-N that larger IP-packet sizes resulted in decreased throughput[6] and that when transmission window increased the throughput efficiency decreased[12][11]. A similar result is thus expected in this work. When packet loss probability increases it is expected to see a steep decline in throughput and throughput efficiency and if window size increases it will also cause a decrease in efficiency.

1.4 Delimitations

In order to limit the scope of the study the main focus will be on high bandwidth transmissions, mainly a 100Mbps channel and a 1Gbps channel. 802.11ax is for example the current wireless standard and allows for example a theoretical limit of 10Gbps download speed, but usually that does not happen and depends on for example how much one pays a service provider[5]. Therefore this study will limit itself to using high bandwidth that is lower than the theoretical limit of the current wireless standard in order to simulate a more realistic setting.

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2 Related Work

There have been plenty of research into the performance of different ARQ-protocols, and in re- cent years the main focus has been on Hybrid ARQ-protocols (HARQ)[6][1][10][12][11]. Ko- tuliakova, Hajkovsky and Kotuliak[6] analyzed the performance of HARQ and ARQ schemes.

One of the reasons was to determine how much impact the length of IP blocks had on performance. One conclusion was that an increasing Signal-to-Noise ratio caused a higher throughput. For both ARQ and HARQ schemes the throughput was shown to decrease for longer blocks whenever errors were detected in received blocks, and the reason for decreased though- put was longer block retransmissions, which was also determined by Garcia[9, pp. 289–296]

when analyzing the impact bandwidth delay product, frame length and error rate had on the performance of Go-back-N.

Figure 1:Transmission efficiency in relation to error probability(left) and frame size(right)[9, pp. 289–296]

A. Garcia in Communication Networks[9, pp. 289–296] studies and analyses the transmission efficiency of the three fundamental ARQ-protocols. Figure 1 showcases transmission efficiency based on both error probability and frame size. The lefthand side of the figure, which focuses on efficiency based on error probability, calculates efficiency based on an example where frame size is 1024 bytes, the underlying transmission channel is a 5ms link, transmission speed is 1.5Mbps and the window size for all ARQ-protocols is 4. As is showcased in the figure Selective Repeat achievies a higher transmission efficiency compared to both Go-Back-N and Stop-And-Wait. As error-probability decreases the transmission efficiency of Go-Back-N and Selective Repeat starts to converge but a higher error-probability presents a clear distinction between GBN and SR in terms of transmission efficiency. Stop-And-Wait can’t achieve a higher transmission efficiency than circa 0.4 regardless of the error-probability.

In general it could be shown that delay bandwidth product, frame error rate and frame length were crucial in determining system performance[9, pp. 289–296].

Then there are studies on the performance of Go-Back-N and other ARQ-protocols and HARQ- protcols in block fading utilizing hidden markov chains[1][10]. Kamtorn and Aria[1] use hidden Markov Models and block transition probabilities which allows them to calculate the throughput of Go-Back-N. What they managed to show was that increasing the block fading length and channel block length, which meant that losses were more clustered, initially in-

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creased throughput but staturated quickly as block fading length surpassed the transmission window size.

Ateeq Ur Rehman has been involved in many studies regarding efficiency of different proposed cognitive HARQ-protocols designed for cognitive radios. There have been two specific studies regarding the efficiency of Cognitive Go-Back-N HARQ-protocols, where the protocol was reformed to match demands of CR systems [12][11]. The studies analyses a CGBN HARQ scheme by using Discrete-Time Markov Modeling[12][11]. The schemes proposed and analyzed in the studies is a mixture of Automatic Repeat Request and Forward Error Correction.

The reason behind using GBN HARQ instead of other schemes is because GBN has a higher throughput than Stop-And-Wait HARQ and lower complexity compared to Selective-Repeat HARQ. The results seemed to show that throughput was effected by the primary user’s channel quality and in order to achieve optimal throughput the number of packets in transmission in each time slot should be carefully selected according to the underlying channel quality. To be more specific they managed to show that for their CGBN-HARQ scheme if the packets in transit at any given timeslot increases then throughput will degrade if the underlying channel becomes more unreliable. In their other study[11] regarding a CBGN-scheme they managed to show that as the allowed packets in transmission increased the throughput also increased in an environment with no errors. But as error probability increased then troughput increased initially with smaller transmission windows but then started to decrease and that this shift happened sooner as error probability increased, meaning that the optimal transmission window decreased as error probability increased.

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3 Theoretical Background

3.1 Automatic Repeat ReQuest

The main purpose of Automatic Repeat ReQuest(ARQ-Schemes and Reliable Data Transfer (RDT) is to provide a reliable service for data transfer. As is depicted in Figure 2 the perceived service from a user-perspective is a reliable channel where data flows back and forth from two end-points without data loss or data corruption. The reality is slightly more com- plicated. There is no such thing as a completely reliable channel that guarantees that no data loss or data corruption occurs whatsoever. Instead certain mechanisms and protocols are implemented on top of this unreliable channel to provide this service. TCP is for example a reliable data transfer protocol implemented on top of the unreliable end-to-end network layer[8, Chapter 3].

Figure 2:Depiction of the perceived service in contrast to the actual implementation[7, Chapter 3]

The traditional application of ARQ-protocols was to ensure reliability in a single noisy channel, which means to ensure high reliability in a single transmission hop. But channels has become more reliable and thus less noisy, meaning that ARQ-protocols are more often than not implemented at the end-points ensuring reliability across multiple hops in a network and multiple channels[9, pp. 272–273].

In order to combat data corruption, ie bit errors, there are three fundamental capabilities that an ARQ-protocol requires[8, Chapter 3].

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3.1.1 Error Detection

Error detection is a mechanism that allows the receiver to detect when bit errors occur[8, Chapter 3]. Some techniques are mentioned by James Kurose and Keith Ross[8, pp. 472–479].

These are Parity Checks, Checksumming methods and Cyclic Redundancy Checks (CRC).

In order to perform a Parity Check the sender adds an extra bit, called parity bit, to a bit- sequence. The value of the parity bit depends on the amount of 1’s in the bit sequence. The total amount of 1’s will be even including the parity bit. The receiver can now check whether or not a bit has been flipped by counting the 1’s. How this is done depends on whether a 2D parity check is done or not. The simplest version is to just count the 1’s which will indicate if a bit error has occured. A 2D parity check allows the receiver to identify which bit has been flipped. In Figure 3 this technique is depicted. This ability to detect and correct bit errors is generally called Foward Error Correction (FEC)[8, pp. 472–479].

Figure 3:On the left is an even parity check. On the right is a two-dimensional parity check[7, Chapter 3]

Checksumming means that bits of data are, for example, treated as a sequence of integers. A simple way of doing checksumming is to sum the sequence of integers and use that sum as error-detection bits[8, pp. 472–479].

The error-detecting method that is widely used today is based on CRC codes, also known as polynomial codes. Before a d-bit piece of data is sent the sender and receiver needs to agree on a r + 1 pattern known as a Generator (G). For any piece of data (D) the sender chooses addtional bits (r) and appends them to D such that the bit pattern d + r is evenly divisible by the generator G using modulo-2 arithmetic. When the data arrives the receiver divides d + r with G. If there is a remainder the receiver can conclude that an error occured[8, pp. 472–479].

3.1.2 Receiver Feedback and Retransmission

The way that the receiver provides feedback to the sender is by for example acknowledgments. These can either be positive (ACK) acknowledgments suggesting that the data was successfully received without errors or they can be negative acknowledgments (NAK) indi- cating that the sent data was received erroneously. In case of corrupted or lost data the sender will need to able to restransmit that specific data.

3.2 Go-Back-N

Go-Back-N is a specific type of an ARQ-scheme. The purpose of Go-Back-N, like all ARQ- schemes, is to provide a service that allows for reliable communication between a sender and receiver.

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The name Go-Back-N refers to the behaviour of the protocol when an error occurs[9, p. 279].

The GBN protocol allows the sender to transmit several packets before receiving an acknowledgement (ACK). One constraint is that there can only be a maximun number of packets N, also called Window Size, in the pipeline. In order to understand how the protocol works certain concepts will be explained[8, Chapter 3].

The Base is the oldest packet that has not yet been acknowledged. The Nextseqsum refers to the sequence number of the packet that will be sent next. The base, nextseqsum, and window size can thus be used to create four different intervals. [0, base-1] signifies the packets that has been transmitted and acknowledged. [base, nextseqsum-1] have also been sent but not yet acknowledged. [nextseqsum, base+N-1] are packets that are allowed to be sent, meaning they are within the window size. The last interval are the packets that can only be sent in due order after data within the transmission window has been acknowledged [8, Chapter 3]. This is illustrated clearly in Figure 4.

Figure 4:The view from sender perspective[7, Chapter 3]

There are a couple of essental events that a sender needs to respond to. Whenever the sender wants to transmit a new packet, they first check whether or not the window is full which essentially means that there are currently N unacklowedged packets. If there is room for a new packet then the packet is created and sent. There is a chance that the window is full and in those cases the sender will return the data to the upper layer and the packet will be transmitted later or they could be buffered[7, Chapter 3].

Then there is the event of an acknowledgedment. When the sender receives an acknowledgment for a packet with sequence number n then it is called a cumulative acknowledgment, which means that the receiver has correctly received all sequence numbers prior to that sequence number n. When the receiver correctly receives packet n and that packet is in order, meaning that the last packet delivered to the upper layer is sequence number n-1, then the data is delivered to the receivers upper layer[7, Chapter 3].

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Figure 5:A visual representation of Go-Back-N in action[7, Chapter 3]

It was mentioned before that the name Go-Back-N elludes to the behaviour in case of an error.

A timer is used for transmitted packets. Whenever a packet is lost or severely delayed during transmission it will cause a Retransmission timeout (See Figure 5) which in turn will cause that packet and all subsequent sent packets to be retransmitted by the sender, meaning we are ’going back’. This behaviour is visualised in Figure 5 where the second packet is lost and the receiver responds with an acknowledgement of the last acknowledged packet. When the timer runs out for the second packet, which is the current base, then the second packet and all the other packets are retransmitted. On the other hand if an acknowledgment for packet x is received by the sender and there are other unacknowledged packets in transmission then the base is updated to x+1 which also means that the window slides forward, the timer restarts and the process continues. Otherwise if no other packets are unacknowledged, meaning no packets are currently being transmitted, then the timer stops[7, Chapter 3].

3.2.1 Transmission Efficiency

Apart from the work by Garcia and Widjaja [9, pp. 289–296](See Related Work) showing the relation between error-probability, frame size and transmission efficiency they also include the theory behind calculating efficiency for the fundamental ARQ-protocols.

Figure 6:How to calculate effective transmission time (Top) and transmission efficiency (Bot- tom) for Go-Bsck-N[9, pp. 289–296]

How to calculate both transmission efficiency and effective transmission time for Go-Back-N is presented in Figure 6. There are a couple of crucial components that needs to be explained in order to understand these equations. The component 𝑛^𝑓 − 𝑛₀represents the information data inside a frame, meaning that the header- and CRC bits are excluded (𝑛 ). 𝐸[𝑡 is the

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average total time to deliver a frame, which means that (𝑛^𝑓 − 𝑛₀)/𝐸 [𝑡𝑡 𝑜𝑡 𝑎𝑙] is the effective transmission time. The transmission efficiency is thus the effective transmission of a frame divided by the maximum bitrate (R).

For Go-Back-N, which is a sliding window protocol, the transmission window is a crucial component in transmission efficiency, which is represented in these equations as 𝑊^𝑠. 𝑃^𝑓 is the frame/packet error probability and is calculated by 1 − (1 − 𝑝)^𝑛^𝑓 where 𝑛^𝑓 is the size of a frame and p is bit error rate.[9, pp. 289–296].

Certain parameters can be expressed in other ways. Window size (𝑊^𝑠) can be extended and expressed as a relation between the delay-bandwidth product (See section 3.3.3) and the frame/packet size:

𝑡_{𝑝𝑟 𝑜 𝑝}× 𝑅

𝑛 𝑓 +1 (3.1)

The expression for efficiency can thus be expressed as:

(1 − 𝑃^𝑓) 1 −𝑛 𝑓^𝑛⁰

1 + (^𝑡^{𝑝𝑟 𝑜 𝑝}𝑛 𝑓+^×𝑅1 −1)𝑃^𝑓 (3.2) This suggests that the model only considers transmissions in one direction and only sending roughly half of the channel-capacity, which can be demonstrated by examening the simplified delay-bandwidth product (𝑡^{𝑝𝑟 𝑜 𝑝} × 𝑅) and comparing it to the actual definition of the delay- bandwidth product (see Section 3.3.3). This means that it ought to be possible to extend the model so it sends the full capacity of data. This should be accomplished by doubling the delay- bandwidth which then represents the required window size for the given propagation delay and transmission speed.

2(𝑡^{𝑝𝑟 𝑜 𝑝}× 𝑅)

𝑛 𝑓 +1 (3.3)

This should now mean that the sender is sending as much data as the channel allows at any given time, implying a uni-directional transmission.

3.3 Delays and Delay-bandwidth product 3.3.1 Transmission Delay

If the length of the packet is denoted by L and the transmission rate on a link between two points is denoted by R then the transmission delay is denoted by L/R. What this essentially means is the time, usually microseconds or milliseconds, it takes to transmit all the packet’s bits into the link[8, Chapter 1].

3.3.2 Propagation Delay

When a bit is pushed into a link it needs to propagate to the next destination. The time for the bit to travel from point A to point B is what is called propagation delay and can be calculated by dividing the distance between A and B (d) by the propagation speed (s), ie.

d/s[8, Chapter 1].

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The explanation might seem similar to that of transmission delay but the difference is the delay for bits to get onto the link (transmission delay) and for a bit to travel to the next destination (propagation delay).

3.3.3 Delay-bandwidth product

The delay-bandwidth product is relevant when determining the maximum limit of data that can be transmitted at any given time. Delay-bandwidth product is calculated by multiplying the bit rate and the delay[9, p. 277] which is 2(𝑡^{𝑝𝑟 𝑜 𝑝} + 𝑡𝑝𝑟 𝑜𝑐)[9, pp. 289–296]. 𝑡^{𝑝𝑟 𝑜 𝑝} signifies propagation delay which was described earlier and 𝑡^{𝑝𝑟 𝑜𝑐}represents the processing delay, which includes examining packet headers, directing the packet and checking for bit-level errors[8, Chapter 1]. The reason the sum is doubled is because the entire process is bidirectional, meaning that data can be transfered in both directions, so the round-trip time is in consider- ation.

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4 Method

4.1 Choice of Method

In order to test the different parameters involving Go-Back-N a testing environment is needed that allows for tuning and testing the different parameters. Setting up a genuine networking environment could work but the scope would be too large for this project. Therefore another solution is needed for this specific project.

A viable option is to utilize an emulator that allows tuning certain parameters such as window size, retransmission time, and certain certain delaying parameters. The specific emulator used in this project is derived from an assignment which can be found in Computer Networking by James Kurose and Keith Ross[8, p. 329]. The reason for using an emulator is because it allows for greater control of the underlying environment such as controling the noise-level of the channel.

4.1.1 Go-Back-N Emulator

The specific implementation of this assignment is an event-based design written in C. The implementation is a basic Go-Back-N protocol that does not include NAK’s thus handling corruption and losses in the same way, meaning timeouts and then retranmissions.

The emulator allows the user to change certain parameters. The parameters that can be changed are:

• Sendlimit: This is the same as Transmission Window Size, meaning the amount of packets that sent at a given time.

• Pktcount: The amount of packets transmitted before the emulator stops.

• Lossp: The propability that a packet is lost during transmission.

• Corrp: The probability that a transmitted package gets corrupted, ie bit-error

• Datarate: The arrival rate of messages from Application Layer.

• Propdelay: Propagation Delay in this emulator is the time of packet transmissions between two points. To see the actual definition see Section 3.3.2

• Transdelay: Time units between transmission of two packets is how Transmission Delay is represented in the emulator but in order to see the real definition see Section 3.3.1.

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4.2 Data Collection

The data will be collected through a series of experiments using the emulator. In order to simulate packet corruption the parameter corrp will be used. The other parameters can also be utilized to simulate different types of transmission links. For example since propagation delay is the ratio between link length and the propagation speed of the specific link it is possible to simulate a certain link type.

4.2.1 Experiments Experiment 1

For this experiments the case that will be considered is a 100Mbps channel where distance between sender and receiver is 5km and each packet has the size of 1024bytes (8192bits). The Transmission delay can thus be calculated as the length of the packet, which is assumed to be 1024byte (8192bit) divided by the transmission speed.

𝑇_𝑑 = 𝐿

𝑅 (4.1)

If we assume that each packet is 1024 bytes and the transmission speed is 100Mbs and these values are converted to bits (8192 bits and 1500000b/s) then the transmission delay (See section 3.3.1 Transmission Delay) would be:

8192

100000000 ≈0.000082𝑠 (4.2)

Since transmission speed is 100Mbps this reflects datarate aswell. The parameter is defined in the emulator as the arrival rate between messages from the upper layer (Application layer).

If each packet is 1024Byte or 8192Bit then divide packet size with transmission speed (same as transmission delay) and approximately 0.000082s becomes the appropiate value. Given that the distance is initially assumed to be 5km it will mean that propagation delay will be aproximately 0.0005 seconds.

By looking at the theoretical model an inital required transmission window size should be:

2(0.0005 × 100000000)

8192 + 1 ≈12 (4.3)

Now when all the parameters are set to simulate a 100Mbps channel and a required baseline is set for the tranmission window it is time to specify the experiments. Testing the tranmission window will be done by two similar experiments. For each bit error rate (𝑝) (See section 3.2.1) the associated packet error ratio, 1 − (1 − 𝑝)^{𝑛 𝑓}, will be calculated.

The first part of the experiment will test the baseline and several trasnmission windows larger than the baseline. The efficiency for each tranmission window size will be calculated and mapped to each packet error ratio.

The second part of the experiment is similar. Instead of increasing the transmission window size the transmission window size will instead be decreased. The efficiency for each tranmission window will be calculated and similarly to the first experiment mapped to each packet error ratio.

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Each stage, meaning transmission window compared to packet error ratio, will be tested approximately 100 times.

Experiment 2

The second experiment will concern the prospect of increasing the trasnmission speed and focusing on a higher bandwidth. The first experiment focused on a 100Mbps channel. Instead the focus in this experiment will be on a 1Gbps channel where propagation delay is the same as the first experiment.

A 1Gbps transmission speed will thus mean that transmission delay is decreased. By looking at previous examples and the theoretical definition (See section 3.3.1) the new tranmission delay (and datarate) for this particular experiment will be:

8192

1000000000 ≈0.0000082𝑠 (4.4)

Where the packet size is 8192bit and tranmission speed is 1000000000bps. The rest of the experiment will be conducted in the same way as the first one. The bit error rate will be gradually increased and for each stage of the bit error rate several tranmission windows will be tested in terms of tranmission efficiency.

The required initial window size give these parameters ought to be, according to the model:

2(0.0005 × 1000000000)

8192 + 1 ≈122 (4.5)

4.3 Data Analysis

Then data will be gathered through simulations utilizing the emulator specifed above by setting the parameters to appropiate values. It has been mentioned before that transmission efficiency will be used to determine the impact packet error ratio has on Go-Back-N. In order to calculate the throughput efficiency from the data gathered by the emulator the throughput will be computed. This is calculated by dividing total amount of data (𝑑^{𝑡 𝑜𝑡 𝑎𝑙}) transfered with the total transmission time (𝑡^{𝑡 𝑜𝑡 𝑎𝑙}). This results in the effective transmission rate (𝑅^{𝑒 𝑓 𝑓}) (throughput). Transmission efficiency (𝜂) is then essentially the ratio between the utilized bandwidth and the maximum bandwidth.

𝑅_{𝑒 𝑓 𝑓} =𝑑_{𝑡 𝑜𝑡 𝑎𝑙}

𝑡_{𝑡 𝑜𝑡 𝑎𝑙} (4.6)

The equation above specifies the efficient transmission (throughput) time which essentially means how much data can be transfered at any given moment given the environment, for example error probability ratio.

𝜂= 𝑅_{𝑒 𝑓 𝑓}

𝑅_{𝑡 𝑜𝑡 𝑎𝑙} (4.7)

This equation is tranmission (throughput) efficiency and as stated above it is the ratio between utilized bandwidth and the maximum bandwidth possible.

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These will be used to analyse the results gathered by experiments utilizing the emulator. These will then be discussed using the theoretical models (See Section 3.2.1 Transmission Efficiency) in order to gain better understanding of the results and also determine the accuracy of the emulator. In order to simulate the theoretical models to a higher degree certain factors in time will be excluded. Since the focus is on transmission efficiency factors like timeouts will be excluded from the calculations, and thus the main focus is on transmission.

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5 Results

5.1 Experiment 1: Testing transmission window and bit error rate for 100Mbps channel

The first experiment is testing the effect transmission window and bit error rate has on efficiency when the bitrate is 100Mbps. Figures 7, 8 & 9 and tables 1 & 2 showcases the results from this experiment when increasing and decreasing the transmission window from a baseline which is presented in Figure 7. The first stage was to test the baseline by itself and then continue the experiment by deviating from the baseline and observe the behaviour. Table 1 and Figure 8 represent the results from increasing the transmission window. Table 2 and Figure 9 represent the behaviour of decreasing the transmission window.

Figure 7:Efficiency of a simulated Go-Back-N where sendlimit (Transmission window) = 12, datarate = 0.082ms, propdelay = 0.5ms & transdelay = 0.082ms. This means a 100Mbps channel with propagation delay of 0.5ms. Y-Axis is transmission efficiency and X-axis is bit error rate. The percentages in the x-axis is the packet error ratio related to the bit error rate.

Table 1 Efficiency derived when increasing transmission window (𝑊^𝑡) in the presence of increasing bit error rate. Percentages are representations of packet error ratio given the bit error rate. Propagation delay = 0.5ms, Transmission delay = 0.082ms, Datarate = 100MBps

𝑊_𝑡 0 E-06 (.815%) 5E-06 (4%) E-05 (7.86%) 5E-05 (33%) E-04 (56%)

12 0,994 0,834 0,497 0,327 0,079 0,033

14 0,994 0,822 0,477 0,309 0,073 0,031

16 0,994 0,811 0,459 0,295 0,068 0,028

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Figure 8:A visual comparison the effects of increasing the transmission window (𝑊^𝑡) in terms of efficiency and bit error rate. The baseline is 𝑤^𝑡 = 12 which was decided using the theoretical model. X-axis represents bit error rate and percentages is the packet error ratio related to the bit error rate. Propagation delay = 0.5ms, Tranmis- sion delay 0.082ms, datarate = 100MBps

Table 2Efficiency derived when decreasing transmission window (𝑊^𝑡) in the presence of increasing bit error rate. Percentages are representations of packet error ratio given the bit error rate. Propagation delay = 0.5ms, Transmission delay = 0.082ms, Datarate = 100MBps

𝑊_𝑡 0 E-06 (.815%) 5E-06 (4%) E-05 (7.86%) 5E-05 (33%) E-04 (56%)

12 0,994 0,834 0,497 0,3268 0,079 0,033

10 0,900 0,771 0,484 0,3266 0,083 0,036

8 0,737 0,651 0,442 0,312 0,086 0.038

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Figure 9:A visual comparison the effects of decreasing the transmission window (𝑊^𝑡) in terms of efficiency and bit error rate. The baseline is 𝑤^𝑡 = 12 which was decided using the theoretical model. X-axis represents bit error rate and percentages is the packet error ratio related to the bit error rate. Propagation delay = 0.5ms, Tranmis- sion delay 0.082ms, datarate = 100MBps

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5.2 Experiment 2: Testing transmission window and bit error rate for 1Gbps channel

In the second experiment, which was similar to the first one, the bitrate was increased to 1Gbps. The results are presented in figures 10 & 11 and tables 3 & 4. Instead of using Figure 7 as baseline the transmission window of size 122 is used as the baseline, which was calculated earlier (See section 4.2.1). After calculating the baseline the behaviour of deviating from it was observed by later stages of this particular experiment. Figure 10 & Table 3 showcases the results when increasing the transmission window and Figure 11 & Table 4 is the result when decreasing the transmission window. Table 5 is the theoretical result from utilizing the theoretical equations (See section 3.2.1).

Figure 10:Efficiency derived when increasing transmission window (𝑊^𝑡), from the baseline of 122, in the presence of increasing bit error rate. Percentages are representations of packet error ratio given the bit error rate. Propagation delay = 0.5ms, Transmission delay = 0.0082ms, Datarate = 1Gbps

Table 3Efficiency derived when increasing transmission window (𝑊^𝑡) in the presence of increasing bit error rate. Percentages are representations of packet error ratio given the bit error rate. Propagation delay = 0.5ms, Transmission delay = 0.0082ms, Datarate = 1Gbps

𝑊_𝑡 0 E-06 (.815%) 5E-06 (4%)

122 0,9824 0,3342 0,0895

128 0,9826 0,3253 0,0882

134 0,9825 0,3199 0,0859

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Figure 11:A visual comparison the effects of decreasing the transmission window (𝑊^𝑡) in terms of efficiency and bit error rate. The baseline is 𝑤^𝑡= 122 which was decided using the theoretical model. X-axis represents bit error rate and percentages is the packet error ratio related to the bit error rate. Propagation delay = 0.5ms, Tranmission delay 0.0082ms, datarate = 1Gbps

Table 4Efficiency derived when decreasing transmission window (𝑊^𝑡) in the presence of increasing bit error rate. Percentages are representations of packet error ratio given the bit error rate. Propagation delay = 0.5ms, Transmission delay = 0.0082ms, Datarate = 1Gbps

𝑊_𝑡 0 E-06 (.815%) 5E-06 (4%)

122 0,9824 0,3342 0,0895

116 0,9472 0,3274 0.0892

110 0,8993 0,3296 0,0895

Table 5 Transmission efficiency derived purely from the theoretical model. Transmission window size (𝑊^𝑡) = 12, overhead (n0) = 0 given that the emulator does not provide that func- tionality.

𝑊_𝑡 0 E-06 (.815%) 5E-06 (4%) E-05 (7.86%) 5E-05 (33%) E-04 (56%)

12 0.9921 0.9031 0.661 0.4902 0.14357 0.0609

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6 Analysis

In Figure 7 the proposed baseline is presented. The derived effiency is based upon that the transmission window is the required size for the propagation delay and transmission speed.

A slight variation of bit error rate (or packet error ratio) decreases the efficiency rapidly, as is showcased by looking at bit error rate 5E-05 which correlates to packet error ratio of 4%.

In the small intervall between 0.815% and 4% the efficiency decreases from close to 100% to approximately 50%. These tests showcase that aproximately 4% packet error ratio seems to be the limit before the protocol becomes inefficient in terms of tranmission efficiency.

6.1 Increasing the transmission window

This section is based on the first experiment, meaning that the efficiency of transmission windows larger than the baseline was tested. The results derived from this experiment is showcased in Figure 8 and Table 1.

In Figure 8 it can be showcased that increasing the transmission window does not change the trend of the transmission efficiency. Each window follows a similar pattern, where the major decrease in efficiency occurs when bit error rate is 0 > 𝑝 > 5𝐸 − 06 meaning packet error ratio is moving towards approximately 4%.

The differences are that increasing the transmission window size increases the difference in tranmission efficiency between smaller transmission windows and larger transmission windows, which can for example be observed at bit error rate 5𝐸 − 06 in Figure 8. This pattern is consistent throughout the different bit error rates as is demonstrated in Table 1. At the endpoints, meaning 𝑝 = 0 or 𝑝 = 𝐸 − 04, the difference in transmission efficiency is close to zero, where 𝑝 = 0 there is virtually no difference at all.

6.2 Decreasing the transmission window

Decreasing the window size gives different results from those presented in Figure 8 and Table 1. The results gathered from decreasing the window size is visualised and presented in Fig- ure 8 and Table 2. The difference in decreasing the window size as opposed to increasing it showcases a pattern where the largest difference in efficiency occurs when bit error rate (𝑝) is moving towards zero.

As bit error rate increases the difference in transmission efficiency decreases. The pattern that occurs is that smaller window sizes eventually converges with the baseline in terms of transmission efficiency, and it occurs at different bit error rates. As transmission window decreases the difference in transmission efficiency compared to the baseline persists for larger bit error rates. By looking at Figure 9 it is showcased that𝑊^𝑡 =10 converges with the baseline (𝑊^𝑡 = 12) when 𝑝 ≈ 5𝐸 − 06 and 𝑊^𝑡 = 8 is the same as 𝑊^𝑡 = 12 in terms of transmission efficiency when 𝑝 ≈ 𝐸 −05. This pattern does not occur when transmission speed is increases,

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see Figure 11.

6.3 Increasing transmission speed

The results from the second experiment, as outlined in Section 4.2.1, are visualised and showcased in figues 10 & 11 and tables 3 & 4. The trend is similar to the results showcased in the first experiments. Increasing the transmission window and thus deviating from the baseline causes a difference in efficiency, see Table 3. Decreasing the transmission window on the other hand creates most difference in efficiency for lower bit error rates and as bit error rate increases the efficiency for the different transmission windows start to converge, see Figure 11 and Table 4.

The major difference between the results of the experiments is that the efficiency for a higher transmission speed (1Gbps) decreases quicker in terms of bit error rate compared to a lower transmission speed (See Figure 8). This can be visualised clearly by comparing the efficiency for bit error rate E-06 in figures 8 & 10 where in the first figure the efficiency is slightly over 80% and in the second figure the efficiency is approximately 33-34%. In Table 3 it also shows that increasing the transmission window causes a drop in efficiency, for example when bit error rate is E-06. The differences are less noticable compared to the tests using lower transmission speed.

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7 Discussion

7.1 Interpretation of Results

7.1.1 The impact of bit error rate on transmission efficiency

The impact of bit error rate seems dependent on the size of the transmission window which can also be validated by studying the theoretical models aswell as looking at figures 8 & 10 where the efficiency decreases more rapidly for higher transmission windows.

One interesting thing to note is the difference in efficiency between the different transmission speeds. We already pointed out that bit error rate E-06 resulted in a efficiency slightly over 80% for 100Mbps channel and 33% for a 1Gbps channel. Why is there such a big difference between efficiency given the transmission speed? Even according to the model this is supposed to happen. By increasing the transmission speed the required window size increases which will also decrease the overall efficiency even though we are utilizing the seemingly optimal window size for those conditions. The other parameter that effects the window size is propagation delay. If propagation delay is constant and transmission speed increases then the proportion between them increases thus requiring a larger transmission window, meaning that the propagation delay in this sense causes a bottleneck. So in order to minimize the required transmission window as transmission speed increases the propagation delay needs to decrease. But one thing that ought to be mentioned is that even if the transmission efficiency of a 1Gbps channel with bit error rate E-06 was roughly 33% that is still a higher throughput compared to a 100Mbps channel where ≈ 80% of the bandwidth was utilized. The throughput is then 0.33GBps compared to 0.08GBps.

7.1.2 The importance of transmission window size on transmission efficiency From the results in either of the experiments it can be surmissed that increasing the transmission window size will cause a decrease in transmission efficiency. Increasing the transmission window is something, at least from the theoretical models (See section 3.2.1), that should have been somewhat predictable. By looking at the models we can say that increasing window size decreases the efficiency since the denomiator 1+(𝑊^𝑠−1)𝑃^𝑓 becomes larger. So the results gathered from the experiments seem to validate those expectations. It should also be mentioned that by increasing the window then we are deviating from the required window size and since propagation delay and transmission speed are constants in the experiments then we are not utilizing the required window. By looking at the extendended model for the transmission efficiency we can see that the window size is dependent on, for example, propagation delay and transmission speed so in order to accommodate a higher transmission window those values would have to be adjusted. In this case they were not so we were deviating from the required window size. A small deviation from the required window size seems to have a larger impact for lower transmission speeds, which is logical given that the proportion between two transmission window sizes is larger when dealing with smaller transmission windows in general, which is dependent on a lower transmission speed.

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The results gathered by deviating from the required window by decreasing the transmission window seems to showcase opposite results from what should be expected by studying the theoretical model. Decreasing the window ought to increase the efficiency. Why are we then given opposite results? Once again it should be mentioned that the theoretical model expects that propagation delay and/or transmission speed is adjusted to accommodate the specific transmission window. So when we are decreasing the window but not adjusting the propagation delay or transmission speed we are deviating from the required window and utilizing a window size which is not large enough for the transmission speed. This means that the transmission window gets filled up too quickly and restricting the overall flow through the channel causing decreased efficiency.

In both cases (100Mbps & 1Gbps) we can see similar results which seems to validate the theoretical model, at least in terms of required transmission window size. In both cases, when decreasing the window size and deviating from the required window the efficiency drops but when we increase and there is no noise the efficiency is optimal but as noise increase it causes a decrease in efficiency.

7.1.3 Comparisons between theory and simulations

By looking at Table 1 where 𝑊^𝑡 = 12 and Table 5 we can see a discrepancy between the expected theoretical results and the results from the emulator. There is quite a difference in efficiency between them. It was not expected that these two were going to be matching ex- actly. So why is there a difference between them? Mostly it has to do with the limitation of the proposed theoretical model. There are a couple of parameters that are included in the emulator but not in the theoretical model, such as transmission delay, which will add to the overall time and thus decrease the efficiency. Another aspect which effects the efficiency from the emulator is the added time of receiving an acknowledgment which will also add time and decrease the efficiency. These discrepencies were also present when increasing the transmission speed but in both cases the efficiency from the emulator was lower than the theoretical efficiency and follows a similar trend so even if there was a discrepancy in efficiency the results still managed to follow general expectations.

7.2 Limitations 7.2.1 Choice of method

Given that we are using an emulator in order to conduct experiments we are limited to the implementation of that specific emulator. Certain delays such as processing delay which was mentioned earlier is excluded, meaning that the results could be slightly missaligned. The emulator utilized transmission delay which was not included in the theoretical model, thus causing a lower efficiency than expected from the theory. This would not impact the overall conclusions but could still impact the results. For example where efficiency is around 33%

for a 1Gbps channel it should in theory be higher. So it was not possible to completely align the results from the emulator with the theoretical model, which was not something that was expected to begin with.

As mentioned before the theoretical models do not account for everyting, which is under- standable given the complexity it would entail. Thus we can conclude that the models are limited as well and do not reflect a realistic setting in which Go Back-N would operate within.

In section 3.2.1 the theoretical models for transmission efficiency were presented. At the end

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it was surmissed that 2(𝑡^{𝑝𝑟 𝑜 𝑝}× 𝑅) ought to be used, which is not the case for all implemen- tations of Go-back-N. The reason for using this specific model was because the emulator was uni-directional, meaning only sending data in one direction, and therefore the sender was able to fill up the channel all by itself, ie. utilize the entire delay-bandwidth.

7.3 Conclusion and Recommendations

Whenever a deviation from the required transmission window size occurs there will be a decrease in efficiency. When lowering the size of the transmission window it causes a decrease in efficiency because the size creates a bottleneck for the overall flow of data. When increasing the size it will also cause a drop in efficiency which will only be tangible when increasing the bit error rate. The difference in efficiency becomes less noticable as transmission speed increases because a higher transmission window is required and small deviations in the size of the transmission window will thus be of a smaller ratio and have less impact. All this seems to suggest that the delay-bandwidth is the deciding factor for deciding how large the minimum transmission window needs to be in order to accommodate the flow of data for Go-Back-N but does not act as an upper limit, at least not when there is small amount of noise.

7.4 Future Work

There are mainly two aspects that would be interesting to research. The first thing would be to extend and further develop the functionalites of the Go-Back-N emulator so that it becomes bi-directional and include most aspects of sending and receiving data, for example processing delay, which would also mean that the theoretical model would have to be adjusted. The adjustments would for example be to revert the delay-bandwidth to half its size giving the ability of another sender to utilize some of the delay-bandwidth. To research the complexity of a channel being utilized of multiple sources at once (ie. flow control) would be very interesting. The second aspect would be to extend the theoretical model so that it also includes the impact of acknowledgments, which would mean that the emulator needs to be further devel- oped. Perhaps it would be possible to then get results that would more accurately represent some theoretical model.

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The impact of noise and Transmission Window on the efficiency of Go-Back-N

ON THE EFFICIENCY OF GO-BACK-N