Fair Backoff Algorithm

Until now, we can make sure what we need for the fairness is a new backoff algorithm which can generate smaller mean and standard deviation values even when the collision happens more on that packet. Those characteristics can improve the overall

Figure 24. Standard deviation of Conventional Backoff Algorithm under different Collision Number

performance of all packets with any kind of collisions, in other words, any kind of traffic loading. When most of the packets under these different loadings can have almost equal chance to be transmitted out, the fairness of each packet is better than that in the IEEE 802.11 [1]. In order to achieve the target, the Gamma distribution for the backoff algorithm is proposed here.

We should take a look at the probability distribution function of Gamma [31], [32]

to understand the mathematical characteristics:

? ? ? ?

Again, according to the definition of mean and variance, we can get:

? ?

?

? ?

E

? ?

? ?

SD

? ?

The Figure 25 is the probability distribution function of Gamma with a is fixed at 2, and ß varies from 0.5 to 3. We can see the standard deviation grows larger when ß varies from 0.5 to 3 in the figure. We can recognize the trend of the distribution with

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different combinations of a and ß.

With the same α, the distribution concentrates much more when β value goes small. For β < 1, since the function of Gamma Distribution has a vector with the inverse of β with the power of α, the value of f(x) goes smaller as β is getting larger based on the formula (3.7). The Figure 25 tells us how the value of β impacts the distribution under the same α. Based on the idea we want to implement, we define the β as the collision number. As to the α, it operates as a based parameter in the (3.7). If α increases, the value of Gamma(α) increases more, and f(x) has a smaller basement. We take the α as the contention window.

We don’t want to change the backoff procedure too much, because we desire to achieve the target with the least modification and hardware requirement. In this case, the backoff timer is generated by the same way as the exponential backoff was, but

Figure 25. Gamma Distribution with different ß and the same a

with a different ‘Random Number’ generator.

The modified Gamma backoff procedure is described in detailed now. As recommended in the IEEE 802.11, we follow the same rule but modifying the method of random number as:

Gamrnd( ) = Pseudorandom integer drawn from a gamma distribution with the parameters α and β, where α is defined as the contention window CW and β is the collision numbers. The CW is an integer within the range of values of the PHY characteristics aCWmin and aCWmax, which is aCWmin ≦ CW ≦ aCWmax.

Whenever collided one more time, the CW decreases one from aCWmax until it reaches aCWmin. The duration between aCWmin and aCWmax is defined as the Contention Window Size (CWS).

aSlotTime = The value of the correspondingly named PHY characteristic.

The contention window shall take the aCWmax as its initial value when the packet is first collided. As the same as the conventional backoff algorithm does, the CW will take the next value when the packet is collided again. The value of CW will decrease one by one whenever the packet is collided until the CW reaches the aCWmin and the CW shall remain at that value until it is reset when the collided packet is sent out or the SLRC reaches the threshold.

As we can tell from the discussion above, we know there are some reasons that will influence the collisions. The station number dominates the traffic loading. The probability of collision of every packet depends strongly on the station number within

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the BSS of an AP. The packet length and the arrival rate of each station also operate an important factor in collisions. We assume those as a fixed value in our simulation, and they result in a constant when we decide the aCWmax and the CWS values.

The aCWmax is the initial value of the contention window, and it should be derived from the station number, packet length and the arrival rate of packet. Take 6 as the basement of the rule because we set the packet length and the arrival rate of packet as fixed values, we follow the rule as below:

1

Then, we can get the values of the aCWmax for light loading, middle loading and heavy loading are 7, 10 and 22 respectively. We assume the STA can learn the loading before it starts to transmit packets; which means the STA will decide the initial value of contention window before the real collision happens. Similarly, the CWS is derived from the same parameters but different weighting. Even in the heavy loading, the number of packets with serious collision is definitely less than that of lightly collided.

We can reduce the duration of contention window and this will help to restrict the diversity of the standard deviation. The way we choose CWS is:

???

According to the rule, we can get the CWS as 4, 6 and 8 for the different loadings in our simulation cases and result in the value of aCWmin for each case as 4, 5, and 15 individually, and again, the aCWmin can be learned from the loading before the STA initiates a transmission.

Then, we take the contention window of the light loading for example. The size ranges from 7 to 4, and those are the series for the values of α. All the criteria are the

same as those of the conventional backoff algorithm except the method of decreasing the window size and the way to generate the random integer. The Figure 26 is the contention window distribution of the Gamma Backoff Algorithm with aCWmax 7.

The initial value aCWmax impacts the overall performance especially when the traffic is under the light loading according to the above description. The Figure 27 tells us the distribution when choosing different initial values, and it also means the distribution for the first collision. When the aCWmax is larger, the mean and standard deviation values are increasing, and that will make the delay time longer even the loading is light. But it do help when there are many stations in the BSS, since every station might choose more different backoff time interval and reduce the possibility of another collision.

Figure 26. Gamma Distribution with different combinations of a and ß

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The collision number is reflected into the value of β, which means β equals to the inverse of collision number. If the packet is collided once, β is set to 1, and when this packet is collided one more time, β will become one over two, and so on.

From the Figure 26, we can recognize that the mean and standard deviation values will decrease when the collision number increases, and also the value is less than that of the exponential backoff algorithm. In this case, we can estimate the collided worse packet will backoff less in probability, and this scenario can enhance the overall throughput of the medium.

The Figure 28 is the mean distribution of the modified backoff algorithm under different loadings. Compare with the Figure 23, the mean of the conventional exponential backoff algorithm, the average delay time of the modified backoff algorithm with the collision number 1 and 2 is worse than those of the exponential

Figure 27. Gamma Distribution with different α (CW)

algorithms. But when the packet is collided more, which part we expect to balance, the modified algorithm shows up its smaller mean value and this value can decide the average delay time of those packets with such collided numbers.

According to the fair algorithm, when the loading is heavy, the STA shall choose a larger aCWmax, which will result in a larger mean value. We can find this characteristic in the Figure 28. In general, when the loading is heavy, the mean of this case will be always larger than other cases with any possible collision number. The decreasing rate slows down much after the collision number is over the contention window size. Take the light loading as the example. Since we get the CWS as 4 from the rule (3.13), we know the α value will keep at 4 even the packet is collided more than four times. But the value of β will present the real collision condition, it still

Figure 28. Mean of Gamma Backoff Algorithm under different Loadings and Collision numbers

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decrease whenever any more collision happens to this packet because β equals to the inverse of the collision number. Following (3.9), we know the mean value equals to the multiply of α and β, and it is only be decided by the β now.

Another important parameter we should pay more attention is the standard deviation of the delay time. This variable can influence the range and precision of the delay time of each collided packet. When the standard deviation value is smaller, the higher precision of delay time can be reached. And we can have more accurately estimation to predict the possible transmitting time of each packet in different loading conditions. From the Figure 24 and the Figure 29, there is a great improvement in the standard deviation especially those seriously collided packets. For the modified Gamma backoff algorithm, we can completely control and predict the difference of delay time since the standard deviation is getting smaller when the collision happens more, comparing with the conventional exponential backoff algorithm.

Figure 29. Standard deviation of Gamma Backoff Algorithm under different Loadings and Collision numbers

Based on the fair backoff algorithm, the standard deviation of heavy loading is a little larger than the value of light loading. The most difference happens when the packet is collided less. As we can understand, the collisions of the overall system will be more when the loading is heavy. From the Figure 29, the variation of standard deviation is getting smaller with more collisions under each loading. When the contention window reaches the lower bound aCWmin, only β, also refers to the inverse of collision number, can determine the characteristic of standard deviation from (3.10), and the effect is not much.

According to these estimations, we implement the Gamma distribution into the backoff procedure, and we will see the improvement in the next section.

3.3 Simulation Results

The simulation condition is the same as that of the conventional backoff algorithm.

Every packet is set to 1000 bytes in length. The arrival rate of generating a new packet in the STA is 500 msec. The RTS/CTS handshaking procedure is implemented and we assume all packets, including the RTS/CTS, Data and ACK, are received correctly within the required duration. We use the new proposed fair backoff algorithm into the simulation case, we can get the simulation results of three different loadings, which are defined as the light, middle and heavy loadings, and we list them in the Figure 30

~ Figure 40. As mentioned above, the contention windows are different from each case because the CWS depends on the traffic loading.

Compare the Figure 11 and the Figure 30, the characteristics under the light loading, the packets seem to be collided more when using the fair backoff algorithm.

But refer to the delay time distribution and the standard deviation in the Figure 31 and Figure 32, we know the overall performance of the modified Gamma backoff algorithm is a little better.

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The fairness is defined as the delay time of the packet, no matter collided or non-collided. When the delay time of every kind of packets is very close, we say the fairness of the packet is better. By using the fair backoff algorithm, under light loading, the mean delay of overall packets is not even improved, but the standard deviation is enhanced better. This result is followed the estimation mentioned in the section 3.2. In more detailed, we find the average delay time of those packets with fewer collisions is larger than that of the conventional backoff algorithm. According to the Figure 28, we know if only one collision happens to the packet, the mean delay time is pretty larger than the corresponding value in the Figure 23. Because we choose a wider distribution G(7,1) other than the conventional one, U(7,0) when the packet is collided once.

Figure 30. Average delay time of each collision number under light load with the MPDU 1000 bytes

Figure 31. Delay time distribution under light load with the MPDU 1000 bytes

Figure 32. Delay time distribution under light load with the MPDU 1000 bytes, and without no-collision packets

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From the probability point of view, we have more chances to select the backoff time interval more than 7, the upper bound of uniform distribution U(7,0), when the packet is first collided and thus the mean value of those packets with only one collision is larger than the value of using the conventional backoff algorithm in statistically. And, the average delay time distribution is no longer be an exponential expansion, but more smooth when the collision number increases.

Under the middle loading, the simulation results are the Figure 33 ~ Figure 36.

The improvement is much more if comparing with the conventional exponential backoff algorithm by the Figure 14, Figure 15 and Figure 16. And we can tell the average delay time and the standard deviation are much limited. Similarly, the collision number is more than that of the conventional backoff algorithm. But we get a great improvement in the average delay time. From the Figure 14, the range of the average delay time is up to 13 msec. As the Figure 33 shows, almost all average delay time can be restricted less than 2 msec.

Figure 33. Average delay time of each collision number under middle load with the MPDU 1000 bytes

Figure 35. Delay time distribution under middle load with the MPDU 1000 bytes

Figure 34. Detail of the average delay time of each collision number under middle loading with the MPDU 1000 bytes

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When we zoom in to get the Figure 34, there is a small ripple between the collision number 5 to the collision number 7. Because the packet number with more collisions is less than that of fewer collisions, we know the sample base is not enough to present the ideal characteristics of the fair algorithm.

The Figure 37 to Figure 40 are the results for the heavy loading. Again, when comparing with the same conditions show in the Figure 17, Figure 18 and Figure 19, we find the mean delay time reduces not much, only 4%, but the standard deviation can be reduced 60%. Of course, the delay time still increases if comparing with the light loading or the middle loading by using the same modified Gamma backoff algorithm. It has to be, because when there are many stations deferring for a busy medium, which is referred to a heavy loading, the probability to get the same backoff timer is higher if the contention window is too limited. When more than two stations Figure 36. Delay time distribution under middle load with the MPDU 1000 bytes,

and without no-collision packets

select the same backoff integer, the packets will be collided one more time and backoff again. Such a case will reveal worse delay time as we can predict. Based on the algorithm described in the section 3.2, we generate different aCWmax and CWS according to the traffic loading to prevent this worse collision condition.

Figure 37. Average delay time of each collision number under heavy load with the MPDU 1000 bytes

Figure 38. Detail of the average delay time of each collision number under heavy loading with the MPDU 1000 bytes.

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Figure 39. Delay time distribution under heavy load with the MPDU 1000 bytes

Figure 40. Delay time distribution under heavy load with the MPDU 1000 bytes, and without no-collision packets

The limitation of the throughput is about 70% in both two backoff algorithms according to the Figure 41. Following the (3.12), (3.13), we get (aCWmax, CWS) for 20 stations as (8, 5), and for 40 stations as (14, 7). Refer to the contention window bounds (aCWmax, aCWmin), (8, 4) is for 20-station, and (14, 8) is for 40-station. We can tell the throughput is kept close to the one of the conventional backoff algorithm.

The fair backoff algorithm cannot enhance the channel utilization because we only try to reduce the backoff time for each collision or every deferment, but not focus on how to lower the handshaking procedure or dummy packets exchange. And, we do not improve the mean delay time of packets under these different loadings. We only restrict the standard deviation of the packet, which also can be referred as the precision time of each packet to achieve the fairness.

We also like to know how is the collision probability when applying the fair backoff algorithm. Similarly, using the upper and lower bounds of contention window

Figure 41. Throughput vs. Station Numbers under two backoff algorithms

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as mentioned above, and we take all collided packets into consideration no matter how many times it has been collided, we can get the collision probability distribution over the station numbers and show it in the Figure 42. It is formed that the overall collision is kept almost the same when the fair backoff algorithm is applied. The collision probability is not getting worse. Also, a tiny improvement will even happen when the traffic loading is heavy, because those packets with one collision will choose a larger backoff timer and reduce the possibility to collide another packet.

Figure 42. Collision Probability vs. Station Numbers under two backoff algorithms

Chapter 4

Conclusion

What we much concern in a wireless environment is the fairness of each packet. As we can understand, when the traffic is getting heavier, the packet will be collided more, and the delay time will be larger.

In this thesis, we have modeled and simulated the performance of the IEEE 802.11 MAC protocol with the conventional Exponential backoff algorithm. The CSMA/CA mechanism and the RTS/CTS handshaking mechanism are simulated to get the real performance and delay time distribution of each collided packet. One important character of this conventional backoff algorithm is the expansion rate of the delay time under different traffic loadings. This results in an unstable delay time of all kinds of packets, especially under a heavy loading.

We have proposed a modified Gamma backoff algorithm and studied the performance. Our simulations show that although the performance of the protocol may not enhanced much, but the fairness of each packet can be improved. The standard deviation of the delay time is more limited no matter how many collisions happened to this packet and this parameter can be presented as the fairness characteristic.

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Reference

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IEEE 802.11b, 1999

3. “Wireless LAN Medium Access Control (MAC) and Physical Layer (PHY) specifications : High-speed Physical Layer in the 5 GHZ Band”, IEEE 802.11a, 1999

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5. “Wireless Medium Access Control (MAC) and Physical Layer (PHY) specifications, Medium Access Control (MAC) Enhancements for Quality of Service (QoS)”, IEEE 802.11e/D5.0, July 2003

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