IEEE 802.11 WLAN utilizes a distributed function at its MAC layer, namely, DCF to access the wireless medium. Due to its distributed nature, DCF is able to guarantee working stability in a wireless medium while maintaining the assembling and maintenance cost in a low level. However, DCF is inefficient in dealing with real-time traffics due to its incapability on providing QoS. IEEE 802.11e was introduced as a supplementary standard to cope with this problem. This standard introduces an Enhanced Distributed Coordination Function (EDCF) that works based on diff-Serve model and can serve multiple classes of traffics (by using different prioritizations schemes). With the emergence of new time-sensitive applications, EDCF has proved to be yet inefficient in dealing with these kinds of traffics because it could not provide network with well-differentiated QoS. In this study, we propose a novel prioritization scheme to improve QoS level in IEEE 802.11e network. In this scheme, we replace Uniform PDF with Gamma PDF, which has salient differentiating properties. We investigate the suitability and superiority of this scheme on furnishing network with well-differentiated QoS using probabilistic analysis. We strengthen our claims by extensive simulation runs.

IEEE 802.11 [

In DCF access mechanism, the station that is going to transmit should firstly sense the channel. This action should be continued until the channel becomes ideal and remains ideal for at least DIFS. After spending this time, station should wait for a random amount of time to be expired before it starts to transmit its frame. This time is known as back-off duration to which a back-off counter is dedicated. Back-off counters decrease their values during channel ideal bursts and stop counting down as soon as channel becomes busy. The countdown process activates again, upon channel becomes ideal, and remains ideal for at least DIFS duration. Finally, the station transmits unconditionally as soon as the counter value reaches zero.

These back-off durations are to be chosen uniformly from the interval [0,

The station should reset its contention window’s length in only two situations: first, when a frame is sent successfully; second, when retransmission counter reaches

After each successful reception of a frame, receiver should send a short control frame, named Ack, back to transmitter. In case the transmitter does not receive this controlling frame within a prespecified amount of time, namely, Ack-timeout, or hears different transmission from another station, it will reschedule its retransmission for a latter time. This retransmission has to be performed using back-off mechanism. This is named the Basic transmission mechanism.

In order to reduce the undesirable effects of hidden terminal problem, which is a common situation in many WLAN scenarios, another mechanism named RTS/CRS is applicable. RTS/CTS is a four-way handshake transmission mechanism.

So far, many researchers have focused on evaluating performance of IEEE 802.11 networks [

In DCF, stations should wait for a long time before starting to transmit. This fact causes many problems when we are to encounter with delay sensitive and time bounded traffics like voice and video [

This article organized as follows: following this section, we introduce common prioritization schemes implemented in EDCF so far. In Section

In general, all priority schemes are put under one of these three categories: Back-off priority schemes [

Back-off priority schemes include

differentiation on

differentiation on PF [

differentiation on

differentiation on Probability Distribution [

differentiation on maximum back-off stages [

combinations of above schemes [

It should be noted that scheme (

Let us suppose that N different traffic classes exist (

(i) Back-off priority schemes: suppose that

To gain a better differentiation, we may combine more than one of the above parameters. Suppose that

(ii) IFS priority schemes: here, instead of using same IFS in all classes, an Arbitration Interframe Space (AIFS

Now, it is time to take a look at one of the existing analytical models of IEEE 802.11e networks.

Suppose that, for a station belonging to class i (

The transition state diagram for a class i transmission entity is depicted in Figure

This diagram is a modified Markovian chain summarizing the back-off procedure in 802.11e networks.

We applied several modifications on this model that were not considered in ZAs [

Our model is suitable for differentiation analysis on 802.11 networks.

Our model considers a limited

Our model takes into account the counter freezing mechanism in EDCF that was not considered in [

Our model considers frame-dropping probability whereas no other model did.

Imagine

Transmission probability (

Collision Probability (

Successful Transmission Probability (

All above network probabilities in one place. These curves are plotted versus transmission probability (

Before further proceed, we need to introduce two of the most important network’s quantities in networks that we will extensively utilize in the next section treatments, that is, throughput and delay.

Throughput (

Delivery delay or Service delay (

In this section, we are going to introduce a new prioritization scheme. This scheme works based on substituting Gamma distribution with legacy Uniform one that has been used in Back-off mechanism. Due to its distinctive differentiating properties, Gamma PDF seems a suitable and useful choice for being used in access granting part of network.

Although the legacy Uniform PDF, which is utilized in back-off procedure of 802.11 networks, reduces collision probability to some extent, however, the uniformity property of this PDF deeply endangers QoS issue in WLANs. This is not a complicated task to prove this claim. Actually, the key purpose of using Uniform PDF in DCF back-off mechanism was to furnish stations with strict access fairness and because there should have been no priority between stations in a 802.11 network. Nevertheless, upon emergence of 802.11e networks, this target (Fairness) was gradually vanished and replaced with prioritization. Our familiarity with mathematical analysis and higher-order statistical moments (Like Kurtosis) further confirms this fact that Uniform PDF’s dispersion is too high to be suitable for differentiation purposes. This property makes it an inappropriate option especially for voice and video servicing at the same time with Best-effort services. To gain the required tools, in next subsection, we first go over few probabilistic means that are required for further proceed.

In current section’s analysis, we do vastly use a probabilistic moment named Kurtosis. Hence, it is necessary to introduce it, in advance. Actually, Kurtosis is a measure of the concentration of a distribution about its mean and larger value of this metric is equivalent to a narrower distribution and more concentration about its mean:

In order to improve strict QoS level in network and especially to better support delay sensitive traffics like voice and video, we apply Gamma PDF instead of Uniform one. Gamma PDF is a continuous two-parameter distribution from which the Chi-Square and Exponential PDFs are derivable. This PDF varies widely as its two parameters change and takes different shapes with distinctive characteristics. The scalability of this PDF makes it suitable for our purpose, which is setting up a wide interclass differentiation. Figure

Gamma PDF curves for different parameters’ values.

The mean, Variance, and Kurtosis of

As it is evident, the Kurtosis of

This PDF has the property to furnish higher-priority classes with PDF of higher kurtosis and lower-priority classes with lower kurtosis. Therefore, the higher-priority class encounters with lower collision probability and hence enjoys higher successful transmission probability. At the same time, the lower-priority class would have a PDF with lower Kurtosis value and so it gains higher freedom to choose diverse back-off values. Therefore, both classes observe improvements in their performance.

According to (

The interesting fact about the use of

The

Furthermore,

To better illustrate above explanations, we talk a little probability mass transfer in

Cumulative probability up to Mean:

Cumulative probability around mean:

The interesting fact is that, like kurtosis, this two metrics are also independent from scale parameter (

Consider two integrals

These explanations emphasize on one important fact: as

This plot illustrates how increasing

In order to set up a correct comparison between scenarios using

Apparently, the discrete

Evidently,

EDCF parameter set.

Voice (VO) | Video (VI) | Best Effort (BE) | Background (BG) | |
---|---|---|---|---|

3 | 7 | 31 | 63 | |

7 | 63 | 1023 | 8192 | |

AIFS | 2 | 2 | 2 | 2 |

TXOP | 3264 | 3264 | 3264 | 3264 |

Common parameter set.

PHY | Transmitted Power (W) | RTS Used | Buffer Size (bit) | Traffic Inter arrival Time (S) | Packet Size (Byte) |
---|---|---|---|---|---|

DSSS-11 Mbit/s | 0.005 | None | 256000 | 0.005 | 1024 |

We go over three different simulation scenarios with

Figures

As illustrated, each bundle includes two simulations: one

As illustrated, each bundle includes two simulations: one Gamma curve and one PDF curve. (right): Video class’s service delay is worse in Gamma case than Uniform case. However, the difference is lessened when number of stations increases. (left): Voice class delay in Gamma Scenarios always is lower than Uniform scenarios.

Transmission probability (

To better illustrate tradeoff procedure between classes (as PDF’s variance increases), we plot throughput and transmission probability separately for voice, video, and best effort classes in Figures

This fact that larger numbers of stations shift benefits toward using Gamma PDF stems from its lowered collision probability. As Background and Best effort traffic classes exhibited the same trends as voice class (improved in Gamma scenarios), we intentionally avoid plotting them at this place.

Thus far, we have verified superiorities of using Gamma PDF compared with Uniform one, in scenarios that mean and variance are forced to be the same. Thereafter, we focus on scenarios in which means are the same (as it is mandatory for valid comparisons) but we change variance and observe the results. The observations reveal that, as variance increases, the total delay decreases, and the total throughput increases up to a limit. After this limit, both trends are reversed with more variance increments. Interestingly, trade-off takes place between classes so that higher-priority class seizes bandwidth from lower-priority class when variance increases more and more. Therefore, collision probability decreases. The underneath reason for the lowered delay is also in exact relationship with collision probability; the less collisions happen, the less retransmission attempts take place, and consequently the lower delay would be obtained.

Fundamentally, Increasing the PDF’s variance intensifies Intra-class contention and decreases Inter-class contention. Intra-class contentions are those that happen between stations in the same class, but Inter-class contention happen between stations belonging to different classes. By increasing PDF’s variance more and more, after a while, the Intra-class contention becomes dominant colliding factor; hence, after passing a limit the trends are reversed and total delay increases while total throughput decreases. These explanations illustrated at Figures

Total throughput and total delay for five different scenarios with the same Gamma PDF mean but different variances (

Mean number of retransmission attempts for five different scenarios with the same Gamma PDF mean but different variances (

Throughput trends of voice, video, and best effort classes for five different scenarios (

Transmission probabilities of voice and video classes for five different scenarios (

To better illustrate tradeoff procedure between classes (as PDF’s variance increases), we plot throughput and transmission probability separately for voice, video, and best effort classes in Figures

As throughput is directly engaged with transmission probability, we expect a correspondence between these two parameters. As an example, let us take a look at voice and video classes transmission probabilities.

As it is obvious, the transmission probabilities of these two classes vary in opposite directions although throughputs in both classes (Figure

Normalized throughput and successful transmission probability versus transmission probability (

Figure

At last, we summarize this article by making a comparison between service delays when different well-known probability density functions are applied on DCF. Here, we compare six scenarios with each other. The applied PDFs are Uniform, Geometric, Pareto, Exponential, Poisson, and Gamma. It is to be noted that variance and mean are the same in all these scenarios to have a valid comparison. Figure

Total delay trends for six different well-known PDFs that implemented instead of Uniform PDF. The Gamma PDF outperforms Uniform PDF with near 65% delay reduction. As Exponential PDF is an especial case of Gamma PDF with

In this study, we proposed a new prioritization scheme that is based on PDF differentiation. In this scheme, we applied

In [