用於無線區域網路之幾個增強型機制設計

行政院國家科學委員會專題研究計畫 成果報告

用於無線區域網路之幾個增強型機制設計(第 3 年) 研究成果報告(完整版)

計 畫 類 別 ： 個別型

計 畫 編 號 ： NSC 96-2221-E-011-020-MY3

執 行 期 間 ： 98 年 08 月 01 日至 99 年 07 月 31 日 執 行 單 位 ： 國立臺灣科技大學資訊工程系

計 畫 主 持 人 ： 馮輝文

處 理 方 式 ： 本計畫涉及專利或其他智慧財產權，2 年後可公開查詢

中 華 民 國 99 年 10 月 07 日

NSC Project Report

Design of Some Enhanced Schemes for Wireless LANs (1st Year)

Project Number: NSC 96-2221-E-011-020-MY3 Project Duration: 2007/08/01–2010/07/31

Project Investigator: Huei-Wen Ferng

Department of Computer Science and Information Engineering National Taiwan University of Science and Technology, Taipei 106, Taiwan

Abstract— How to simultaneously achieve fairness and quality of service (QoS) guarantee in QoS-oriented wireless LANs is an important and challenging issue. Targeting at this goal and taking priority setting, fairness, and cross-layer design together into account, four scheduling schemes designed for the QoS- oriented LAN mainly based on concepts of deficit count and allowance are proposed in the first year of the project to provide better QoS and fairness. Using multiple deficit count to inter frame space (IFS) and allowance to IFS mappings for different priorities, enhanced distributed deficit round robin (EDDRR) and enhanced distributed elastic round robin (EDERR) schemes are designed to reduce (or even eliminate) possible collisions, while EDDRR with backoff interval (EDDRR-BI) and EDERR with backoff interval (EDERR-BI) schemes still keep the backoff procedure but dynamically adjust backoff intervals depending on the priority setting and deficit count or allowance with a cross- layer design. Through extensive numerical examples, we show that the proposed schemes outperform the closest scheduling schemes in the literature and exhibit much better QoS as well as station-level and flow-level fairness.

Index Terms— Wireless LAN, quality of service, scheduling, fairness.

I. MOTIVATION, LITERATUREREVIEW,ANDPURPOSE

With the rapid technological development of wireless local area networks (LANs) and the popularization of various kinds of mobile devices, we have witnessed that intensive wireless LANs have been deployed in metropolitan areas to facilitate wireless access in many famous cities, including Philadelphia, Cleveland, and Taipei etc. Pervasion of wireless LANs stimu- lates diverse and multimedia applications run over wireless LANs due to users’ needs, e.g., voice over IP (VoIP) [4], [13] and video on demand (VoD) [12] etc. To support multi- media applications over wireless LANs, bandwidth has been expanded from 2 Mbps (defined in the IEEE 802.11 standard [14]) to 54 Mbps (defined in the IEEE 802.11a/g standard [15], [17]). Except the fundamental bandwidth requirement to support multimedia applications, how to achieve QoS re- quirements requested by voice, video, and data, respectively, in wireless (multimedia) networks is a challenging issue and has drawn much researchers’ attention in the past, e.g., [1], [6], [13], [35], [36]. Unfortunately, QoS is not well taken care and defined in IEEE 802.11 [14], 802.11a [15], 802.11b [16]

standards. Hence, IEEE 802.11 task group E then modified the


  



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Fig. 2. EDCA vs. legacy DCF.

distributed coordination function (DCF) previously defined in the medium access control (MAC) layer of the IEEE 802.11 standard to form the so called enhanced DCF (EDCF) or enhanced distributed coordination access (EDCA) (see Fig. 1) defined in the hybrid coordination function (HCF) of IEEE 802.11e [18] so that multimedia transmission in IEEE 802.11 wireless LANs can be supported. EDCA is able to strengthen some functions of DCF, for example, multiple queues of different priorities for fulfillment of QoS guarantee are defined (see Fig. 2). In the literature, some papers, e.g, [9], [10],

[13], [19], [23], [24], [28], [31], [35], [36], further addressed the QoS-related issue in the IEEE 802.11e-based network. In [9], [10], Gannoune and Robert proposed the dynamic tuning method on the maximum and minimum contention windows to enhance performance of high-priority services in the ad hoc mode. To support VoIP, a framework was proposed by Hwang and Cho [13] for the IEEE 802.11e network. Iera et al. [19]

enhanced QoS of multimedia flows by dynamically adjusting transmission rates for multimedia flows. In [23], Kim and Cho estimated the status of contention using the virtual group (VG) scheme to reduce collision rates. Lan et al. [24] proposed a contention adaption (CA) scheme to reduce collision rates and shorten delay time. In [28], a priority-based scheme for band- width assignment depending on different traffic categories was proposed by Mangold. In [31], a dynamic adjustment method of the minimum contention window based on the network status and needs of applications was proposed by Romdhani et al. to achieve reduction of the collision rate and increase of the medium utilization. Vinnakote et al. [35] shortened delay time by adjusting the size of contention window and the length of the arbitrary inter frame space (AIFS). In [36], Wong and Donaldson proposed an age-dependent backoff (ADB) scheme for adjusting the contention window according to time spent in queue of real-time services to shorten delay of real-time services.

For QoS-oriented wireless LANs, e.g., the IEEE 802.11e- based wireless LAN, QoS guarantee is definitely an issue of extreme importance. Except QoS guarantee, how to fairly allo- cate resources of networks to different services is an extremely important issue deserved to be addressed as well. Hence, a fair scheme, for example, a fair scheduling scheme, to guarantee fair resource sharing among services of different priorities in the QoS-oriented wireless LAN is desirable and necessary.

To address this issue, literature review on scheduling is given as follows. In the past, scheduling schemes for either wired or wireless networks were extensively studied, e.g., [5], [21], [22]. For having more specific discussion on fair scheduling in wireless LANs, one may pay special attention to distributed weighted fair queueing (DWFQ) [2], distributed elastic round robin (DERR) [8], enhanced EDCF (EEDCF) [25], backoff- interval based weighted fair scheduling with strict priority (BIWF-SP) [26], IFS-based distributed fair queueing with strict priority (IDFQ-SP) [26], adaptive fair enhanced DCF (AFEDCF) [27], distributed deficit round robin (DDRR) [30], and distributed fair scheduling (DFS) [34]. DWFQ [2] and AFEDCF [27] ensure fairness by adjusting the contention window, while DFS [34] adjusts the backoff interval to achieve fairness. With the aid of mapping functions from allowance [8], finish tag derived via DFS [26], and deficit count [30] to values of IFS, no backoff is involved in DERR [8], IDFQ- SP [26], and DDRR [30], which can achieve fairness by suitably controlling parameters, including allowance, finish tag, and deficit count etc. In [25], EEDCF was proposed to address fairness and QoS together by incorporating the allowance concept into the backoff interval adjustment and using different values of weights to set different priorities for offering differentiated services, while BIWF-SP [26] applies the concept of DFS to the backoff procedure of EDCA to

achieve fairness and QoS guarantee.

Except the aforementioned papers, there are some other papers addressed QoS and scheduling together, e.g., [3], [7], [11], [20], [29], [32]. In [11], Grilo et al. proposed a scheduling algorithm called scheduling based on estimated transmission times - earliest due date (SETT-EDD) for HCF to achieve better performance than the TGe scheduler [33] in IEEE 802.11e wireless LANs. Applying the concept of the virtual packet, Fallah et al. [7] proposed a scheduling framework called multiple access hybrid scheduling (MAHS) at the access point for IEEE 802.11e wireless LANs to enable the use of conventional schedulers for scheduling both uplink and down- link packets. Utilizing adaptive service intervals, transmission opportunities, and polling order, an application-aware adaptive 802.11e QoS scheduler for the centralized polling-based HCF controlled channel access (HCCA) was proposed by Inan et al [20]. In [32], a traffic scheduling algorithm performing channel allocation based on the actual traffic for HCCA called adaptive resource reservation over WLANs (ARROW) was proposed by Skyrianoglou et al. In [29], Park et al. proposed a fair QoS agent (FQA) for simultaneously providing per-class QoS and per-station fair channel sharing in wireless access LANs. To provide fair services and support QoS requirements in IEEE 802.11 networks with multiple access points, Bejerano and Bhatia [3] presented a framework called MiFi based on the centralized coordination.

In this project, we also aim at proposing fair schedul- ing schemes, i.e., EDDRR, EDERR, EDDRR-BI, EDERR- BI, which are capable of handling the interplay of fairness and QoS simultaneously in the QoS-oriented IEEE 802.11e- based wireless LAN based on concepts of deficit count and allowance with cross-layer consideration. The proposed scheduling schemes are designed for EDCA, while scheduling schemes or frameworks proposed in [3], [11], [20], [32] are designed for HCCA. Unlike DDRR [30] and DERR [8], the proposed schemes employ multiple types of deficit count and allowance so that QoS handling becomes easy. Moreover, the proposed scheduling schemes are easy to implement because of low complexity as compared to the DFS-based schemes, e.g., IDFQ-SP [26], BIWF-SP [26]. Last but not least, the proposed scheduling schemes not only provide better QoS but also achieve better flow-level and station-level fairness, while FQA [29] only provides per-station fairness with per- class QoS. In this project, reasonable definitions of weights are also explicitly given for EDDRR , EDERR, EDDRR-BI, and EDERR-BI, but only manual setting on weights is employed by EEDCF [25], resulting in an indirect or even unreasonable way to handle QoS requirements.

The rest of the project is organized as follows. In Section II, the proposed schemes are described in detail. To reflect fairness, definitions of weights are definitely important. Hence, Section III defines different types of weight. To examine the performance of the proposed schemes, Section IV provides extensive numerical examples with discussions. We show that the proposed schemes not only offer better fairness but also improve transmission efficiency. Finally, Section V gives the self evaluation for the project.

II. THEPROPOSEDSCHEMES

In this section, four fair scheduling schemes mainly de- signed for the IEEE 802.11e wireless LAN are proposed.

These four schemes can be categorized into schemes with backoff intervals and schemes without backoff intervals.

Among the four proposed schemes, two of them are designed based on the concept of deficit counts and the remaining two are designed based on the concept of allowances. Let us now elaborate on these four schemes in the following four subsections, respectively.

A. Enhanced Distributed Deficit Round Robin with Backoff Interval (EDDRR-BI)

The deficit count (deficit counter) previously employed by DDRR [30] plays an important role in scheduling for EDDRR- BI (so does EDDRR described in the next subsection) in which three types of deficit count rather than a single type of deficit count as in DDRR are defined for access categories of audio, video, and data (the access category of background is not considered in this project). For convenience, we shall use dummy variable l to denote the type of access category (service class), e.g., l = a is used to denote the access category of audio, l = v is used to denote the access category of video, and l = d is used to denote the access category of data. In the following, DC_l,i^j (t) is defined to denote the deficit count at time t of the ith flow of access category l in station j. DC_l,i^j (t) will accumulate according to (1) when no data is transmitted.

DC_l,i^j (t) = DC_l,i^j (t⁰) + K_l,i^j × (t − t⁰), l = a, v, d, (1) where t⁰ (t⁰ ≤ t) denotes a time instant ahead of t and K_l,i^j stands for the desired throughput of the ith flow of access category l in station j. The definition of deficit counts in (1) explicitly shows the following two aspects: i) deficit counts accumulate linearly as time goes; ii) deficit counts are proportional to the desired throughput. Note that only the desired throughput K_l,i^j is used in this project for the definition of deficit counts, while a fixed quantum Q and a variable time interval T are required for the definition of the deficit count in [30]. Hence, our definition of deficit counts eases parameter setting. For the situation when a frame of the ith flow of access category l in station j is transmitted at time t, the frame size should be deducted from the corresponding deficit count, namely,

DC_l,i^j (t) = DC_l,i^j (t) − F_s^l(t), l = a, v, d, (2) where F_s^l(t) is the frame size corresponding to access category l transmitted at time t. The deficit counts governed by (1) and (2) can be used to well handle the fair scheduling issue because of their linear accumulation with respect to time, their proportional property with respect to the desired throughput, and their faithful reflection on transmission.

To incorporate the aforementioned idea of fair scheduling into the IEEE 802.11e wireless LAN, we need to relate deficit counts to backoff intervals. In the following, we make a connection between the deficit count and the backoff interval through the temporary backoff interval at time t of the ith flow

of access category l in station j, i.e., T BI_l,i^D,j(t) (l = a, v, d), defined as follows:

T BI_l,i^D,j(t) = CW_max^l − φ^D_l DC_l,i^j (t), l = a, v, d, (3) where the superscript^D is used to explicitly denote EDDRR- BI, CW_max^l is the maximum window size for access category l, φ^D_l is a selected constant used to make the resultant T BI_l,i^D,j(t) fall within the IEEE 802.11e specification on the inter frame space. In the IEEE 802.11e standard, different values of CW_max^l for different access categories are specified, e.g., CW_max^a = 2⁴− 1, CW_max^v = 2⁵− 1, and CW_max^d = 2¹⁰−1, to achieve differentiated QoS. By using (3), the follow- ing two characteristics can be exhibited. i) QoS preservation:

The access category of audio has a more chance than the access category of video (similarly, the access category of video has a more chance than the access category of data) to have a shorter temporary backoff interval under a fixed deficit count because different values of the maximum window size are set to different access categories. ii) Consideration of fairness: No starvation occurs using EDDRR-BI since an access category with a lower priority can have a shorter cor- responding temporary backoff interval than access categories with higher priorities because its deficit count gets larger as time goes. Combining the previously described characteristics and a cross-layer design idea, (4) determines the backoff interval at time t of the ith flow of access category l in station j, i.e., BI_l,i^D,j(t), with the aid of information on the collision rate to reach fair scheduling and performance improvement in the QoS-oriented environment.

BI_l,i^D,j(t) = max(0.2, 1 − c)T BI_l,i^D,j(t), l = a, v, d, (4) where c (0 ≤ c ≤ 1) denotes the collision rate and the superscript ^D is used to explicitly denote EDDRR-BI again.

Note that max(0.2, 1 − c) decreases linearly in terms of c, i.e., max(0.2, 1 − c) = 1 − c, when 0 ≤ c ≤ 0.8, while max(0.2, 1 − c) is fixed at 0.2 when 0.8 < c ≤ 1.

Therefore, shorter backoff intervals are set when the collision rate gets higher as compared to temporary backoff intervals.

This definitely speeds up the alleviation of collision, thus improving system performance.

Regarding the adjustment of the backoff interval caused by a collision, it may still follow the IEEE 802.11e standard [18]

or other new schemes in the literature. As for this part, it falls out of the scope of this project. Hence, we do not further address this issue in this project.

B. Enhanced Distributed Deficit Round Robin (EDDRR) We now design EDDRR in contrast to EDDRR-BI for IEEE 802.11e. Like EDDRR–BI, the same deficit counts defined for EDDRR–BI, i.e., DC_l,i^j (t), l = a, v, d, are also used by EDDRR. When no data is transmitted, the deficit counts accumulate according to (1), while (2) is used to deduct the frame size from the corresponding deficit count when a frame is transmitted. In addition, EDDRR works analogously to EDCA except the following changes to the inter frame space

via mapping from the deficit count to the inter frame space.

IFS^D,j_a,i (t) = SIFS + PIFS

2 − α^D_aDC_a,i^j (t)rand(1, βD),(5) IFS^D,j_v,i (t) = PIFS − α^D_vDC_v,i^j (t)rand(1, βD), (6) IFS^D,j_d,i (t) = DIFS − α^D_dDC_d,i^j (t)rand(1, βD), (7) where the superscript ^D or the subscriptD is used to denote EDDRR, rand(1, βD) denotes a random number between 1 and βD (βD > 1), and IFS^D,j_l,i (t) denotes the inter frame space at time t of the ith flow of access category l (l = a, v, d) in station j. Note that different constants α^D_l , l = a, v, d, are defined to make the resultant inter frame space IFS^D,j_l,i (t) fall within [SIFS, (SIFS + PIFS)/2] for the access category of voice, i.e., l = a, [(SIFS + PIFS)/2, PIFS] for access the category of video, i.e., l = v, and [PIFS, DIFS] for the access category of data, i.e., l = d to achieve that i) a higher priority corresponds to a shorter inter frame space; ii) a larger deficit count may have a shorter inter frame space in order to get the medium more easer; iii) the same deficit count can have a different inter frame space by using rand(1, β_D).

Therefore, the above design allows EDDRR to guarantee QoS of different access categories, to avoid starvation so that fairness can be taken care, and to circumvent backoff if perfect discrimination on values of the inter frame space can be achieved (or less collisions occur for EDDRR as compared to EDCA if no perfect discrimination on values of the inter frame space is assumed and these collisions can still invoke backoff procedures as those specified by IEEE 802.11e).

C. Enhanced Distributed Elastic Round Robin with Backoff Interval (EDERR-BI)

Instead of using deficit counts, some elastic and adjustable amounts of traffic data allowed for transmission called al- lowances [8] are adopted in EDERR-BI to govern the kernel of scheduling. Note that only one single type of allowance is defined in [8] using a fixed quantum Q and a variable time interval T . Once an allowance is set, the traffic data associated with that allowance can be consecutively transmitted until the amount of the traffic data is a bit more than the allowance.

More specifically, three types of allowance are defined in EDERR-BI for access categories of audio, video, and data.

The definitions of these allowances at time t of the ith flow of access category l in station j denoted by A^j_l,i(t) are given as follows:

A^j_l,i(t) = K_l,i^j × (t − t⁰) − E_l,i^j (t⁰), l = a, v, d, (8) where E_l,i^j (t⁰) is the excess amount at time t⁰(t⁰≤ t) of the ith flow of access category l in station j, which can be expressed in terms of allowance at time t⁰ and the total amount of traffic data transmitted at time t⁰ by the ith flow of access category l in station j denoted by F_l,i^j(t⁰) as follows:

E_l,i^j (t⁰) = F_l,i^j(t⁰) − A^j_l,i(t⁰), l = a, v, d. (9) From (8) and (9), one may easily understand that i) allowances are in proportional to the desired throughput so that allowances are allotted according to different demands; ii) allowances

increase linearly as time goes so that starvation for low-priority access categories can be avoided; iii) deduction of the excess amount at the latest time instant from the allowance enforces fair scheduling. Compared to the definition of the allowance in [8], our definitions of allowances give direct parameter setting and ease operations.

Complying with the MAC operation and QoS requirement in the IEEE 802.11e LAN necessitates the following relationship between the allowance and the temporary backoff interval like EDDRR-BI.

T BI_l,i^E,j(t) = CW_max^l − φ^E_l A^j_l,i(t), l = a, v, d, (10) where superscript ^E is used to explicitly denote EDERR–

BI and constant φ^E_l should be properly selected to make T BI_l,i^E,j(t) fall within a suitable range according to the IEEE 802.11e standard. Applying a similar design principle employed by (4), the backoff interval BI_l,i^E,j(t) at time t of the ith flow of access category l in station j can be defined below using the temporary backoff interval T BI_l,i^E,j(t) and the collision rate c.

BI_l,i^E,j(t) = max(0.2, 1 − c)T BI_l,i^E,j(t), l = a, v, d. (11) Hence, the backoff interval determined by (11) simultaneously considers concepts of fair scheduling, QoS requirement, and cross-layer design for performance improvement. For the same reasoning in EDDRR-BI, the adjustment of the backoff interval caused by a collision is not further addressed in this project.

D. Enhanced Distributed Elastic Round Robin (EDERR) In contrast to EDERR-BI, we now design EDERR for IEEE 802.11e. Using the three types of allowance defined for EDERR–BI, i.e., A^j_l,i(t), l = a, v, d, EDERR accumulate allowances according to (8) in which the previous excess amount defined by (9) is deducted. Similar to EDDRR, ED- ERR works like EDCA but changes the inter frame space using the mapping from the allowance to the inter frame space given below.

IFS^E,j_a,i(t) = SIFS + PIFS

2 − α^E_aA^j_a,i(t)rand(1, βE),(12) IFS^E,j_v,i(t) = PIFS − α_v^EA^j_v,i(t)rand(1.0, βE), (13) IFS^E,j_d,i(t) = DIFS − α^E_dA^j_d,i(t)rand(1, βE), (14) where the superscript^Eor the subscriptEdenotes EDERR and rand(1, βE) represents a random number between 1 and βE, where βE > 1, and IFS^E,j_l,i (t) denotes the inter frame space at time t of the ith flow of access category l (l = a, v, d) in station j. Like EDDRR, three constants α^E_l , l = a, v, d, are defined so that the resultant inter frame space IFS^E,j_l,i (t) can fall within [SIFS, (SIFS + PIFS)/2] when l = a, [(SIFS + PIFS)/2, PIFS]

when l = v, and [PIFS, DIFS] when l = d, respectively. The ideas behind (12)–(14) are i) QoS guarantee: setting a shorter inter frame space for a higher priority enables service differ- entiation and QoS guarantee; ii) fair scheduling: no starvation exists since a shorter inter frame space may be set for a larger amount of allowance so that getting the medium becomes more easer; iii) collision reduction/elimination: different values of the inter frame space are set for the same allowance with

the aid of random number rand(1, β_E). Compared to EDCA, this definitely reduce collisions or even eliminates collisions if discrimination on values of the inter frame space is totally viable. Of course, backoff procedures as those specified by IEEE 802.11e may still be employed for EDERR if collisions occur.

III. DEFINITIONS OFWEIGHTS

For EDDRR-BI, EDERR-BI, EDDRR, and EDERR, proper definitions of weights are necessary so that measure of fairness can be defined based on weights. In the following, weights for flows within the same access category l (l = a, v, d) denoted by w^[s],j_l,i (here superscript^[s]is used to denote the same access category), weights for flows across different access categories denoted by w^[d],j_l,i (here superscript ^[d] is used to stand for different access categories), and weights for different stations denoted by wj are defined to make definitions of flow-level and station-level fairness feasible. These three types of weight are now defined as follows:

w_l,i^[s],j = K_l,i^j P

j

P

iK_l,i^j , (15)

w^[d],j_l,i = K_l,i^j P

l

P

j

P

iK_l,i^j , (16) wj =

P

l

P

iK_l,i^j P

l

P

j

P

iK_l,i^j . (17) Note that one may use the reciprocal of the standard deviation for throughput-to-weight ratios to represent the degree of fairness (see [8]). Hence, weights should be proportional to the (desired) throughput. This gives the reason why values of the desired throughput are used to define weights in (15)–

(17). Further note that no direct and reasonable definitions of weights are given in [25] as compared to definitions of weights here; hence, no station-level fairness was associated with EEDCF [25].

Following the aforementioned definitions of weights, weights for all schemes in the following simulation experi- ments are defined accordingly, even for EEDCF.

IV. NUMERICALRESULTS ANDDISCUSSIONS

In this section, we now study performance (including throughput, delay, and collision rate) and fairness for the four proposed scheduling schemes, EDCA, EEDCF¹ [25], and DERR [8] through a simulation approach which is done by ns–2 [37] along with some modifications provided by [27]. In the following, we first elaborate on arrangement of simulation experiments and define related performance metrics. Then, extensive simulation results are shown along with discussions.

A. Arrangement of Simulation Experiments

The simulation programs of this project are built upon the well-know network simulator ns–2 [37]. Fig. 3 shows

1No special backoff interval adjustment is employed except that defined in IEEE 802.11e.









 

 



    

 

 



Fig. 3. Simulation topology.

TABLE I

SOME PARAMETERS USED IN SIMULATIONS FOR ACCESS CATEGORIES OF AUDIO,VIDEO,AND DATA

Audio Video Data

Priority 3 2 0

Packet Size 160 bytes 1280 bytes 1500 bytes Packet Interval 20 ms 10 ms 12.5 ms

the simulation topology considered, i.e., a star topology in which a central station (denoted by STA 0) and n surrounding stations (denoted by STA i, i = 1, 2, . . . , n) are assumed.

For each station, there are three access categories, i.e., audio, video, and data. In Table I, some related parameters for these three access categories are given. About setting of desired throughput (flow rates), there are two different ways depending on the purpose of simulation programs. The desired flow rates for audio, video, and data are fixed at 8 KB/s, 128 KB/s, and 120 KB/s, respectively, for the purpose to get performance of throughput, delay, and collision rate. But for the purpose to get the degree of fairness, three stations are arranged as one group in which different flow rates are set to the three videos (data), while the same rate (8 KB/s) is set to all audio. By adding more such identical groups, more stations are involved. Since we considered the QoS-oriented wireless LAN, both IEEE 802.11a and 802.11e standards are employed in our simulations with transmission rate of 36 Mbps. Shown in Table II is some important parameters for the MAC layer. In addition, α^D_a, α^D_v, α^D_d, α^E_a, α_v^E, and α^E_d are set to 1.25×10⁻⁵, 1.45 × 10⁻⁵, 1.65 × 10⁻⁵, 1.85 × 10⁻⁵, 2.15 × 10⁻⁵, and 2.65 × 10⁻⁵, respectively; φ^D_a, φ^D_v, φ^D_d, φ^E_a, φ^E_v, φ^E_d are set to 0.012, 0.084, 0.132, 0.08, 0.24, and 0.32, respectively; and βD = βE = 1.9. About the collision rate, it is calculated every 5000 time slots. To collect performance metrics, more than 100 seconds are required for each simulation run.

To study the performance of different schemes, metrics listed below are utilized to gauge performance:

TABLE II

SOME PARAMETERS OF THEMACUSED IN SIMULATIONS Parameter Value / Choice

Slot time 9 µs

SIFS 16 µs

PIFS 25 µs

DIFS 34 µs

Channel Rate 36 Mbps

3 6 9 12 15 18 0

20 40 60 80 100 120 140

Number of stations

Throughput (KB/s)

Audio, EDCA Audio, EEDCF Audio, EDDRR−BI Audio, EDERR−BI Video, EDCA Video, EEDCF Video, EDDRR−BI Video, EDERR−BI Data, EDCA Data, EEDCF Data, EDDRR−BI Data, EDERR−BI

(a) Individual throughput.

0 2 4 6 8 10 12 14 16 18

0 500 1000 1500 2000 2500

Number of stations

Total throughput (KB/s)

EDCA EEDCF EDDRR−BI EDERR−BI

(b) Total throughput.

Fig. 4. Throughput comparison among EDCA, EEDCF, EDDRR–BI, and EDERR–BI.

• throughput,

• delay,

• collision rate,

• measures of fairness: the reciprocal of standard deviation about throughput-to-weight ratios can be employed to indicate the degree of fairness [8]. Alternatively, the closeness of fairness index F_I, which is formally defined as

FI = (X

f

Sf

wf

)²/X

f

X

f

(Sf

wf

)²,

where Sf and wf represent throughput and weight, respectively, of flow (station) f , to the fairness index of the ideal/perfect case with value of 1 can be applied to represent the degree of fairness as well. For example, the reciprocal of difference of fairness indices with respect to the ideal case, i.e., 1/(1 − F_I), can be simply used to show the degree of this closeness [8], thus providing another way to exhibit the degree of fairness.

B. Simulation Results

QoS-related performance, including throughput, delay, and collision rate, and degree of fairness for different schemes, including EDCA, EEDCF, EDDRR–BI, EDERR–BI, DERR, EDDRR, and EDERR, are given as follows.

1) Throughput:

Let us first examine individual throughput given in Figs. 4(a) and 5(a). First, one can see that constant throughput is kept for the access category of audio because it has the highest priority for all schemes. Second, throughput for the access category of video starts to decrease when the number of stations reaches 9, 12, and 15 for DERR, EDCA, and EEDCF, while the

3 6 9 12 15 18

0 20 40 60 80 100 120 140

Number of stations

Throughput (KB/s)

Audio, EDCA Audio, DERR Audio, EDDRR Audio, EDERR Video, EDCA Video, DERR Video, EDDRR Video, EDERR Data, EDCA Data, DERR Data, EDDRR Data, EDERR

(a) Individual throughput.

0 2 4 6 8 10 12 14 16 18

0 500 1000 1500 2000 2500

Number of stations

Total throughput (KB/s)

EDCA DERR EDDRR EDERR

(b) Total throughput.

Fig. 5. Throughput comparison among EDCA, DERR, EDDRR, and EDERR.

same level (128 KB/s) is kept for EDDRR-BI, EDERR-BI, EDDRR, and EDERR. Considering results at 18 stations, we note that 8% (10 KB/s), 1.5% (2 KB/s), and 12% (14 KB/s) of improvement for EDDRR-BI, EDERR-BI, EDDRR, and EDERR as compared to EDCA, EEDCF, and DERR, respectively, can be observed. Third, a notable decreasing trend in throughput for the access category of data is observed for all schemes when the number of stations is over 9. Fixing the number of stations at 18, we have 14% (3 KB/s), 28% (6 KB/s), 38% (8 KB/s), and 47% (10 KB/s) of improvement for EDDRR-BI, EDERR-BI, EDDRR, and EDERR as compared to EDCA; we have 41% (7 KB/s) and 58% (10 KB/s) of improvement for EDDRR-BI and EDERR-BI as compared to EEDCF; we have 7% (2 KB/s) and 14% (4 KB/s) of improvement for EDDRR and EDERR as compared to DERR.

Regarding throughput for the access category of data, EEDCF even performs worse than EDCA, while DERR performs much better than EDCA. Moreover, EDERR performs best and EDDRR, DERR, EDERR-BI, and EDDRR-BI follow suc- cessively. From the above observations, we see that EDERR and EDDRR can provide better throughput for all access categories among schemes without backoff intervals, while EDDRR-BI and EDERR-BI can provide better throughput for all access categories among schemes with backoff intervals.

As for total throughput, one may see Figs. 4(b) and 5(b) for details. We note that comparable throughput is observed for all schemes when the number of stations is less than or equal to 9. Over 9 stations, the best to the worst schemes are EDERR, EDDRR, EDERR-BI, EDDRR-BI, and EDCA, respectively. As for DERR and EEDCF, they perform worse than EDCA within the interval [9, 13] but better than EDCA when the number of stations reaches 14 and beyond.

3 6 9 12 15 18 0

500 1000 1500 2000 2500 3000 3500 4000 4500

Number of stations

Mean delay (ms)

Audio, EDCA Audio, EEDCF Audio, EDDRR−BI Audio, EDERR−BI Video, EDCA Video, EEDCF Video, EDDRR−BI Video, EDERR−BI Data, EDCA Data, EEDCF Data, EDDRR−BI Data, EDERR−BI

(a) EDCA, EEDCF, EDDRR–BI, and EDERR–

BI.

3 6 9 12 15 18

0 500 1000 1500 2000 2500 3000 3500 4000 4500

Number of stations

Mean delay (ms)

Audio, EDCA Audio, DERR Audio, EDDRR Audio, EDERR Video, EDCA Video, DERR Video, EDDRR Video, EDERR Data, EDCA Data, DERR Data, EDDRR Data, EDERR

(b) EDCA, DERR, EDDRR, and EDERR.

Fig. 6. Mean delays for different access categories and schemes.

2) Delay:

With the highest priority, all mean delays of all considered schemes for the access category of audio are (almost) zero as shown in Figs. 6(a)–(b). For the access category of video, an approximately linear trend is observed (see Figs. 6(a)–(b)).

For the comparison purpose, the following results obtained from comparison on mean delays for the access category of video between different schemes are given when the number of stations is fixed at 18. Mean delay of EDCA is 84%, 126%, 151%, and 162% higher than those of EDDRR-BI, EDERR- BI, EDDRR, and EDERR, respectively; mean delay of EEDCF is 17% and 44% higher than those of EDDRR-BI and EDERR- BI, respectively; mean delay of DERR is 184% and 197%

higher than those of EDDRR and EDERR, respectively. As far as the delay of the access category of video is concerned, schemes without backoff intervals perform much better than schemes with backoff intervals except DERR. One may note that DERR performs even worse than EDCA. To further distinguish the corresponding performance among EDCA, EEDCF, EDDRR-BI, and EDERR-BI, we note that EDERR- BI performs best. The successive followers are EDDRR-BI, EEDCF, and EDCA, respectively. Likewise, EDERR performs best among schemes without backoff intervals; EDDRR and DERR follow successively. As shown in Figs. 6(a)–(b), sharp increase for data in mean delays can be observed when the number of stations is over 9. For the comparison purpose again, we note that mean delay of EDCA is 5%, 8%, 14%, and 17% higher than those of EDDRR-BI, EDERR-BI, EDDRR, and EDERR, respectively; mean delay of EEDCF is 9%

and 12% higher than those of EDDRR-BI and EDERR-BI, respectively; mean delay of DERR is 3% and 5% higher than those of EDDRR and EDERR, respectively, when the

0 2 4 6 8 10 12 14 16 18

0 100 200 300 400 500 600 700 800 900 1000

Number of stations

Number of collisions per sec.

EDCA EEDCF EDDRR−BI EDERR−BI

(a) EDCA, EEDCF, EDDRR–BI, and EDERR–

BI.

0 2 4 6 8 10 12 14 16 18

0 100 200 300 400 500 600 700 800 900 1000

Number of stations

Number of collisions per sec.

EDCA DERR EDDRR EDERR

(b) EDCA, DERR, EDDRR, and EDERR.

Fig. 7. Collision rates for different schemes.

number of stations is fixed at 18. Obviously, mean delays of all schemes for the access category of data are comparable.

3) Collision rate:

Results from Fig. 7(a) when the number of stations is 18 reveal that 22% of improvement for EDDRR-BI and 31% of improvement for EDERR-BI in terms of collision rate can be obtained as compared to EDCA. As for collision rates for EEDCF, EDDRR-BI, and EDERR-BI, they are almost comparable. To further distinguish them, EDERR-BI has the lowest collision rate; EEDCF has a bit higher collision rate than EDERR-BI; and EDDRR-BI has a bit higher collision rate than EEDCF. As shown in Fig. 7(b), collision rates for DERR, EDDRR, and EDERR can be kept to zero since possible collisions can be avoided if perfect IFS discrimination is assumed.

4) Fairness:

In the following, we observe fairness among flows within the same access category, flows across different access cate- gories, and stations. Let us first discuss fairness among flows within the same access category. Because the highest priority with the same weight is set for the access category of audio, perfect fairness (zero standard deviation) is shown in Fig. 8 for all schemes. Shown in Fig. 9 is the throughput-to-weight ratio among flows within the access category of video. We note that values of the standard deviation regarding throughput-to- weight ratios for different schemes are 0.0071 for EDDRR- BI, 0.0067 for EDERR-BI, 0.0069 for EDDRR, 0.0051 for EDERR, 0.0077 for EEDCF, 0.011 for DERR, and 0.0084 for EDCA, respectively. Using these values, one can calculate the degree of fairness which reveals the following comparison results: i) 18%, 25%, 22%, 65% of improvement are achieved by EDDRR-BI, EDERR-BI, EDDRR, and EDERR, respec-