A k-round Elimination Contention Scheme for ... - Semantic Scholar

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K-ROUND ELIMINATION CONTENTION (K-EC) SCHEME

In this section, we introduce the details of our novel contention resolution algorithm, the k-EC scheme. Our newly designed k-EC scheme offers a fast contention resolution while it does not suffer from the contention resolution failure problem. Each round of contention contains several contention slots. The length of a single round is optimized for collision rates under the bounded CRP. More importantly, this optimal value is independent of the number of contending nodes, packet size, or traffic pattern. Furthermore, k-EC can achieve any intended collision rate by selecting a suitable value of k. Analyses and simulations have demonstrated its high efficiency and robustness either in lightly or heavily loaded networks accommodating several to hundreds of contending nodes. Other enhancements such as QoS capabilities can be easily incorporated into kEC. In addition, the features of k-EC make it possible to separate k-EC from the MAC protocol and to implement it directly into the front-end hardware. This can dramatically simplify the MAC protocol, and thus improve the system performance. For

convenience,

we

list

the

abbreviations and acronyms used in this paper in Table I. A. The Basic Idea

We define the throughput (ρ) of the basic access scheme of the IEEE

TABLE I. AP BEB BS CONTI CRP CSMA/CA CV DCF DIFS DSSS KIFS MACA MPDU PCF SAP SRT k-EC WLAN

ABBREVIATIONS AND ACRONYMS

Access Point Binary Exponential Backoff Base Station Constant-Time Contention Resolution [AC05] Contention Resolution Period Carrier Sense Multiple Access with Collision Avoidance Contention Vector Distributed Coordination Function Distributed InterFrame Space Direct Sequence Spread Spectrum k-EC Interframe Space Multiple Access with Collision Avoidance MAC sublayer Protocol Data Unit Point Coordination Function Service Access Point Single Round Time k-round Elimination Contention Wireless Local Area Network

802.11 DCF as,

ρ=

TData , E ( N C ) ⋅ E (TC ) + E (TS )

(1)

where TData is the average amount of the actual transmission time relevant to a data transmission, E(NC) is the average number of collisions encountered by a successful data

0, it senses the medium until the ith C-slot. In the case that it senses the medium being jammed before the i-th C-slot, it loses the contention, retires from the contention, and cancels the scheduled pulse transmission. Otherwise, it immediately transmits an energy pulse indicating a winner at the i-th C-slot. It is worthwhile to note that a contention ends as soon as the medium has been successfully jammed, i.e. it ends at the time of the earliest energy pulse having been successfully transmitted during the current round. So, the actual length of a contention round is bounded within [1 C-slot, m C-slots]. The actual length of a CRP is in turn bounded within [k C-slots, m*k C-slots]. Figure 2 illustrates an example of a k-EC where k equals 6. In Figure 2, the black bar denotes the time when the medium is jammed. The figure shows the medium is jammed at 0th, 3rd, 5th, 8th, 11th, and 14th C-slot. The actual length of the CRP is 15 C-slots. According to the k-EC mechanism there will be at least one winner after each round. If the total number of the contending nodes is n, we can roughly estimate the expected number of the final winners by 1+(n-1)/mk (note: the

Figure 2 An example of a 6-EC

(m − 1) • C − slot

(3)

where aKIFSTime is the length of the KIFS, and m is the maximal length of a single round time (mSRT). Proof: During each round of a CRP, every contending node schedules an energy pulse transmission at the i-th C-slot where i is a random integer between 0 and m-1. Since any single contention ends with the earliest successful energy pulse transmission, there is at least one winner in any single round. Thus, the maximal idle duration between any two consecutive rounds is (m-1) C-slots. This guarantees that a new contention resolution procedure, which follows an idle time of aKIFSTime, cannot be initiated during any CRP if (3) is met. Therefore, the k-EC scheme is free from the contention resolution failure problem and contention deadlock problem. In the k-EC system, as we will see later, where the length of a single contention is optimized as 3, i.e. m=3, the minimal length of the KIFS

C-slot

KIFS

should meet the following requirement:

aRXTXSwitchTime

Medium Busy

aKIFSTime > (m-1)*C-slot=20µs. In the simulations of this paper, we use:

Rx/Tx

TxKIFS Slot Boundary

δ TxC-slot Slot Boundary

aKIFSTime = aDIFSTime = 50µs. Figure 3 illustrates the slot boundaries of the

Rx/Tx Tx/Rx

RxC-slot Slot Boundary

Figure 3 The MAC Slot Boundaries

KIFS and C-slot. D. The maximal contention space

Providing a service with a bounded access time is essential in order to guarantee QoS for multimedia traffic. It has been shown in the above analysis that the number of contending nodes

1 ⎪n τ (1 − j ⋅ τ ) ps = ⎨ ∑ j =1 ⎪⎩ 1 ,n =1

(11)

It therefore follows that the collision probability of a transmission is: pc = 1 − ps .

(12)

Taking the derivation of (11) with respect to τ, we can easily verify that dps < 0 ; when n > 1. dτ

(13)

Equation (13) shows that ps is a decreasing function of τ. Therefore, maximizing ps is equivalent to minimizing τ, i.e. maximizing S. Theorem 4 is proved. From Theorem 2, 3, and 4, we have the following inference. Inference 1: Given a bounded CRP, the optimal single round length (m), which maximizes the successful transmission probability, is 3 C-slots for the k-EC scheme.

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LCRP =

∑ nτ [1 − ( j − 1)τ ]

n −1

j =1 S

∑ nτ [1 − ( j − 1)τ ]

Lj ,

(14)

n −1

j =1

where Lj is the length of the j-th CV in the contention space. After some simplifications, we obtain S

LCRP =

∑j

n −1

j =1

S

LS − j +1

∑j

.

(15)

n −1

j =1

We denote the j-th CV as [l1,l2,…lk] where li ∈ {0, 1, …, m-1}. For the first CV, l1 =l2=…=lk=0. For the last (S-th) CV, l1 =l2=…=lk=m-1. We have the following relationships k

j = 1 + ∑ li ⋅ m k − i ,

(16)

i =1

and k

L j = ∑ (1 + li ) .

(17)

i =1

G. The average number of nodes moving to the next round

Since the maximum single round length is m, the probability of selecting any of the numbers from 0 to m-1 is

λ = 1/ m .

(18)

After one round of contention, the probability that i nodes, out of n contention nodes move to the subsequent round is given by the following expression. ⎧m −1 ⎛ n ⎞ i n −i ⎪ ⎜⎜ ⎟⎟λ (1 − jλ ) ; 1 ≤ i ≤ n − 1 p(i ) = ⎨∑ i j =1 ⎝ ⎠ ⎪ mλn ; i=n ⎩

(19)

> pc and Ts >> (Ts – Tc), we have the following approximation: Tave ≈ Ts

(26)

Tδ = Tave + TCRP .

(27)

Let’s denote

The probability of a node successfully transmitting a packet after a CRP is given by ⎧ S −1 n−1 , n >1 ⎪ τ (1 − j ⋅τ ) ps* = ⎨∑ j =1 . ⎪⎩ 1 , n =1 = ps / n

(28)

The average delay is given as ∞

d ave = ∑ { p s* (1 − p s* ) j [ j (Tave + TCRP ) + (Ts + TCRP )]} j =0

∞

≈ p s* (Tave + TCRP )∑ [( j + 1)(1 − p s* ) j ]

(29)

j =0

= Tδ / p s* The probability density function (p.d.f.) of the transmission delay is pd {d = j ⋅ Tδ } = ps* (1 − ps* ) j −1 ,

j > 0.

(30)

The cumulative distribution function (c.d.f.) of the transmission delay is j

pd {d ≤ j ⋅ Tδ } = ∑ [ ps* (1 − ps* )i −1 ] , i =1

J. Jitter

j > 0.

(31)

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Figure 12 presents a comparison of the average delay between k-EC and DCF when the network size varies from 10 to 100 at the data rate of 2 Mbps. The packet size is set to 512 and 1024 bytes, respectively. The simulation time is 100 sec. The figure shows the trend of the delay increasing as the number of contending nodes increases, as expected. This is because more contending nodes lead to less frequent transmissions from a node. It can be observed that the DCF delay is larger than that of the k-EC in any case. Moreover, the disparity between DCF and k-EC increases as the network grows. This is because 1) the average contention resolution period of k-EC is much smaller than that of DCF; 2) the high collision rate of DCF leads to frequent retransmissions, and thus much extra overhead. The low 850

0.10

800

1.0

750

k-EC(Simulation,512) k-EC(Analytical,512) DCF(512) k-EC(Simulation,1024) k-EC(Analytical,1024) DCF(1024)

650 600 500 450

0.06

400 350 300 250

0.8

0.6

k-EC(pdf)

p.d.f.

delay (ms)

550

k-EC(cdf) DCF(cdf)

0.08

c.d.f.

700

CONTI(pdf) DCF(pdf)

0.04

0.4

200 150 100

0.02

50

0.2

0 0

20

40

60

Network size

80

100

0.00 0

Figure 12. Average delay

40

80

120

0.0 200

160

Delay (ms)

Figure 13. Delay distribution (p.d.f. and c.d.f.) 1400

0.10

1200

k-EC(Simulation,512) k-EC(Analytical,512) DCF(512) k-EC(Simulation,1024) k-EC(Analytical,1024) DCF(1024)

0.8

0.06

0.6

0.04

0.4

c.d.f.

800

0.08

p.d.f.

Jitter (ms)

1000

1.0

k-EC(cdf) DCF(cdf)

600

400

k-EC(pdf) DCF(pdf)

0.02

200

0 0

20

40

60

Network size

Figure 14 Average jitter

80

100

0.2

0.00 0

20

40

60

80

Jitter (ms)

Figure 15. Jitter distribution

100

120

0.0 140

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IMPLEMENTATION

The k-EC mechanism is quite simple but very efficient. Since there is no specific content included in the energy pulse, it does not need to be decoded. This simplifies the implementation and makes it possible to implement the k-EC mechanism in the physical layer. If the k-EC mechanism is implemented in the physical layer, the MAC protocol can be released from the task of contention resolution and is free to focus on QoS issues. This will dramatically reduce the MAC complexity and enhance the system performance. We define the following two primitives: PHY-MEDIUM.request and PHY-MEDIUM.confirm that need to be added to the PHY service, i.e. PHY-SAP [7], which is provided from the physical layer convergence protocol sublayer to the MAC entity at the station (STA) through a service access point (SAP). A. PHY-MEDIUM.request 1) Function

This primitive is issued by the MAC entity to the PHY to the local PHY sublayer to acquire the medium for data transmission. 2) Semantics of the service primitive

The semantics of the primitive are as follows: PHY-MEDIUM.request This primitive has no parameters. 3) When generated

This primitive will be issued by the MAC sublayer to the PHY entity whenever the MAC sublayer needs to acquire the medium for a transmission. 4) Effect of receipt

The effect of receipt of this primitive by the PHY entity will be to start the contention resolution procedure.

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This primitive is issued by the PHY sublayer to the local MAC entity to confirm the acquisition of the medium. The PHY sublayer will issue this primitive in response to every PHYMEDIUM.request primitive issued by the MAC sublayer after it successfully acquires the medium through the k-EC scheme. 2) Semantics of the service primitive

The semantics of the primitive are as follows: PHY-MEDUIM.confirm There are no parameters associated with this primitive. 3) When generated

This primitive will be issued by the PHY sublayer to the MAC entity when the PHY has acquired the medium after a PHY-MEDIUM.request from the MAC entity. 4) Effect of receipt

The receipt of this primitive by the MAC entity will cause the MAC to send a PHYTXSTART.request [7], which is one of the primitives of the PHY-SAP service, to the local PHY entity in order to begin the transmission of a MAC sublayer protocol data unit (MPDU). With the above primitives, the task of the contention resolution for the MAC is just to send a PHY-MEDIUM.request to the PHY entity and wait for the PHY-MEDIUM.confirm from the PHY entity. The MAC is now free to focus on other (e.g. QoS) issues. VI.

CONCLUSIONS

Inspired by the efficiency of the elimination tournament, we have devised a novel contention resolution scheme, termed. k-round elimination contention (k-EC) scheme for wireless LAN MAC protocols. We have proved that the optimal single round length (m), which provides the lowest collision rate, is 3 under a bounded contention resolution period (CRP). This optimal value
