82	5. Evaluation of IEEE 802.11e with the IEEE 802.11a Physical Layer

be the stationary distributions of all states of the backoff process s (t ). The transition probabilities in this model can be easily derived from the definitions given earlier in this section. At a particular slot, the probability that the system changes to one of the three states “H,” “M,” “L” is given by the probability that at least one backoff entity of this AC accesses the channel at this slot, and none of the backoff entities of the other ACs access this same slot:

Pslot ,H

Pslot ,M

Pslot ,L

=ξslot [High] (1 −ξslot [Medium]) (1 −ξslot [Low]),

=ξslot [Medium] (1 −ξslot [High]) (1 −ξslot [Low]),

=ξslot [Low] (1 −ξslot [High]) (1 −ξslot [Medium]).

The probability that at a particular slot, a collision of frames transmitted by backoff entities of different ACs occurs, is given by

P

=ξ

slot [

High

]

ξ

slot [

Medium

]

1 −ξ

slot [

Low

])

+

slot ,C

(

ξslot [High] ξslot [Low] (1 −ξslot [Medium])+

ξslot [Medium] ξslot [Low] (1 −ξslot [High])+

ξslot [High] ξslot [Medium] ξslot [Low].

Finally, the probability that the system changes from one idle slot to the next idle slot state is derived from the probability that no backoff entity attempts to transmit at this slot:

			0,	slot >CWmax
Pslot ,slot +1	=				else .
		1 −(Pslot ,H + Pslot ,M + Pslot ,L + Pslot ,C ),

Note that, depending on the position of the backoff windows, some transition probabilities are 0 for the respective AC:

(slot < AIFSN [AC ])or (slot >CWmax [AC ]) Pslot , AC = 0 .

5.1.3.2.3The Priority Vector

The stationary distributions of the states of the Markov model are not needed to

calculate the access priorities of			the ACs. Instead, it is sufficient to calculate a
vector that	determines the		transition	probabilities per AC	to	states
{C, H, M, L}from		a particular	idle state	{1, 2, ..., CWmax+1}.	From the
definitions of	the	stationary distributions,		the transition probabilities		from

state “1” to the states “H,” “M,” “L,” and “C” can be derived. These four transition probabilities define the actual priority in channel access. The stationary distribution of state “H” is given by

5.1 HCF Contention-based Channel Access						83
	CWmax +1	slot −1			=: η[AC=High] p1 .
pH = P1,H +	∑	Pslot ,H ∏ Pi ,i +1		p1		(5.6)
	slot =2	i =1
	=: η AC=High
(this defines the relative priority of the AC "High")

In this equation, a new parameter η High is defined that determines the relative priority of the AC “High.” The stationary distributions of the states “M,” “L,” and “C” are similarly defined:

			CWmax +1		slot −1			=: η[Medium] p1
pM	= P1,M + ∑			Pslot ,M	∏ Pi ,i +1		p1		,
			slot =2		i =1
			CWmax	+1	slot −1		p1 =: η[Low] p1,
pL	= P1,L	+	∑	Pslot ,L	∏ Pi ,i +1				(5.7)
			slot =2		i =1
			CWmax +1		slot −1
pC	= P1,C	+	∑	Pslot ,C	∏ Pi ,i +1		p1.
			slot =2		i =1

The priority vector η is found as

η = (ηH ,ηM ,ηL )= ∑η1[AC ](η[High],η[Medium],η[Low]). (5.8)

AC

The stationary distribution p1 is given in the following equation as p1 = pH + pM + pL + pC .

The priority vector η determines the relative priorities of the three ACs. Once the system changes from ongoing transmission to the backoff phase s(t), the system will change to one of the states “H,” “M,” “L” according to the priority vectorη . With the help of the priority vectorη , the saturation throughput

Thrpshare (or the share of capacity) that an arbitrary number of backoff entities of each of the three ACs may achieve when all backoff entities operate in paral-

lel, can be calculated. Any number of backoff entities per AC is possible in this model, and any setup of the EDCF parameters. The achievable saturation throughput Thrpshare for the three ACs is approximated by

		Thrp		[High] η		H
			sat
Thrp	=Thrp	η = Thrp	sat	[Medium] η			M	.	(5.9)
share	sat			[Low] η
		Thrp			L
			sat