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

5.1.3.2Calculation of Access Priorities from the EDCF Parameters

With the assumption of σ -persistent CSMA, it is now possible to derive a method to determine the access priorities from the EDCF parameters. A scenario of three rather than the available number of four ACs is used for the sake of simplicity. The ACs are labeled with “High,” “Medium,” and “Low,” according to their priorities. A fundamental approximation taken here is that, once the characteristics of the backoffs of the ACs are found with the modified Bianchi model, these characteristics are assumed to remain constant even in contention with other ACs.

That means that for example the expected size of the contention window per AC are as found in the isolated scenario, mutual influences between the ACs on this expected size are neglected. Note that this assumption is taken for all ACs. What is determined here is the access priority, not the actual resulting capacity share (throughput). This resulting capacity share is calculated based on the access priorities by considering all ACs.

When calculating the access priorities, care must be taken about the fact that the different ACs start their backoffs at different slots, according to the AIFSN parameter. As a first step, the contention windows are therefore shifted by the AIFSN parameters, hence,

E AIFS [AC ]+CW [AC ] = AIFS [AC ]+ E CW [AC ] = AIFS [AC ]+ σ [AC1 ].

The access probability of the backoff entities of an AC at a certain slot is in the following referred to as ξslot [AC ] with1 ≤ slot ≤ max (CWmax [AC ])+1 .

	0.6							3 backoff entities per AC[higher]								higher pr.
																medium pr.
	0.5	AIFSN[higher pr.]=2						3 backoff entities per AC[medium]								lower pr.
prob(access)								3 backoff entities per AC[lower]
	0.4
	0.3	AIFSN[medium pr.]=2
	0.2								AIFSN[lower pr.]=9
	0.1
	0	34	43	52	61	70	79	88	97	106	115	124	133	142	151	160	169
	25
									slot [ s]

Figure 5.11: Access probability per slot for 3 backoff entities per AC, each AC operating isolated. Three ACs with EDCF parameter sets as defined in Table 5.2. Note that a legacy backoff is assumed, i.e., earliest backoff is DIFS when AIFSN=2.

5.1 HCF Contention-based Channel Access

79

	0.6	AIFSN[higher pr.]=2						8 backoff entities per AC[higher]								higher pr.
																medium pr.
	0.5							8 backoff entities per AC[medium]								lower pr.
prob(access)								8 backoff entities per AC[lower]
		AIFSN[medium pr.]=2
	0.4
	0.3								AIFSN[lower pr.]=9
	0.2
	0.1
	0	34	43	52	61	70	79	88	97	106	115	124	133	142	151	160	169
	25
									slot [ s]

Figure 5.12: Access probability per slot for 8 backoff entities per AC, each AC operating isolated. Three ACs with EDCF parameter sets as defined in Table 5.2.

The largest value of the maximum size of the contention window defines over how many slots the access probabilities are calculated. Usually this is the value of the lowest priority AC. Of course, in saturation, ACs with smaller CWs and thus

typically higher priorities access the channel with probability 1 within their CWs.

The access probability for slot < AIFS [AC ] is ξslot [AC ]= 0 , because for slots earlier than AIFS [AC ], backoff entities of this AC will not access the channel.

However, the access probability for slot >CWmax [AC ]+ AIFS [AC ] is also given byξslot [AC ]= 0 , because for slots later thanCWmax [AC ], backoff enti-

ties of the respective AC will not access the channel neither. It is again emphasized that CWmax [AC ] is in this study defined by not only the EDCF parame-

ters known from 802.11e, but also depending on a number of parameters such as
the RetryCounter [AC ],	the PF [AC ], and	the	initial	contention window
size,CWmin [AC ]7.	See Section 4.2.2.3,	p. 50,	for	the definition of

CWmax [AC ] in 802.11e. Using the assumption explained in the previous sec-

tion, especially Equation (5.4), the access probability to a particular slot follows from the geometric distribution

ξ	[AC ]=1 − 1 −		σ [AC ] 1 −σ [AC ] slot −AIFS[AC ]		N [AC ]	(5.5)
slot		(	(	)	)

if AIFS [AC ]< slot ≤CWmax [AC ], and 0 otherwise.

5.1.3.2.1Markov Chain Analysis

The access probability functions of the three ACs, and thus the share of capacity per AC can be derived from a Markov model, illustrated in Figure 5.13. It represents the process s (t ) of all contending backoff entities of the three considered

7 More parameters than defined in the 802.11e MAC enhancements are evaluated in this thesis.

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

priorities. In what follows, this process is referred to as CSMA regeneration cycle. The system alternates between states representing idle phases during which the backoff phase is ongoing and a busy phase during which at least one backoff entity transmits a frame. Takagi and Kleinrock (1985) call this a regeneration cycle. Each alternation is a “probabilistic replica” (Takagi and Kleinrock, 1985) of the previous alternation.

Four states “C,” “H,” “M,” and “L,” represent the system in the busy phase during ongoing transmissions, and a number of states “1,” “2,”..., “CWmax+1” represent the system during the backoff (idle phase). There is one state for each slot of the backoff, beginning with slot =1 , which is equivalent to AIFSN =1 and thus AIFS =PIFS = 25 µs . According to 802.11e, the earliest time when backoff entities access the channel is one slot after AIFS. Thus, the second slot represents the first possible access time SIFS+2 ×aSlotTime for backoff entities that operate according to the HCF contention-based channel access, without regard to the individually selected AIFSN [AC ] parameter. The access probability per slot of the set of backoff entities of one AC is given by Equation (5.5), The access probability for slots earlier than AIFSN [AC ] is 0.

The last slot possible for access is determined by the value ofCWmax +1 ; it is calculated as the maximum of all contention window sizes per ACs:

CWmax = max (CWmax [High],CWmax [Medium],CWmax [Low]).

Typically, but not necessarily, CWmax =CWmax [Low], since a large value implies a lower priority in channel access. If the backoff entities of one AC operate with a smaller value for CWmax [AC ] than given in Equation (5.5), then the access probability for this slot is set to 0. If at least one backoff entity of the AC “High” attempts to transmit by accessing the channel as the first backoff entity, for example by accessing the channel at the first slot, and if no other backoff entity from the other ACs accesses the channel at this slot or earlier, then the system changes from state slot (idle) to state “H” (busy). At least one high priority frame exchange is then ongoing. Note that this includes collisions of frames transmitted by backoff entities that belong to this priority “High.” The states “M” and “L” represent the busy periods for the ACs “Medium” and “Low,” respectively. However, if more than one backoff entity of different ACs start their transmission attempts at the same slot, a collision of frames transmitted by backoff entities that belong to different ACs occurs and the system changes to the state “C.” From the four states “C,” “H,” “M,” and “L,” the system always transits back to state “1.”

5.1 HCF Contention-based Channel Access

81

C:

inter-AC collision

H:

high priority access

M:

medium priority access

L:

low priority access

1

1

1

1

C

H

M

L

P1,C

P

P1,M

P1,L

1,H

1

P1,2 P

P2,M

P2,L

P2,C

2,H

2

P2,3

Pslot-2, slot-1

P

P

slot-2,L

Pslot-1,C

Pslot-1,H

slot-1,M

slot-1

Pslot-1, slot

P

P

Pslot,C

Pslot,H

slot,M

slot,L

slot

Pslot, slot+1

PCWmax+1,H

PCWmax+1,L

PCWmax+1,M

PCWmax+1,C

PCWmax, CWmax+1

CWmax

+1

CWmax = max(CWmax[AC])

Figure 5.13: State transition diagram for the Markov chain of the CSMA regeneration cycle process. There are states C, H, M, L representing a busy system. There are states 1, 2, 3..., CWmax+1 representing an idle system. Time is progressing in steps of a slot. The state of the chain changes with the state transition probabilities indicated here.

5.1.3.2.2 State Transition Probabilities Let

P {s (t +1)= AC|s (t )= slot}= Pslot , AC , AC H, M, L, P {s (t +1)=C|s (t )= slot}= Pslot ,C ,

P {s (t +1)= slot +1|s (t )= slot}= Pslot ,slot +1, slot =1…CWmax +1 be the transition probabilities as indicated in Figure 5.13, and let

lim P {s (t )= AC}= pAC ,	AC H, M, L,
t →∞
lim P {s (t )=C}= pC ,
t →∞
lim P {s (t )= slot}= pslot ,	slot =1…CWmax +1
t →∞