Delay Analysis of IEEE 802.11e EDCA Under ... - Semantic Scholar
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2007 proceedings.
Delay Analysis of IEEE 802.11e EDCA Under Unsaturated Conditions Jing Liu, Zhisheng Niu Dept. of Electronic Engineering, Tsinghua University, Beijing 100084, China Abstract— With the successful development of IEEE 802.11 based wireless LAN(WLAN), applications with QoS requirements are asked to be provided in WLANs. Because of their delay restrictions, realtime applications should work under unsaturated conditions. In this paper, firstly, traffic models for different kinds of applications are proposed to convert the unsaturated system into an equivalent saturated system and calculated out the queueing delay in the sender buffer; then, a new analysis model is presented to analyze the backoff delay and packet loss rate of all kinds of applications under the IEEE 802.11e Enhanced Distributed Channel Access(EDCA), this model well embodies the function of the Arbitration Inter Frame Space(AIFS) and other EDCA parameters; finally, access delay can be get from the backoff delay and queueing delay. Practical scenarios of Voice over IP(VoIP) and data combined system are simulated. Simulation results show the accuracy and efficiency of our model under unsaturated conditions.
applications, thus, a delay analysis model under unsaturated condition is necessary. In this paper, we consider a cell associated with one AP, IEEE 802.11e WLAN is employed by the cell. Several kinds of access classes are provided by this system, We assume applications of the same kinds of traffic class have the same traffic characteristics. The paper is organized as follows. Section II presents the EDCF mechanisms of 802.11e, the traffic model of different applications and the delay analysis model separately. Section III give out the validation of those models. Section IV give out the conclusions.
I. I NTRODUCTION IEEE 802.11 based wireless LAN has been massively deployed in public and residential places, because of their low cost, simplicity of installation and high data rates. Hence, applications with different QoS requirements are expected to be provided in WLAN. For some realtime applications, delay is the most important QoS parameters. The IEEE 802.11e drafts specify a distributed access mechanism called EDCA(Enhanced Distributed Channel Access) to support service differentiation in MAC layer[1]. It ensures that the packets sent by each mobile station can be differentiated by assigning different access parameters. However, service differentiation can not fully guarantee the QoS requirements of each traffic class because of the shared channel provided by contention-based distributed WLANs. The practical capacity for real-time applications such as VoIP on WLAN is also far below the bandwidth of WLAN because of the PHY and MAC layer overhead and the potential collisions[6]. The increasing of accessed stations will greatly increase the access delay and decrease the QoS of each station, thus delay analysis is important to see how many users can be accept by the system with certain delay requirements. Many papers focus on 802.11 WLAN’s delay analysis and the capacity of Voice on WLAN, reference [7] gives a classic MAC model based on DCF mechanism, reference [3][4][5] give a new delay model on EDCF separately, they all assume a saturated conditions[7][3]. That means stations in the WLAN always have packets waiting to be transmitted. However, the saturated assumption is unlikely to be valid for 802.11 networks which providing realtime applications. For the delay in saturated conditions is too large to satisfied the delay requirements of many real-time
The fundamental access method in IEEE 802.11e EDCA is Enhanced Distributed Coordination Function(EDCF), which is based on Carrier sense multiple access with collision avoidance(CSMA/CA) protocol. With IEEE 802.11e EDCA, transmissions are regulated by the following backoff algorithm. Upon starting the backoff process, a station of Class i initializes its backoff time counter to a random value uniformly distributed in the range [0, CWi − (min) 1], with CWi initially set to CWi . The backoff time counter is decremented once every time interval σ as long as the channel is sensed idle, ”frozen” when a transmission is detected on the channel, and reactivated when the channel is sensed idle again for a period of time equal to AIF Si . The value of σ is a constant defined by the standard, and AIF Si takes a value of the form SIF S + Ai σ, where Short Inter Frame Space(SIF S) is another constant defined by the standard and Ai is a nonnegative integer. The station transmits when the backoff time counter reaches zero. A collision occurs when two or more stations start transmission simultaneously. After each unsuccessful transmission, (max) CWi is doubled, up to a maximum value CWi , and the backoff process is restarted. If the number of failed retries reaches a predetermined retry limit Ri , the packet is discarded. (max) (min) Here we define CWi = 2Mi CWi , and generally Ri is larger than Mi . From the above explanation, it can be seen that the behavior of a station depends on a number of (min) configurable parameters {CWi , Ai , Mi , Ri } that can be set to different values for different Access Class i. Consider a cell with 802.11e EDCA stations, each station belongs to some class i, i ∈ {1, . . . , I} and I as the largest access class index.
II. S YSTEM M ODEL A. MAC Layer Description
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This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2007 proceedings.
The rest of this paper is devoted to the study of the delay as a function of the number of stations and configuration of each AC. B. Traffic Model For a station of AC i, the data buffer can be modeled as a queueing system. Suppose the packet generate interval of access class i is ti , and the backoff delay of a packet of AC i is di , they are all random variables with certain distribution. And the expectation of ti and di is E(di ) and E(ti ) separately. We can simplified the queueing model and suppose ti and di are of poisson distribution. So the queue is a M/M/1 queueing system, and we can get the probability that the queue is not empty as E(di ) . (1) p{L > 0} = E(ti ) Consider a system under unsaturated conditions, and the system has ni stations of AC i. Firstly, many kinds of applications are not always active during the living period, such as some realtime applications have sleep mode or silence (a) periods. So a parameter pi is used to denote the active rate of stations of AC i. Then, at a certain point, not all the active stations have packets to transmit because the packet generate (a) with intervals. So, the number of stations ni which have packets to transmit is a random variable. Supposing the system is in stable states, we can get the the expression of the average (a) of ni as (a) (a) E(di ) . (2) E(ni ) = ni pi E(ti ) Then we can convert an unsaturated system with ni stations to a equivalent saturated system having ni stations. And the two system have the similar delay and packet loss state. With (a) random variable ni and equation 2, ni can be expressed as (a) E(di )
ni = ni pi
+ α. (3) E(ti ) Here α is an amendment on expression of the ni , because (a) the system delay is nonlinear to the active number ni in a (a) short period while the ni doesn’t change, so the long time (a) average delay of a system with ni stations is not just equal (a) to the system with a fixed number E(ni ). And the average queueing delay can also be calculated out as E(di )2 (q) di = . (4) E(ti ) − E(di ) C. Backoff Delay Analysis At each transmission attempt, we assume that each class i packet has common probability pi of involving in collision when it is transmitted. Suppose that a class i station that has involved in l times of collision will select the backoff time counter Bil before transmission. Let Ci denote the number of collisions that a AC i station has involved. Then the expected backoff time counter E[Bi ] is ∞ E[Bil ]P {Ci = l}. (5) E[Bi ] = l=0
The distribution of Ci is l pi (1 − pi ); P {Ci = l} = piRi +1 ;
l ≤ Ri , others.
(6)
After l times collision, the current CWil is set as (min) min(Mi ,l) (min) min(Mi ,l) 2 . For every k ∈ [0, CWi 2 − CWi 1], probability mass function of backoff time counter Bil is derived as 1
P {Bil = k } =
(min) min(Mi ,l) CWi 2
.
(7)
The expectation of Bil is derived as E[Bil ] =
(min) min(Mi ,l)
2
CWi
2
−1
.
(8)
According to equations 6 and 8, 5 is expressed as mi −1 Ri (1 − pi ) 1 ( 2l pli + 2mi pli ) − . 2 2 l=0 l=mi (9) Then, the probability that a station of class i transmits upon a backoff counter decrement can be computed as (min)
E[Bi ] =
CWi
τi =
1 . E[Bi ] + 1
(10)
We define k=k +AIF Si , here k is the backoff number, k is the whole backoff number adding AIF Si . Bi is defined as the set of the class i’s possible value of k in (max) }; Aj is defined as the set {AIF Si , . . . , AIF Si + CWi of classes who’s Bi include j. Stations of classes with larger AIF Si value can’t infect class stations with Bi less than AIF Si . so pi is derived as qik (1 − (1 − τi )ni −1 (1 − τj )nj ). (11) pi = j∈Ak ,j=i
k∈Bi
Here, qik is the probability that the current AC i station’s whole backoff time counter choose k, it is expressed as qik
= P {Bi = k } =
Ri
P {Bil = k }P {Ci = l}
l=0
=
Ri
pli (1 − pi )
(min)
l=log(k /CWi
)
(min) min(Mi ,l) 2
CWi
.
(12)
Set pi ∀i as variables, withe equations 9 and 10 we can compute τi ∀i. Then after compute qk ∀k with equation 12, we can express pi with τi ∀i. Therefore we have I equations on I variables pi , and pi can resolved with numerical techniques, then τi can also be derived. With pi and τi , the average backoff delay di of a nondropped packet of class i can also be derived as follows di =
∞ l=0
P {Ck = l}dil .
(13)
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2007 proceedings.
...
collision
success
success time
:empty slot Fig. 1.
collision nested with transmission and collision because of the AIF Si for different ACs. So, T si and T ci is different with AC i and not equal to the time one transmission or one collision occurs. Define Ttx and Tco is separately the average channel busy time for one transmission and one collision, they can be calculated as
:decreasing point
Component of delay between decrements.
Here dil is the average delay in case of lth retries CWil −1
dil =
{P {Bil = k}
k
dilt }.
(14)
t=0
k=0
Here dilt is the average duration of the time between t-1 and tth backoff counter decrements of a class i packet after the lth collision, as show by 1 dilt = pcit T ci + psit T si + peit σ.
(15)
Here,T c and T s are the average duration between two backoff counter decrements which respectively contains a collision and success of other stations, with the following analysis, we can see they are different with different ACs. While with no transmission, the duration between two decrements is the same with the slot time σ. The probability of the 3 different stages during a decrement can be computed with pi and τi as peit = (1 − τj )nj . (16) j∈At
psit =
(nj τj (1 − τj )nj −1
(1 − τk )nk ).
(17)
k∈At k=j
j∈At
pcit =1 − peit − psit .
(18)
Here for the consider station of AC i, ni =ni − 1, current station is reduced. pei , psi and pci is separately the probability that no statioin transmitting, only one transmitting, and more than one transmitting. In stages of success transmission and collision, the backoff counter will freeze. Consider a station of class i, during the first Ai − A0 slot times after SIF S, the backoff counter of AC i is not unfreeze, only the class j that j < i can decrease and transmit. So we define the probability of the 3 stages during the first Ai − A0 slot times as pei
=
psi =
Ai −A0
k=1
j∈Ak
A i −A0 k−1
{
k=1
(1 − τj )nj .
(nj τj (1 − τj )nj −1
pci =1 − pei − psi .
(22)
Tco =H + Tdata + τ + SIF S.
(23)
Here H is the physical overhead of a packet, τ is the propagation delay. After the transmission or collision, the channel is idle, but the backoff counter will keep freeze for Ai slots. Define Coi = Tco + Ai σ and Sui = Ttx + Ai σ as the time when the channel will be idle till the AC i’s backoff counter unfreezes, and define X the average additional time duration if the channel will busy again during the AIF Ss, X can be expressed and calculated out by a nested equation as X = (Coi + X)pci + (Sui + X)psi .
(24)
Then the Tc and Ts is derived following Coi pci + Sui psi . 1 − pci − psi Coi pci + Sui psi . T si = Sui + X = Sui + 1 − pci − psi
T ci = Coi + X = Coi +
(25) (26)
With the given ni ∀i the pi ∀i and τi ∀i calculated beforehand, we can calculate out the value of pcit , psit , peit , pci , psi and pei , then using them to get the value of T si and T ci , finally using all this values and equation 15, 14 and 13 calculate out the average backoff delay di of class i. And then using with equation 4 the whole access delay is get. III. N UMERICAL AND S IMULATION R ESULTS A. Validation of Traffic Model In the analysis, consider a single cell providing VoIP and data combined service. The WLAN parameters of the cell are shown in table II.
(19)
(1 − τj )nj
t=1 j∈At
j∈Ak
Ttx =H + Tdata + 2τ + 2SIF S + TACK .
(1 − τt )nt )}.
(20)
t∈Ak ,t=j
(21)
Here pei , psi and pci is separately the probability that no higher priority stations transmitting, only one transmitting, and more than one transmitting. Fore analysis shows that between lower priority’s two decrements can have the probability that transmission and
Fig. 2.
4 state Markov chain for conversation speech.
A practical voice traffic model model is presented as an example using the conversation model specified in the ITU P.59 recommendation[2]. It models the conversation between two users A and B as a four state Markov chain. The duration of each state is mutually independent and identically distributed
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2007 proceedings.
exponential random variables. With those model and the giving experiential value, we can get the traffic characteristic of voice and listed as table I with data traffic. TABLE I PARAMETERS OF VOICE AND DATA APPLICATIONS parameters packets interval Ti (voice) average packet length(voice) active ratio(voice) mean packets length(data) active ratio(data)
value 20 24 0.38 500 0.45
units ms Bytes / Bytes /
TABLE II PARAMETERS OF 802.11 E parameters slot time SIFS PHY header ACK Mandatory data rate Data rate CW1mim (voice) CW2mim (data) A1 (voice) A2 (data) m1 m2 R
value 20 10 192/96 14 1 11 16 32 1 2 2 6 6
units µs µs µs Bytes Mbps Mbps / / / / / / /
First we validate the voice traffic model under unsaturated conditions. Two scenarios is setting, one is voice users only, the other is voice with fixed number of background data users. We simulate the system in saturated conditions, plot the delay with voice user number n as x-axis; an unsaturated system with n users is also simulated, after calculated out the delay, we transfer the n into corresponds n, using the equation 3 with pa and Ti in table I, then plot them. We can observed that, two curve is nearly the same when the delay is below 800 slots. Ti is set as 20ms, and the interval is 1000 slots, when the delay beyond 800 slots, the system is approach saturated condition, so the model for unsaturated system no longer match the simulation. Then we validate the data model under unsaturated conditions. Data model only using the active factors without intervals. so the two curve almost exactly coincide with each other as show by figure 4. Simulation shows the accuracy of our traffic model. B. Validation of Delay Analysis Model Using the WLAN parameters list in table II, we compare the results of our analysis model with the simulation and the bianchi model in reference [7]. We can see that the upper three curve is the delay curve for data applications, the lower three curve is for voice application, and the x-axis N is the total number of two kinds of stations, and the proportion of voice stations and data stations is 1:1. Two cluster of curve nearly the same, but our delay analysis model is more exactly in unsaturated conditions, it due to the
Fig. 3.
validation of voice traffic model.
Fig. 4.
Validation of data traffic model.
more consideration on the EDCF mechanism especially the AIF Si . Nested transmissions and collisions of voice stations may occurs during the AIF Si of data stations. So we can see with our model the voice application delay is a little lower and the data application delay grows a little faster than the compared bianchi model and closer to the simulation results. This group of results shows the accuracy of the proposed delay analysis model. We also compare the analysis model with simulation under different ratio of voice stations and data stations. Figure 6 show the system with the proportion of voice stations and data stations as 2:3. Figure 7 have the ratio as 2:1. We can see that increasing of voice stations will make the delay of data stations increase more quickly, while, the infect of data stations’s number to the voice station’s delay is slighter. It shows 802.11e EDCA mechanisms can well differential classes. We can also get the throughput of the system either by analysis and simulation. we can also find out that in unsaturated conditions, the analytical results coincide well with the simulation results. With the increasing of the user number, the system gradually come into the saturated state, the results of
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2007 proceedings.
our model no longer coincided with the simulations.
Fig. 5.
validation of delay analysis model. Fig. 8.
Throughput:analysis versus simulation
IV. C ONCLUSION
Fig. 6.
Delay:analysis versus simulation.(voice:data=2:3)
In this paper, firstly, we proposed queueing models to describe the characteristics of applications under unsaturated conditions, and convert the unsaturated system into a equivalent saturated system. Then we proposed a backoff delay analysis model for 802.11e EDCA mechanism. Our new delay analysis model consider the nested transmission and collision of higher priority stations during the AIF S slots of lower priority AC i, well embodies the AIF S’s function to differential different ACs; the new model also consider the different collision probability of the first AIF S slots and the following slots, so this model well accord to the practical system. Simulations in different scenarios is done to validate our models. The results of our model coincide with the simulation results under unsaturated conditions, and well embodies the different parameters’ effect on the system’s state. Those results shows our delay analysis model is fit for the delay analysis for unsaturated WLAN systems providing realtime applications. R EFERENCES
Fig. 7.
Delay:analysis versus simulation.(voice:data=2:1)
[1] Part 11: Wireless LAN Medium Access Control(MAC) and Physical Layer(PHY) specifications, IEEE Draft Supplement to IEEE Std 802.11, Rev. 802.11e/D9.0, July 2004. [2] ”Artificial Conversational Speech”, ITU Recommendation P.59,March 1993. [3] A. Banchs, L. Vollero, ”A Delay Model for IEEE 802.11e EDCA,” IEEE Communications Letters, vol. 9, n. 6, pp. 508 - 510., Jun. 2005. [4] Y. Kuo, C. Lu, E.H. Wu, and G. Chen, “An Admission Control Strategy for Differentiated Services in IEEE 802.11,” in Proc. IEEE Global Telecommunications Conf., vol.2, pp. 707 - 712., Dec. 2003. [5] Yang Xiao, ”Enhanced DCF of IEEE 802.11e to support QoS”, Wireless Communications and Networking, Vol. 2, pp. 1291 - 1296., 16-20 March 2003. [6] Medepalli, K.; Gopalakrishnan, P.; Famolari, D.; Kodama, T.; ”Voice Capacity of IEEE 802.11b, 802.11a and 802.11g Wireless LANs”, in Proc. IEEE Globecom’04, Volume 3, 29 Nov.-3 Dec. 2004 Page(s):1549 - 1553 Vol.3. [7] Giuseppe Bianchi, ”Performance Analysis of the IEEE 802.11 Distributed Coordination Function”, IEEE Journal on Selected Areas in Communications, Volume 18, No.3, pp. 535 - 547, March 2000.
Delay Analysis of IEEE 802.11e EDCA Under Unsaturated Conditions Jing Liu, Zhisheng Niu Dept. of Electronic Engineering, Tsinghua University, Beijing 100084, China Abstract— With the successful development of IEEE 802.11 based wireless LAN(WLAN), applications with QoS requirements are asked to be provided in WLANs. Because of their delay restrictions, realtime applications should work under unsaturated conditions. In this paper, firstly, traffic models for different kinds of applications are proposed to convert the unsaturated system into an equivalent saturated system and calculated out the queueing delay in the sender buffer; then, a new analysis model is presented to analyze the backoff delay and packet loss rate of all kinds of applications under the IEEE 802.11e Enhanced Distributed Channel Access(EDCA), this model well embodies the function of the Arbitration Inter Frame Space(AIFS) and other EDCA parameters; finally, access delay can be get from the backoff delay and queueing delay. Practical scenarios of Voice over IP(VoIP) and data combined system are simulated. Simulation results show the accuracy and efficiency of our model under unsaturated conditions.
applications, thus, a delay analysis model under unsaturated condition is necessary. In this paper, we consider a cell associated with one AP, IEEE 802.11e WLAN is employed by the cell. Several kinds of access classes are provided by this system, We assume applications of the same kinds of traffic class have the same traffic characteristics. The paper is organized as follows. Section II presents the EDCF mechanisms of 802.11e, the traffic model of different applications and the delay analysis model separately. Section III give out the validation of those models. Section IV give out the conclusions.
I. I NTRODUCTION IEEE 802.11 based wireless LAN has been massively deployed in public and residential places, because of their low cost, simplicity of installation and high data rates. Hence, applications with different QoS requirements are expected to be provided in WLAN. For some realtime applications, delay is the most important QoS parameters. The IEEE 802.11e drafts specify a distributed access mechanism called EDCA(Enhanced Distributed Channel Access) to support service differentiation in MAC layer[1]. It ensures that the packets sent by each mobile station can be differentiated by assigning different access parameters. However, service differentiation can not fully guarantee the QoS requirements of each traffic class because of the shared channel provided by contention-based distributed WLANs. The practical capacity for real-time applications such as VoIP on WLAN is also far below the bandwidth of WLAN because of the PHY and MAC layer overhead and the potential collisions[6]. The increasing of accessed stations will greatly increase the access delay and decrease the QoS of each station, thus delay analysis is important to see how many users can be accept by the system with certain delay requirements. Many papers focus on 802.11 WLAN’s delay analysis and the capacity of Voice on WLAN, reference [7] gives a classic MAC model based on DCF mechanism, reference [3][4][5] give a new delay model on EDCF separately, they all assume a saturated conditions[7][3]. That means stations in the WLAN always have packets waiting to be transmitted. However, the saturated assumption is unlikely to be valid for 802.11 networks which providing realtime applications. For the delay in saturated conditions is too large to satisfied the delay requirements of many real-time
The fundamental access method in IEEE 802.11e EDCA is Enhanced Distributed Coordination Function(EDCF), which is based on Carrier sense multiple access with collision avoidance(CSMA/CA) protocol. With IEEE 802.11e EDCA, transmissions are regulated by the following backoff algorithm. Upon starting the backoff process, a station of Class i initializes its backoff time counter to a random value uniformly distributed in the range [0, CWi − (min) 1], with CWi initially set to CWi . The backoff time counter is decremented once every time interval σ as long as the channel is sensed idle, ”frozen” when a transmission is detected on the channel, and reactivated when the channel is sensed idle again for a period of time equal to AIF Si . The value of σ is a constant defined by the standard, and AIF Si takes a value of the form SIF S + Ai σ, where Short Inter Frame Space(SIF S) is another constant defined by the standard and Ai is a nonnegative integer. The station transmits when the backoff time counter reaches zero. A collision occurs when two or more stations start transmission simultaneously. After each unsuccessful transmission, (max) CWi is doubled, up to a maximum value CWi , and the backoff process is restarted. If the number of failed retries reaches a predetermined retry limit Ri , the packet is discarded. (max) (min) Here we define CWi = 2Mi CWi , and generally Ri is larger than Mi . From the above explanation, it can be seen that the behavior of a station depends on a number of (min) configurable parameters {CWi , Ai , Mi , Ri } that can be set to different values for different Access Class i. Consider a cell with 802.11e EDCA stations, each station belongs to some class i, i ∈ {1, . . . , I} and I as the largest access class index.
II. S YSTEM M ODEL A. MAC Layer Description
1525-3511/07/$25.00 ©2007 IEEE
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2007 proceedings.
The rest of this paper is devoted to the study of the delay as a function of the number of stations and configuration of each AC. B. Traffic Model For a station of AC i, the data buffer can be modeled as a queueing system. Suppose the packet generate interval of access class i is ti , and the backoff delay of a packet of AC i is di , they are all random variables with certain distribution. And the expectation of ti and di is E(di ) and E(ti ) separately. We can simplified the queueing model and suppose ti and di are of poisson distribution. So the queue is a M/M/1 queueing system, and we can get the probability that the queue is not empty as E(di ) . (1) p{L > 0} = E(ti ) Consider a system under unsaturated conditions, and the system has ni stations of AC i. Firstly, many kinds of applications are not always active during the living period, such as some realtime applications have sleep mode or silence (a) periods. So a parameter pi is used to denote the active rate of stations of AC i. Then, at a certain point, not all the active stations have packets to transmit because the packet generate (a) with intervals. So, the number of stations ni which have packets to transmit is a random variable. Supposing the system is in stable states, we can get the the expression of the average (a) of ni as (a) (a) E(di ) . (2) E(ni ) = ni pi E(ti ) Then we can convert an unsaturated system with ni stations to a equivalent saturated system having ni stations. And the two system have the similar delay and packet loss state. With (a) random variable ni and equation 2, ni can be expressed as (a) E(di )
ni = ni pi
+ α. (3) E(ti ) Here α is an amendment on expression of the ni , because (a) the system delay is nonlinear to the active number ni in a (a) short period while the ni doesn’t change, so the long time (a) average delay of a system with ni stations is not just equal (a) to the system with a fixed number E(ni ). And the average queueing delay can also be calculated out as E(di )2 (q) di = . (4) E(ti ) − E(di ) C. Backoff Delay Analysis At each transmission attempt, we assume that each class i packet has common probability pi of involving in collision when it is transmitted. Suppose that a class i station that has involved in l times of collision will select the backoff time counter Bil before transmission. Let Ci denote the number of collisions that a AC i station has involved. Then the expected backoff time counter E[Bi ] is ∞ E[Bil ]P {Ci = l}. (5) E[Bi ] = l=0
The distribution of Ci is l pi (1 − pi ); P {Ci = l} = piRi +1 ;
l ≤ Ri , others.
(6)
After l times collision, the current CWil is set as (min) min(Mi ,l) (min) min(Mi ,l) 2 . For every k ∈ [0, CWi 2 − CWi 1], probability mass function of backoff time counter Bil is derived as 1
P {Bil = k } =
(min) min(Mi ,l) CWi 2
.
(7)
The expectation of Bil is derived as E[Bil ] =
(min) min(Mi ,l)
2
CWi
2
−1
.
(8)
According to equations 6 and 8, 5 is expressed as mi −1 Ri (1 − pi ) 1 ( 2l pli + 2mi pli ) − . 2 2 l=0 l=mi (9) Then, the probability that a station of class i transmits upon a backoff counter decrement can be computed as (min)
E[Bi ] =
CWi
τi =
1 . E[Bi ] + 1
(10)
We define k=k +AIF Si , here k is the backoff number, k is the whole backoff number adding AIF Si . Bi is defined as the set of the class i’s possible value of k in (max) }; Aj is defined as the set {AIF Si , . . . , AIF Si + CWi of classes who’s Bi include j. Stations of classes with larger AIF Si value can’t infect class stations with Bi less than AIF Si . so pi is derived as qik (1 − (1 − τi )ni −1 (1 − τj )nj ). (11) pi = j∈Ak ,j=i
k∈Bi
Here, qik is the probability that the current AC i station’s whole backoff time counter choose k, it is expressed as qik
= P {Bi = k } =
Ri
P {Bil = k }P {Ci = l}
l=0
=
Ri
pli (1 − pi )
(min)
l=log(k /CWi
)
(min) min(Mi ,l) 2
CWi
.
(12)
Set pi ∀i as variables, withe equations 9 and 10 we can compute τi ∀i. Then after compute qk ∀k with equation 12, we can express pi with τi ∀i. Therefore we have I equations on I variables pi , and pi can resolved with numerical techniques, then τi can also be derived. With pi and τi , the average backoff delay di of a nondropped packet of class i can also be derived as follows di =
∞ l=0
P {Ck = l}dil .
(13)
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2007 proceedings.
...
collision
success
success time
:empty slot Fig. 1.
collision nested with transmission and collision because of the AIF Si for different ACs. So, T si and T ci is different with AC i and not equal to the time one transmission or one collision occurs. Define Ttx and Tco is separately the average channel busy time for one transmission and one collision, they can be calculated as
:decreasing point
Component of delay between decrements.
Here dil is the average delay in case of lth retries CWil −1
dil =
{P {Bil = k}
k
dilt }.
(14)
t=0
k=0
Here dilt is the average duration of the time between t-1 and tth backoff counter decrements of a class i packet after the lth collision, as show by 1 dilt = pcit T ci + psit T si + peit σ.
(15)
Here,T c and T s are the average duration between two backoff counter decrements which respectively contains a collision and success of other stations, with the following analysis, we can see they are different with different ACs. While with no transmission, the duration between two decrements is the same with the slot time σ. The probability of the 3 different stages during a decrement can be computed with pi and τi as peit = (1 − τj )nj . (16) j∈At
psit =
(nj τj (1 − τj )nj −1
(1 − τk )nk ).
(17)
k∈At k=j
j∈At
pcit =1 − peit − psit .
(18)
Here for the consider station of AC i, ni =ni − 1, current station is reduced. pei , psi and pci is separately the probability that no statioin transmitting, only one transmitting, and more than one transmitting. In stages of success transmission and collision, the backoff counter will freeze. Consider a station of class i, during the first Ai − A0 slot times after SIF S, the backoff counter of AC i is not unfreeze, only the class j that j < i can decrease and transmit. So we define the probability of the 3 stages during the first Ai − A0 slot times as pei
=
psi =
Ai −A0
k=1
j∈Ak
A i −A0 k−1
{
k=1
(1 − τj )nj .
(nj τj (1 − τj )nj −1
pci =1 − pei − psi .
(22)
Tco =H + Tdata + τ + SIF S.
(23)
Here H is the physical overhead of a packet, τ is the propagation delay. After the transmission or collision, the channel is idle, but the backoff counter will keep freeze for Ai slots. Define Coi = Tco + Ai σ and Sui = Ttx + Ai σ as the time when the channel will be idle till the AC i’s backoff counter unfreezes, and define X the average additional time duration if the channel will busy again during the AIF Ss, X can be expressed and calculated out by a nested equation as X = (Coi + X)pci + (Sui + X)psi .
(24)
Then the Tc and Ts is derived following Coi pci + Sui psi . 1 − pci − psi Coi pci + Sui psi . T si = Sui + X = Sui + 1 − pci − psi
T ci = Coi + X = Coi +
(25) (26)
With the given ni ∀i the pi ∀i and τi ∀i calculated beforehand, we can calculate out the value of pcit , psit , peit , pci , psi and pei , then using them to get the value of T si and T ci , finally using all this values and equation 15, 14 and 13 calculate out the average backoff delay di of class i. And then using with equation 4 the whole access delay is get. III. N UMERICAL AND S IMULATION R ESULTS A. Validation of Traffic Model In the analysis, consider a single cell providing VoIP and data combined service. The WLAN parameters of the cell are shown in table II.
(19)
(1 − τj )nj
t=1 j∈At
j∈Ak
Ttx =H + Tdata + 2τ + 2SIF S + TACK .
(1 − τt )nt )}.
(20)
t∈Ak ,t=j
(21)
Here pei , psi and pci is separately the probability that no higher priority stations transmitting, only one transmitting, and more than one transmitting. Fore analysis shows that between lower priority’s two decrements can have the probability that transmission and
Fig. 2.
4 state Markov chain for conversation speech.
A practical voice traffic model model is presented as an example using the conversation model specified in the ITU P.59 recommendation[2]. It models the conversation between two users A and B as a four state Markov chain. The duration of each state is mutually independent and identically distributed
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2007 proceedings.
exponential random variables. With those model and the giving experiential value, we can get the traffic characteristic of voice and listed as table I with data traffic. TABLE I PARAMETERS OF VOICE AND DATA APPLICATIONS parameters packets interval Ti (voice) average packet length(voice) active ratio(voice) mean packets length(data) active ratio(data)
value 20 24 0.38 500 0.45
units ms Bytes / Bytes /
TABLE II PARAMETERS OF 802.11 E parameters slot time SIFS PHY header ACK Mandatory data rate Data rate CW1mim (voice) CW2mim (data) A1 (voice) A2 (data) m1 m2 R
value 20 10 192/96 14 1 11 16 32 1 2 2 6 6
units µs µs µs Bytes Mbps Mbps / / / / / / /
First we validate the voice traffic model under unsaturated conditions. Two scenarios is setting, one is voice users only, the other is voice with fixed number of background data users. We simulate the system in saturated conditions, plot the delay with voice user number n as x-axis; an unsaturated system with n users is also simulated, after calculated out the delay, we transfer the n into corresponds n, using the equation 3 with pa and Ti in table I, then plot them. We can observed that, two curve is nearly the same when the delay is below 800 slots. Ti is set as 20ms, and the interval is 1000 slots, when the delay beyond 800 slots, the system is approach saturated condition, so the model for unsaturated system no longer match the simulation. Then we validate the data model under unsaturated conditions. Data model only using the active factors without intervals. so the two curve almost exactly coincide with each other as show by figure 4. Simulation shows the accuracy of our traffic model. B. Validation of Delay Analysis Model Using the WLAN parameters list in table II, we compare the results of our analysis model with the simulation and the bianchi model in reference [7]. We can see that the upper three curve is the delay curve for data applications, the lower three curve is for voice application, and the x-axis N is the total number of two kinds of stations, and the proportion of voice stations and data stations is 1:1. Two cluster of curve nearly the same, but our delay analysis model is more exactly in unsaturated conditions, it due to the
Fig. 3.
validation of voice traffic model.
Fig. 4.
Validation of data traffic model.
more consideration on the EDCF mechanism especially the AIF Si . Nested transmissions and collisions of voice stations may occurs during the AIF Si of data stations. So we can see with our model the voice application delay is a little lower and the data application delay grows a little faster than the compared bianchi model and closer to the simulation results. This group of results shows the accuracy of the proposed delay analysis model. We also compare the analysis model with simulation under different ratio of voice stations and data stations. Figure 6 show the system with the proportion of voice stations and data stations as 2:3. Figure 7 have the ratio as 2:1. We can see that increasing of voice stations will make the delay of data stations increase more quickly, while, the infect of data stations’s number to the voice station’s delay is slighter. It shows 802.11e EDCA mechanisms can well differential classes. We can also get the throughput of the system either by analysis and simulation. we can also find out that in unsaturated conditions, the analytical results coincide well with the simulation results. With the increasing of the user number, the system gradually come into the saturated state, the results of
This full text paper was peer reviewed at the direction of IEEE Communications Society subject matter experts for publication in the WCNC 2007 proceedings.
our model no longer coincided with the simulations.
Fig. 5.
validation of delay analysis model. Fig. 8.
Throughput:analysis versus simulation
IV. C ONCLUSION
Fig. 6.
Delay:analysis versus simulation.(voice:data=2:3)
In this paper, firstly, we proposed queueing models to describe the characteristics of applications under unsaturated conditions, and convert the unsaturated system into a equivalent saturated system. Then we proposed a backoff delay analysis model for 802.11e EDCA mechanism. Our new delay analysis model consider the nested transmission and collision of higher priority stations during the AIF S slots of lower priority AC i, well embodies the AIF S’s function to differential different ACs; the new model also consider the different collision probability of the first AIF S slots and the following slots, so this model well accord to the practical system. Simulations in different scenarios is done to validate our models. The results of our model coincide with the simulation results under unsaturated conditions, and well embodies the different parameters’ effect on the system’s state. Those results shows our delay analysis model is fit for the delay analysis for unsaturated WLAN systems providing realtime applications. R EFERENCES
Fig. 7.
Delay:analysis versus simulation.(voice:data=2:1)
[1] Part 11: Wireless LAN Medium Access Control(MAC) and Physical Layer(PHY) specifications, IEEE Draft Supplement to IEEE Std 802.11, Rev. 802.11e/D9.0, July 2004. [2] ”Artificial Conversational Speech”, ITU Recommendation P.59,March 1993. [3] A. Banchs, L. Vollero, ”A Delay Model for IEEE 802.11e EDCA,” IEEE Communications Letters, vol. 9, n. 6, pp. 508 - 510., Jun. 2005. [4] Y. Kuo, C. Lu, E.H. Wu, and G. Chen, “An Admission Control Strategy for Differentiated Services in IEEE 802.11,” in Proc. IEEE Global Telecommunications Conf., vol.2, pp. 707 - 712., Dec. 2003. [5] Yang Xiao, ”Enhanced DCF of IEEE 802.11e to support QoS”, Wireless Communications and Networking, Vol. 2, pp. 1291 - 1296., 16-20 March 2003. [6] Medepalli, K.; Gopalakrishnan, P.; Famolari, D.; Kodama, T.; ”Voice Capacity of IEEE 802.11b, 802.11a and 802.11g Wireless LANs”, in Proc. IEEE Globecom’04, Volume 3, 29 Nov.-3 Dec. 2004 Page(s):1549 - 1553 Vol.3. [7] Giuseppe Bianchi, ”Performance Analysis of the IEEE 802.11 Distributed Coordination Function”, IEEE Journal on Selected Areas in Communications, Volume 18, No.3, pp. 535 - 547, March 2000.
