4.5 DDCF Simulation
4.5.5 DDCF Analytical Model
In this section, an analytical model of the DDCF protocol is proposed. The DDCF priority mechanism assigns different MAC parameters (contention window, inter- frame space) to each node according to the role assigned by the clustering scheme. The DDCF scheme works in a similar way than the 802.11e EDCA scheme, although it provides differentiated access between nodes rather than between data flows. For this reasons, the analytical model proposed here follows the same approach of the 802.11e EDCA analytical model described in [Xia04, EO05].
Chapter 4. MAC and Clustering Integration in MANETs 67
from the model proposed by Bianchi [Bia00] to calculate saturate throughput of the legacy 802.11 DCF protocol. Xiao [Xia04] proposes an analytical model of the 802.11e EDCA MAC protocol, by taking into account the role of variable contention windows, but without considering the role of variable interframe spaces. The ana- lytical model described in [EO05] enhances the Xiao’s model by considering the role of variable interframe spaces, and by predicting the performance in both saturated and non-saturated network conditions.
The analytical model of the DDCF scheme is based on the works described
in [Xia04, EO05]. Without loss of generality, the model proposed here uses the
following assumptions:
• all the nodes are inside a single domain of collision. The multi-hop environ- ment is not taken into account;
• each node has always a packet to transmit, i.e. only the saturation case is considered;
• the effect of the retry retransmission limit is not evaluated, i.e. each packet is retransmitted just one time after the contention window has reached the CWM AX value;
• the post-backoff mechanism is not modelled;
Let i={0,1,2,3} denote the Priority Levels (PL) defined in Table 4.1 and assigned by the AC Clustering scheme. We consider a network composed by N nodes, where ni represents the number of nodes of priority i, andP3i=0ni = N . Wi,j denotes the
the contention window size for a node of class i in the backoff stage j, i.e. after the j-th unsuccessful retransmission. Hence, Wi,0 = CWmin,i, where the value of
CWmin,i and CWmax,i are shown in Table 4.1.
Figure 4.21 illustrates the Markov chain for a node with priority i. Each state of the Markov chain is represented by a tuple < i, j, k >, where:
68 Chapter 4. MAC and Clustering Integration in MANETs
i,0,0 i,0,1 i,0,2 i,0,Wi,0-1
i,1,0 i,1,0 i,1,2
i,j,0 i,j,1 i,j,2
i,0,Wi,1-1
i,j,Wi,j-1
i,M,0 i,M,1 i,M,2 i,M,Wi,j-1
...
...
...
...
pi/Wi,1 pi/Wi,1 pi/Wi,1 pi/Wi,1 pi/Wi,2 pi/Wi,2 pi/Wi,2 pi/Wi,2 1-pi* 1-pi* pi* pi* pi* 1-pi* pi* pi* pi* 1-pi* 1-pi* pi* pi* pi* pi* pi* pi* 1-pi* 1-pi* 1-pi* DROPFigure 4.21: DDCF Markov chain
• i is the class priority assigned by the clustering scheme; • j is the current backoff stage;
• k is the current value of the backoff window in stage j.
Let τi indicate the probability of transmission in a slot, pi the probability to find
the channel busy while transmitting and p∗i the probability to find the channel busy during the backoff procedure. The probability p∗i depends on the setting of the interframe space (AIF S[i]), and can be approximated as [EO05]:
p∗i = min 1, pb+ AIF S[i] · pb 1 − τi (4.4) The probability pi captures the condition where a node of class i attempts to trans-
mit while at least one node is transmitting:
pi = 1 − " (1 − τi)ni −1 · 3 Y j=0,j6=i (1 − τj)nj # (4.5)
Chapter 4. MAC and Clustering Integration in MANETs 69
In general, let pb indicate the probability the channel is busy:
pb = 1 − 3
Y
j=0
(1 − τj)nj (4.6)
Based on pi, pi,sdenotes the probability that a packet from any of the node with
class i is transmitted successfully in a time slot:
pi,s= niτi (1 − τi) 3 Y c=0 (1 − τc) nc (4.7) The probability of a successful transmission for all the priority levels is ps, with
ps =P3i=0pi,s.
Let b(i, j, k) denote the state distribution for state < i, j, k >. From chain regularities, we get:
b(i, j, k) = pi Wi,j
· b(i, j − 1, 0) + (1 − p∗i) · b(i, j, k + 1) (4.8)
b(i, j, 0) = pi· b(i, j − 1, 0) (4.9)
from which b(i, j, k) = Wi,j−k Wi,j·(1−p∗i) · p
j
i · b(i, 0, 0). At the same time, τi represents
the probability to be in a state < i, j, 0 >, and can be derived as follows:
τi = 7
X
j=0
bi,j,0 (4.10)
The value of τi, pi, p∗i for each i ∈ {0, 1, 2, 3} can be numerically computed by solving
the system composed by equations4.5,4.10and by the conditionsP
i,j,kb(i, j, k) = 1.
For each priority class i, the throughput for class Tican be written as the average
real-time duration of a successfully transmitted packet by the average real-time duration of a ”logical” slot [Xia04, EO05]:
Ti =
pi,s· Ts
(1 − pb) · σ + ps· Ts+ (pb− ps) · Tc
(4.11) where the value of σ, Ts, Tc denotes the value of an empty slot, the average time to
70 Chapter 4. MAC and Clustering Integration in MANETs 0 100000 200000 300000 400000 500000 600000 700000 800000 10 20 30 40 50 60 70 80 90 100 Goodput (bit/sec) Number of stations
DDCF Goodput, Analytical vs Simulation, Distribution A Simulation, Priority 0 Analytical, Priority 0 Simulation, Priority 1 Analytical, Priority 1 Simulation, Priority 2 Analytical, Priority 2 Simulation, Priority 3 Analytical, Priority 3
Figure 4.22: DDCF, Analytical Model vs Simulation, Distribution A
0 100000 200000 300000 400000 500000 600000 700000 800000 10 20 30 40 50 60 70 80 90 100 Goodput (bit/sec) Number of stations
DDCF Goodput, Analytical vs Simulation, Distribution B Simulation, Priority 0 Analytical, Priority 0 Simulation, Priority 1 Analytical, Priority 1 Simulation, Priority 2 Analytical, Priority 2 Simulation, Priority 3 Analytical, Priority 3
Chapter 4. MAC and Clustering Integration in MANETs 71
The exact values of σ, Ts, Tc depend by the physical layer, and are not reported
here for space reasons. The reader may find the exact value of σ, Ts, Tc in [Bia00,
Xia04,EO05].
We have compared numerical computations of the model described above with the simulation results obtained with the ns2 simulator. Figure 4.22 compares the analytical model with the simulation results in a configuration with 1 CH, 20% SN1 nodes, 20% SN2 nodes, 60% LNs (Distribution A). We can observe that the analytical model gives a qualitatively good match when compared with simulations. The accuracy of the analytical model is also confirmed by Figure 4.23, where a configuration with 1 CH, 10% SN1 nodes, 10% SN2 nodes, 79% LNs (Distribution B), is considered.