2 and 33 However the probability q r that a node transmits Eq 34b is an

# 2 and 33 however the probability q r that a node

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So far this analysis is similar to that in Sections 3.2 and 3.3. However, the probability qrthat a node transmits, Eq. (3.4b), is an independent variable that is controlled to achieve desired performance. Conversely, the probability qchere is a dependent variable that is derived from other protocol parameters as follows. The node’s state is defined by two random variables: the backoff stage K, which takes values {0, …, l}, and the channel contention counter C, which for K=ktakes values {0, …, CWk1}, The state transition diagram is represented as the Markov chain model in Figure 4-19. We introduce the backoff stage K= 1 in order to account for the fact that the station does not enter backoff countdown if a new packet arrives during an idle channel state. In addition, we truncate the chain, so the packet is dropped after lretransmissions. The transition probabilities P{Kt+1=k, Ct+1=i| Kt=l, Ct=j} are as follows: P{1, 0 | k, 0} = idlesuccpp~, 1 kl1 (4.4a) P{1, 0 | l, 0} = pidle(4.4b) P{0, i| 1, 0} = 0~~CWpppcollbusysucc+, 0 iCW01 (4.4c) P{k, i| k, i} = pbusy, 0 kland 1 iCWk1 (4.4d) P{k, i| k, i+1} = pidle, 0 kland 1 iCWk2 (4.4e) P{0, i| k, 0} = 0~CWppbusysucc, 0 kl1 and 0 iCW01 (4.4f) P{0, i| l, 0} = 0CWpbusy, 0 iCW01 (4.4g) P{k, i| k1, 0} = kcollCWp~, 0 kland 0 iCWk1 (4.4h) BusyRTSDIFSBackoffSIFS CTSData ACK TimeVulnerable period without hidden stations = 1 backoff slot SIFS SIFS Vulnerable period with hidden stations = RTS + SIFS + 1 slotFigure 4-18: Definition of the vulnerable period for the cases with and without hiddenstations.
Chapter 4 IEEE 802.11 Wireless LAN 91For example, Eq. (4.4a) means that the node will transition to the state {1, 0} from any state {k, 0} if the previous packet transmission is successful and the new packet arrives while the channel is idle. Let bk,idenote the probability that the node is in the state {Kt=k, Ct=i}. Then 110,===lkkCWiikb. The state probabilities can be determined from the stationary distribution of the Markov chain: {}∑ ∑===l10,,,,llCWjjlikjlikPbb, 0 kland 0 iCWk1 (4.5) The details are omitted for brevity and can be found in references cited in Section 4.7 below. A node transmits if its backoff counter reaches zero; thus: qc= ()0,12210,010,110,~~~~1~~1++++=+=+=bpppppppbppbbidlesucccollcollbusycollbusysucccollkklllll0 CW01K = 1 C = 0 K = 0 C = 0 K = 5 C = 0 K = lC = 0 K = 1 C = 0 0 1 1 1 5 1 l1pbusypidlepbusypidlepbusypidlepbusypidlepidlepidlepbusy1 CW11 pidlepidlepbusy5 CW51 pidlepidlepbusy lCW51 pidlepidlepbusy CW1pcoll~ CW1pcoll~CW1pcoll~CW2pcoll~CW2pcoll~CW5pcoll~CW5pcoll~ CW5pcoll~CW5pcoll~CW5pcoll~psuccpidle~ psuccpidle~psuccpbusy/CW0~(psuccpbusy +pcoll)/CW0~~psuccpbusy/CW0~CW5pcoll~ pbusy/CW0pidlepsucc~1
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