Latency-Reliability Tradeoff for Different Hop-Level ARQ-based Error - - PowerPoint PPT Presentation
Latency-Reliability Tradeoff for Different Hop-Level ARQ-based Error Recovery in a Multi-Hop Wireless Network Teeraw at I ssariyakul ( teeraw at@trlabs.ca) Ekram Hossain ( ekram @ee.um anitoba.ca) Attahiru Sule Alfa ( alfa@ee.um anitoba.ca)
Latency-Reliability Tradeoff for Different Hop-Level ARQ-based Error Recovery in a Multi-Hop Wireless Network
Teeraw at I ssariyakul ( teeraw at@trlabs.ca) Ekram Hossain ( ekram @ee.um anitoba.ca) Attahiru Sule Alfa ( alfa@ee.um anitoba.ca)
studies
communications
– Increase data rate – Reduce delay – Reduce energy consumption
from the base station to the mobile
– Increase coverage of service area – Better load balance Short Range Long Range
Base st at ion
collision free and error-free I EEE 802.11 two-hop (3 nodes) network (WCNC’04)
an H-hop chain topology for a single packet (Globecom’04)
and infinite persistent ARQ (WN27-1)
time (e.g., ODMA)
with probability perr
. . .
N packets
Source Destination
– Queuing, – non-zero error probability, and – ARQ
(s= { 0,1,… ,N} )
– Find Pr{ s packets are delivered} – Find pmf (probability mass function) of associated delay
– ARQ0: zero retransmission (stop immediately) – ARQ∞: infinite retransmission (never stop) – ARQF: finite retransmission (stop after M failures) – ARQP: probabilistic retransmission with infinite persistence (stop with probability d after each failure)
ARQP
– The transmitting node will reset itself. – It will flush the buffer, and will not receive any incoming packet. – Transmission at the other nodes can still continue.
Source Destination
TRANSI ENT STATES
pij is t he t r ansit ion probabilit y f r om st at e i t o j A B X1
pAB pBA pAC pCA 1 Xn 1
ABSORBI NG STATE
I R Q
=
X … B A
To From
P=
I … X pBX … pBB pBA B pAX … pAB pAA A
. . . . . . . . .
(α,α0) = the initial probability matrix
Expected Delay Absorbing Probability
absorption in an absorbing Markov process
reach the absorbing state
1 −
R Q I α E
2
) ( [k]
−
− =
> = =
−
; ;
1
k k
k k
R αQ f α
Delay PMF
...
Absorbing state = (0,0,s) No packet in the network (X1= 0,X2= 0) Finishing point Initial state = (N,0,0) N packets are supplied to the source node Starting point Markov Chain Multi-Hop Network
1 2 3
α= e i = [ 0 … 0 1 0 … 0]
page)
process to find
The state where N packets are supplied to the source node
SN = { (X1,X2,X3): X1+ X2= N, X3= N-X1-X2}
– Packets in the system always decrease – Lower-triangular – will later be used to derive ARQP
– Delay PMF: – Pr{ m pkts successfully TX} : – Expected Latency:
( ) R
Q I α f
1 −
− =
R Q I α E
2
) ( [k]
−
− =
> = =
−
; ;
1
k k
k k
R αQ f α
e fd
D d
f =
[ ]e
E d E = [D]
) , 1 ( m m fM f =
Q R I
P=
(X1,X2,X3)
Q
R
absorbing state initial state
X1 does not change X1 decreases
S = Success, F = Fail
S = Success, F = Fail
Probabilistic Retransmission ARQ (ARQP)
(SN)
Probabilistic Retransmission ARQ (ARQP)
Stay in SN = TPM of ARQ∞ Drop 1 packet Drop 2 packets All packets in the system Si are delivered
– Delay PMF: – Pr{ m pkts successfully TX} : – Expected Latency:
e fd
D d
f =
[ ]e
E d E = [D]
) , 1 ( m m fM f =
( ) ω
1 −
Ω − = I α f
ω
2
) ( [k]
−
Ω − = I α E
> = Ω =
−
; ;
1
k k
k k
ω α α f
Probabilistic Retransmission ARQ (ARQP)
Probabilistic Retransmission ARQ (ARQP)
Q1 Q2 Q3
E[M] and E[D]
Several packets might be dropped during one connection reset
E[M]/E[D]
Decrease in slope
E[D]
CDF (Fk)
End-to-end latency (k) 95%
% 12 . 52 ] [ = D E FD
PMF (fM(m))
p=0.7 p=0.9
multi-hop wireless network in terms of
– link-error probability, – hop-level ARQ parameters, and – end-to-end latency distribution
– Increases reliability – Increases end-to-end delay
model
high batch delivery
– Increases reliability – Increases end-to-end delay
model
batch delivery
expense of increasing latency
Rayleigh Fading or FSMC)
congestion control (window= batch)