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within the communication range r of a node are con-
sidered as its neighbors for the GPSR, whereas a sub-
set is selected for the e-GPSR according to its selec-
tion criteria explained in the following.
The sink node (SN) is assumed to have a commu-
nication range R able to cover the entire area, such
that downlink communications are direct and without
errors. The SN queries to the network the position of
a randomly chosen node. Every node receiving the
query verifies whether it is the right destination: if
not, it discards the packet. Otherwise, it sends back to
the SN the reply packet through a multi-hop path, re-
actively created by means of one of the two versions
of the geographic algorithm under test.
The physical layer is modeled by the cascade of
a SNR Evaluator and a Decider. The SNR Evaluator
computes the signal-to-noise ratio (SNR) associated
to the received packets and the Decider compares its
output with a threshold SNR
th
, discarding the packets
whose SNR is below.
The MAC layer implements a pure aloha scheme.
At the NWK layer we adopt a routing scheme
based on the GPSR (Karp and Kung, 2000). Two
versions of the GPSR are compared, the traditional
and the energy-aware version in (Persia and Cassi-
oli, 2007). The difference between these two ver-
sions stays in the selection criteria of the next hop
in the Greedy mode, whereas there is no difference
in the Perimeter mode, which is the recovery strat-
egy in case of failure of the Greedy approach. During
the Greedy mode the traditional GPSR selects the next
hop according to the MFR (Most Forward within Ra-
dius) approach, i.e. the neighbor geographically clos-
est to the packet destination is selected. The e-GPSR
adds to the MFR two other criteria in the Greedy mode
which take into account both energy and latency con-
straints. For each node j, the possible candidates for
the next hop constitute a subset, N
(j)
Θ
∩
˜
N
(j)
, of the N
(j)
neighbors of the present hop node j, such that the fol-
lowing conditions are verified:
N
(j)
Θ
⊆ N
(j)
| ∀i ∈ N
(j)
Θ
, α
i
≤ Θ
(j)
(6)
˜
N
(j)
⊆ N
(j)
| ∀k ∈
˜
N
(j)
, E
k
≥ E
(j)
T H
(7)
where N
(j)
Θ
and
˜
N
(j)
are the subsets of nodes that ver-
ify (6) and (7), respectively, α
i
is the angle between
the line that joins the node j with the i-th node and the
line that joins the node j with the destination (the SN
for our cases), and E
k
is the residual charge of the k-th
neighbor node. The condition (6) can be seen as a la-
tency constraint, whereas (7) is the power constraint.
Each forwarding node j adaptively sets the angle
Θ
(j)
as Θ
(j)
= α
(j)
+ x
Θ
· (90 − α
(j)
) and the thresh-
old E
(j)
T H
as E
(j)
T H
= (1 − x
C
) · E
(j)
charge
, where α
(j)
is the
Table 1: Simulations’ setup.
RANDOM WAY POINT Speed: 0.5 m/s
MOBILITY MODEL Pause time: 0.1 s
DATA RATE R
b
= 1 Mb/s
TRAFFIC MODEL CBR at 1 packet/s
84 bits per packet
BATTERY CHARGE Initial: E
I
= 10 mAh
minimum angle obtained by considering, among all
neighbors of the node j, the nearest node to the j − D
line, E
(j)
charge
is the maximum residual charge among
the residual charges E
k
of its neighbors, and x
C
∈ [0,1]
and x
Θ
∈ [0,1] are routing design parameters (Persia
and Cassioli, 2007), which modulate the number of
neighbors of each node that varies not only due to the
coverage range.
Performance analysis has been carried out by dy-
namic system simulations in Omnet++. The simula-
tion assumptions and parameters are listed in Table 1.
For each case under study, we average the statistics
over a set of 5 independent stochastic discrete-event
simulations, each having a duration of 100 s. Fig. 2
shows the average and standard deviation (STD) of
residual charge for all nodes. In the presence of bea-
con traffic for the GPSR, the average level of resid-
ual charge increases with increasing beacon inter-
vals, whereas the STD decreases for large beacon in-
tervals, indicating a not uniform discharge through-
out the WSN. For the e-GPSR, the average resid-
ual charge slightly decreases in the presence of bea-
con traffic, and its dependence on the beacon in-
terval is negligible. The STD is constant with re-
spect to the beacon interval and slightly greater than
the ideal case. Hence, nodes discharge quite uni-
formly over the whole network, increasing the net-
work lifetime and the reliability of links and position-
ing. Nevertheless, the above analysis does not take
Figure 2: Average (upper plot) and standard deviation
(lower plot) of the residual charge of network nodes.
ENERGY/LATENCY TRADE-OFFS IN GEOGRAPHIC ROUTING FOR ULTRAWIDEBAND WIRELESS SENSOR
NETWORKS
117