![](bg2.png)
given j for all i < j,
δ
j
.start ≥ δ
i
.start + δ
i
.duration if δ
i
.src = δ
j
.src
δ
j
.start ≥ δ
i
.start +δ
i
.duration+max(
T(δ
i
.src,δ
i
.dst) −T(δ
j
.src,δ
i
.dst),
T(δ
i
.src,δ
j
.dst) −T(δ
j
.src,δ
j
.dst))
if δ
i
.src 6= δ
j
.src
Figure 2: Set of simplified scheduling constraints.
the algorithm proposed in (van Kleunen et al., 2011),
which allows exploiting the long propagation delays
in underwater acoustic communication, can be re-
duced to allow scheduling of large-scale underwater
networks. This reduced complexity centralized ap-
proach can be used in scenarios in which the com-
munication overhead is not an issue and the aim is to
achieve the best possible schedule.
We will also present how a clustered approach can
significantly reduce the computational and communi-
cation overhead of scheduling large-scale underwater
networks. A large part of the communication of our
distributed clustered approach is done locally (sin-
gle hop) and the computational communication is low
enough to be implemented on embedded processors.
The distributed clustered approach calculates less ef-
ficient schedule but the communication and computa-
tional overhead scales much beter to larger-scale un-
derwater networks.
The outline of the paper is as follows: in Sec-
tion 2 the related work will be discussed. An extended
set of simplified scheduling constraints for scheduling
multi-hop networks will be presented in Section 3.
In Section 4 a centralized algorithm with reduced
complexity is proposed. Section 5 describes our dis-
tributed scheduling technique, which uses a clustering
concept to split up the scheduling problem. Evalu-
ation of the communication and computational com-
plexity of different approaches is presented in Sec-
tion 6, while performance evaluations of the different
approaches will be presented in Section 7. In Sec-
tion 8 conclusions are drawn and future directions are
highlighted.
2 RELATED WORK
Scheduling approaches for underwater acoustic trans-
missions, which allow mitigating the effects of the
propagation delay, already exist in literature. These
approaches range from centralized to distributed ap-
proaches. ST-MAC (Hsu et al., 2009) is a centralized
scheduling approach, which uses timeslots to form a
collision free schedule. In (van Kleunen et al., 2011)
we have shown that the slotted approach used by ST-
MAC leads to suboptimal results.
STUMP-WR (Kredo II and Mohapatra, 2010)
provides a fully distributed approach to schedule un-
derwater communication. It also uses timeslots, sim-
ilar to the approach of ST-MAC, which has been
shown to lead to suboptimal results. STUMP-WR de-
rives a node schedule from local interference patterns
and link schedules from neighbouring nodes. Nodes
broadcast their route as well as link schedule updates
during control frames until the network converges.
This approach is quite interesting because it is fully
distributed. Nodes are able to schedule their transmis-
sions based on their own information and schedules of
neighbours. This may, however, require a significant
amount of communication between nodes and special
attention should be paid to ensure that the nodes con-
verge to a schedule in networks facing packet loss.
Because of the way STUMP-WR works, the pos-
sibilities of ordering the transmissions are limited.
The first schedules will be formed using a limited
amount of transmissions. Other nodes will extend
their schedules using their transmissions but will
not move existing transmissions to improve schedule
times. This will result in less optimal schedules from
a throughput point of view.
Another problem with STUMP-WR (Kredo II and
Mohapatra, 2010) might be that transmissions still
cause interference at certain nodes. This is because
in a real network setup, nodes may not always be able
to communicate with nodes that they might interfer.
The interference range might actually be larger than
the communication range. The completely distributed
approach is an interesting approach nonetheless.
In (van Kleunen et al., 2011), we have already
shown how the scheduling constraints for underwa-
ter communication can be reduced to a simplified set.
Using these constraints we introduced two scheduling
algorithms: one algorithm assumes a given order of
transmissions and the other one selects the most op-
timal order of transmissions and derives a schedule.
The set of scheduling constraints assumes all nodes
are within transmission range of each other and all
schedulings are done in a centralized manner. This
necessitates availability of knowledge from all nodes
and transmissions at a central place in the network,
which introduces a significant communication over-
head. In Figure 2 the set of simplified scheduling
constraints are given. The set gives a constraint be-
tween two transmissions (δ
i
and δ
j
), which both have
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