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TDMA protocols have attracted a lot of attention for underwater acoustic sensor networks (UWSNs), because of the unique characteristics of acoustic signal propagation such as great energy consumption in transmission, long propagation delay and long communication range. Previous TDMA protocols all allocated transmission time to nodes based on discrete time slots. This paper proposes an efficient continuous time scheduling TDMA protocol (ECS) for UWSNs, including the continuous time based and sender oriented conflict analysis model, the transmission moment allocation algorithm and the distributed topology maintenance algorithm. Simulation results confirm that ECS improves network throughput by 20% on average, compared to existing MAC protocols.

Underwater acoustic sensor networks (UWSNs) have a promising future in the area of information collection with more and more applications in recent years, such as ocean environmental surveillance, resource exploration and disaster prevention [

First, underwater sensor nodes consume much more energy in transmission than terrestrial sensor nodes, not only that used in reception, but also in transmission [^{8} m/s) [

The unique characteristics of UWSNs bring about new challenges for MAC protocol design. Great energy consumption in transmission produces collision free protocols more suitable for UWSNs. Long communication ranges make the receiver the only point where the packets’ confliction is detected. However, the long propagation delay makes handshake protocols like RTS and CTS inefficient for UWSNs, as they would greatly decrease the network throughput.

Consequently, TDMA protocols are of great importance in UWSNs. Many TDMA approaches have been proposed for UWSNs, largely falling into two categories: one-slot approaches and multi-slot approaches, depending on how many time slots can be exploited to finish transmission of one packet between one-hop neighbors. One-slot approaches require the transmission to be accomplished in a single slot, so the length of a time slot should be designed to be at least one frame time plus the longest propagation delay of all links in the transmission range [

The core of TDMA protocols is to assign different transmission moments to transmitters. However, previous approaches are all based on allocating discrete time slots to nodes. If we treat the allocation problem of transmitting moment to nodes as one continuous function, we can further eliminate the idle time between the transmissions of different pairs of neighbors, and improve the throughput of the whole system, which is the motivation of this paper. Continuous allocation of transmitting moments brings new challenges to the MAC protocol design: the local conflict graphs (LCG) of the nodes have to be constructed based on continuous time and the transmission forbidden time of each node should be calculated as a continuous period. After that, continuous transmitting moments have been allocated to each node according to the transmission forbidden time of these nodes, which is an NP-hard problem to ascertain the optimum global allocating scheme.

In this paper, we propose the Efficient Continuous Scheduling algorithm (ECS) to solve the MAC problem of UWSNs. ECS contains three parts: a transmitting forbidden time calculation algorithm based on nodes’ local conflict graph (LCG), an allocation algorithm for nodes to decide their own transmitting moment based on a group of heuristic rules, and a distributed maintenance problem to solve the situations of neighbor death or joining of new nodes. Major contributions of this paper are:

Aimed at the unique phenomenon of UWSN MAC issue that the delay differences of dissimilar links could not be ignored, a sender oriented conflict model based on continuous time allocation is proposed. A distributed algorithm to generate local conflict model (LCG) is also advanced based on this model.

An efficient TDMA protocol (ECS) for UWSNs based on a group of heuristic rules is proposed. According as LCG, a node uses degree, load and link delay to calculate priority, and selects its transmission moment in priority order. The ECS algorithm could reduce the running time of nodes’ transmission moment allocation.

Compared to slotted schemes, continuous time based allocation could reduce idle times of receivers and improve network throughput. Simulation results confirm that ECS improves network throughput by 20% on average compared to existing MAC protocols.

The rest of the paper is organized as follows. Section 2 discusses the related work. We present ECS in detail in Section 3. Section 4 shows the simulation results and we conclude our work in Section 5.

As the transmission costs great energy in UWSNs, all existing MAC approaches try to avoid packet collisions, and can be further divided into three categories: (1) contention-based MAC without RTS/CTS, (2) contention-based MAC with RTS/CTS, and (3) contention-free MAC.

Therefore, TDMA protocols have attracted a lot of attention, falling into two categories: one-slot approaches and multi-slot approaches. One-slot approaches require that the transmission must be accomplished in a single slot, so the length of a time slot is at least one frame time plus the longest propagation delay of all links in the transmission range [

Contention based MAC approaches will cause energy wasting because of data collisions, and scheduling schemes are almost always based on time slots. They all ignore the feasibility of allocating transmission moments on a continuous time axis without slotting, which could further improve channel utilization and network throughput.

In this section, we first demonstrate our metrics to design ECS in underwater environments and present the conflict model based on continuous time. Then we introduce the exact design of ECS and present basic ideas of ECS via an example. Finally we give maintenance schemes to deal with the cases of node death or joining in the network.

The most important problem in UWSN MAC design is the measurement of conflicts by receiving ends. See _{AC}_{BC}_{a}_{b}

In TSNs, the propagation delay of an RF signal could be ignored because it is very small. We define the length of a TDMA slot as _{BC}

An ideal TDMA scheme is shown in _{a}_{a}_{AC}_{a}_{AC}_{b}_{b}_{a}_{AC}_{BC}

In conclusion, compared with traditional slot schemes, a continuous time allocation based TDMA scheme could improve network throughput and decrease idle time of receiving ends. This scheme fully utilized the characteristics of long propagation delay and short packets of UWSNs, and this are the key metrics in the design of ECS.

We make three assumptions before discussion:

The nodes’ communication model is a disk model; a node’s communication range and interference range are both cyclical regions. All nodes in the network are homogenous, and they all have the same transmission radius (

Clock synchronization is needed for TDMA transmission scheduling. Recent works [

Each node could get its geographical positions from positioning devices such as GPS or use an localization algorithm to calculate it. Lots of recent research has been done on UWSN nodes’ localization such as [

The continuous time based conflict model is composed of local conflict graph (LCG) and the algorithm to calculate forbidden time. Now we give the related definitions:

_{n}, y_{n})

_{n},y_{n})

For a node

For node

Physical topology condition:

Logical topology condition:

According to this definition, all conflict neighbors and conflict targets of a node

See

If _{ij}(k)_{ik}_{jk}

For standardization, define _{ii}_{ij}(k)_{ij}(k)_{ij}(k)_{ij}(k)

E.g., in _{ij}(k)

For node _{ik}(k)_{ik} − W_{kk}

For node _{T}_{I}_{if}(i)_{ii}_{if}_{if}(k)_{ik}−D_{fk}

The forbidden time is used to guarantee that the arriving time ranges of two nodes’ frames on the receiver’s time axle do not overlap completely. As shown in _{j}

The physical meaning of forbidden time is that, if a conflict neighbor _{j}_{ij}(k)_{j}_{f}

ECS uses two steps to get nodes’ transmission moments. First, each node generates its local conflict graph (LCG). Then each node runs the marking algorithm to calculate transmitting moment on its LCG. The allocation order of transmitting moment depends on node’s marking priority, which is calculated by a group of heuristic rules.

Each node

Definition 4 is used to judge whether a node _{ij}(k)

Let _{LCG}(i)_{ij}(k))

In the case of

CreateLCG().

1: Input: |

2: Output: _{LCG}(i) |

3: |

4: if (_{T}_{I}_{I}_{T} |

5: return |

6: else |

7: return |

8: } |

9: |

10: if(∃ |

11: return |

12: else |

13: return |

14: } |

15: new _{LCG} |

16: while (_{LCG} |

17: ∀ |

18: _{LCG}=V_{LCG}-{j}; |

19: new |

20: while ( |

21 ∀ |

22: |

23: If ( |

24: _{ij}(k)=D_{ik}−D_{jk} |

25: _{LCG}(i)=S_{LCG}(i)∪{(i, j, k, W_{ij}(k))}; |

26: } //end if |

27: } //end while ( |

28: } //end while(_{LCG} |

29: return _{LCG}(i) |

After generating the local conflict graph, each node calculates its marking priority, and then begins to choose its transmission moment. The node with the highest priority will mark its transmission moment firstly; the basic idea is to choose the earliest available time on its time axle (keep away from forbidden time). The main process of ECS contains five steps:

Step 1: Each node generates its LCG and calculates its marking priority. Each node run step 2–5 in distributed manner.

Step 2: Node broadcasts its priority to all LCG neighbors. All the nodes set the status to ‘unmarked’.

Step 3: If the node has the highest marking priority in all its unmarked LCG neighbors, it calculates its transmitting moment and broadcasts it to all LCG neighbors, and then sets the status to ‘marked’.

Step 4: If exists a higher priority neighbor for a node, it must wait for its neighbor to mark and receive the neighbor’s transmission moment, then update its forbidden time due to the neighbor’s selection. Return to step 3.

Step 5: If all nodes in LCG are ‘marked’, the algorithm stops.

Define _{c}(i)_{uc}(i)

Mark().

1: _{c}(i)=null |

2: _{uc}(i) |

3: while(∃_{uc}(i) |

4: receve node _{j} |

5: _{c}(i)=S_{c}(i)∪{j} |

6: _{uc}(i)=S_{uc}(i)-{j} |

7: for each |

8: calculate |

9: } // end while |

10: loop: //highest priority; ordinal marking, find the earliest available time |

11: _{i} = |

12: for each _{c}(i) |

13: if(_{i}<Fr(i, j, k) |

14: _{i} = Fr(i, j, k) |

15: } |

16: } |

17: |

18: return _{i} |

The length of a TDMA period is decided by _{i}_{ik})_{p}(i)_{i}_{ik}_{p}_{p}_{wait}_{p}_{wait}_{p}_{wait}

In UWSN environments, allocating continuous time to all nodes is equivalent to the problem of distribute coloring on a continuous color axis, which is a well known NP-hard problem to ascertain the optimum global allocating scheme [

Nodes that have largest degree in its LCG should be marked preferentially. A node’s degree is the number of edges in its LCG. A node that has large degree predicates that it could collide with large amount of nodes. Therefore, this kind of node should transmit as early as possible to move up other nodes’ forbidden time. Then the length of transmission period of the network can be shortened.

Nodes that have higher traffic load should transmit as early as possible. A node has high traffic load will take more time to transmit, so it should also transmit earlier to reduce average packet delay.

Nodes with larger propagation delay link should transmit earlier. If the large latency link transmits late, the receiver will get the packet even later. It is helpful to improve transmission parallelism if large latency link transmits earlier and small latency link transmits later.

Marking priority could be calculated due to the three heuristic rules. Define _{i}_{max}_{i}_{max}_{ik}_{max}

The importance of different parameters is reflected in

In this subsection, we give an example to illustrate the process of ECS in detail. In

Second, all nodes calculate their marking priority. In

As a conclusion of this instance, ECS could improve network transmission parallelism. Both

UWSNs are deployed in severe environments. In the harsh underwater environment links will be intermittent and nodes may be mangled or be divorced from the network because of many uncertainties. The security and reliability of UWSNs is worse than that of TSNs, so deploying new nodes and changing network topology are frequent in UWSNs. As nodes’ disappearance and entering are usual, network protocols must be designed flexibly and vigorous enough to suit to these changes. However, compared with competition based protocols, the adaptability of scheduling based protocols is worse, because strategy is usually pre-established and could not change after network beginning, then existing TDMA protocols are almost not involving network maintenance, including ST-MAC.

ECS uses a flexible and simple scheme to deal with the change of network topology. Nodes’ death or entering denotes the reallocation of transmission moment. The conversion of a node’s transmission moment will cause ripple effect in the whole network. Therefore, the key problem is to keep the effect of topology change in local scope.

If a node does not receive packets of its child node in continuous

In the example of

Maintenance().

1: If a node |

2: Broadcast message ‘i_death’ to |

3: Loop{ |

4: choose the highest priority node |

5: if(∃_{k}_{k}_{k} |

6: choose the node that priority is second to |

7: continue loop; |

8: else |

9: calculate _{k} |

10: break; |

11: } |

12: broadcast _{k} |

If an old node rejoins in the network, e.g., link quality is improved or the node recovers from faults. Nodes that occupy its transmission moment should abdicate and the network returns to previous scheduling. If a new node joins in the network, it must keep jamming the channel for one TDMA period to inform its neighbors. Then in next period, the neighbors send their transmission moments and geographical positions to the new node. According to the regulations of ECS, the new node must know all information in its interference range to generate its local topology. New node calculates all of its forbidden time, and chooses the earliest available time as its transmission moment, then broadcasts to all LCG neighbors. If the new node could not find transmission moment on time axle, it turns to sleep and becomes a spare node. This case is unfamiliar because new nodes are usually deployed in sparse region or the region that has dead nodes.

Join(i).

1: jam the channel; |

2: receive information of all LCG neighbors and calculate their forbidden time, create LCG(i); |

3: _{i} |

4: for (all node |

5: if(∃_{i}<Fr(i, j, k) |

6: _{i}= Fr(i, j, k) |

7: } |

8: if (_{i}_{max} |

9: node |

10: else{ |

11: broadcast _{i} |

12: return _{i} |

13: } |

In this section, we describe simulation conditions and results, and analyze the performance of ECS in terms of topology and throughput. Emulator is run in Matlab software. In our simulation the frame time

Network throughput is defined as the number of packets transmitted in the network per second. For network topology has great relationship with transmission parallelism, we simulated both common topology (nodes are deployed randomly and self-organized to aggregation tree) and special topology such as line, star and grid.

Four communication-scheduling algorithms are simulated in the simulations:

Optimal: the theoretically most excellent scheme, it chooses the scheme with the shortest TDMA super frame among all possible schemes, which means nodes use the shortest time to achieve transmission in a round. Therefore, it has the highest throughput and gives the upper bound of all heuristic algorithms.

ECS: the continuous time allocation based TDMA protocol proposed in this paper.

ST-MAC: multi-slot TDMA protocol proposed in [

S-TDMA: a classical traditional single slot TDMA [

Network throughput increases as network scale increases in any topology except star. The reason of this special phenomenon is that, in star topology all nodes transmit to the sink by one hop, any two nodes are potential conflict nodes. In other words, all nodes only share one channel, so transmission parallelism cannot be improved by network scale.

When the network scale is small, ECS and ST-MAC both perform close to Optimal. However, as the network scale becomes large, both of them perform worse than Optimal, but ECS is always better than ST-MAC (20% better on average), and achieves 80% capability of Optimal. S-TDMA is the worst strategy. Large idle time exist in S-TDMA because of its long time slot.

ST-MAC uses a slot scheme to allocate transmission moments for all nodes. Any packet must be sent at the beginning of a slot, so it is a conservative strategy compared with continuous time allocation. Moreover, ST-MAC works under the assumption that the propagation delay of any link must be an integral multiple of the frame time, so the frame size must be designed as small as possible. Short data packets will decrease the scale of valid data, because other information such as parity bit and frame header is not become shorter when data packet becomes short. ECS uses continuous time allocation scheme and do not need the assumption of ST-MAC, so ECS could use longer data packet and further improve network throughput.

End to end delay is also considered in simulations, and the results in popular tree topology are shown in

ST-MAC and ECS are both TDMA based protocols and have no collision in data transmission phase. Therefore, their energy efficiency is both high. The additional energy consumption is only come from initialization phase. In ST-MAC, base station should collect information and dispense control message to the whole network. Any node should communicate with the base station by multi-hop transmission. The whole communication cost is O(N!) level. However, ECS is a distribute algorithm, node could only exchange information with local neighbors, and the whole communication cost is O(N) level, where N is the network scale. When network scale becomes large, the communication cost of ST-MAC is pretty much more than that of ECS.

As a conclusion, ECS has achieved a good tradeoff for network throughput and communication cost for protocol running. The performance of distribute and heuristic allocation algorithm is close to theoretically optimal scheme. What’s more, it performs better than existing approaches such as ST-MAC.

In this paper, we have proposed an efficient TDMA protocol (ECS) for UWSNs, including the continuous time based and sender oriented conflict analysis model, the transmission moment allocation algorithm and the distributed topology maintenance algorithm.

ECS is different from previous TDMA approaches in allocating transmission moments to nodes based on continuous time, not on discrete time slots. ECS exploits well the characteristics of acoustic signal propagation such as long propagation delay and long communication rage. By using continuous time based transmission moment allocation scheme, differences of link delays are further utilized and channel utilization of receiver node is improved. Simulation results confirm that compared with traditional slotted TDMA protocols, ECS has higher network throughput and better efficiency.

The research of this paper is supported by the National Natural Science Foundation (NSF) of China under Grant No. 60703082, 60873248, 60933011 and 60970129; and partly supported by Science and Technology Development Program of Qingdao under Grant No. 10-3-4-1-6-jch.

Different UWSN transmission moment allocations.

Local network topology of node

Calculation of forbidden time.

Local conflict graph (LCG) of node

ECS process:

A node may be incapable to use the transmission time of a dead node.

Network throughput in different topologies:

End-to-end delay of different TDMA protocols.

Efficiency of ECS in underwater harsh environments.