Analyzing the performance of Aloha in string multi-hop underwater acoustic sensor networks
© Yu et al.; licensee Springer. 2013
Received: 25 October 2012
Accepted: 31 January 2013
Published: 12 March 2013
In this article, we intend to investigate the performance of channel access protocols in multi-hop underwater acoustic sensor networks, which are characterized by long propagation delays and limited channel bandwidth. An analytical model specifically designed for contention-based protocols in multi-hop underwater acoustic networks is identified and validated. The model is based on an underwater network model, called string topology network model, which provides a method for computing the expected network throughput and the probability of packets’ delivery to the gateway from an arbitrary sensor. This study demonstrates an improvement of an existing model, in which a node is implicitly assumed to be able to transmit two packets at the same time, which is not realistic due to the half-duplex character of underwater acoustic channels. Based on our findings, we propose a modified analytical model and evaluate it using NS-3 simulator. Results show that our analytical model is more precise than the existing one.
Underwater sensor networks are becoming an important research topic. They enable a wide range of collaborative applications, such as navy military surveillance, oceanographic data collection, ocean resource exploration, disaster prevention, and so on. Since both radio and optical signals suffer significant attenuation in salty water , acoustic technology is the typical physical layer communication method adopted by the underwater sensor networks, namely, underwater acoustic sensor networks (UASNs). However, the speed of acoustic waves in water is only approximately 1500 m/s, which is five orders of magnitude lower than the radio propagation speed. And the bandwidth of acoustic channels in water is one-thousandth that of the radio channels. Thus, compared with wireless sensor networks (WSNs), the research on UASNs is featured by long propagation delay and limited bandwidth, which pose grand challenges to almost every layer of network protocol stack and applications [2–8].
Similar to the WSNs, medium access control (MAC) protocols play a very important role in UASNs, which has high impact on the performance of the networks. Currently, theoretical analyses regarding MAC methods for UASNs focus on single-hop topology, which are summarized in surveys [5, 9]. In particular, Xie and Cui  presented some theoretical analyses of contention-based protocols such as Aloha for UASNs. However, in reality, multi-hop network is more practical and it can provide wider coverage . Therefore, in this article we focus on the study of multi-hop underwater scenarios.
Pure Aloha is one of the contention-based MAC protocols, which allows nodes to transmit whenever it is needed. And Aloha has become the basis of many wireless MACs since its proposal in the 1970s . Due to the long propagation delay and limited bandwidth of acoustic channels, contention-based protocols tend to be effective for multi-hop UASNs .
In , the first analytical model is proposed for the contention-based protocols in string multi-hop networks, called string topology network model (STNM). The model provides a method for computing the expected network throughput and the probability of packets’ delivery to the gateway from an arbitrary sensor. As a follow-up work, the performance of p-persistent Aloha is analyzed in . In addition, a summary of these models are provided in .
In fact, the analytical model in  is questionable in three aspects. First, since the node cannot transmit two packets simultaneously, there is no collision among the packets sent by the same node. However, the analytical model includes the corresponding probability, and thus the collision probability of a packet reception must be higher than the actual one. Second, the packet transmitting rate is equal to the aggregate traffic rate of the same node in the analytical model. But in fact the former should be less than the latter, since the generated packet will be dropped when the node is sending packet. Third, the analytical model is not validated by the simulations or experiments, which make it less convincing.
In this article, we propose a modified analytical model of Aloha protocol for string multi-hop UASNs. In order to validate the new analytical model, we simulate Aloha protocol in a string multi-hop network via NS-3. A comparison between STNM and our analytical model is done. The results show that the analytical results obtained from our analytical model are more accurate than the ones obtained from STNM. Besides, based on our analytical model, we derive expressions for the system throughput and average end-to-end packet delay.
The remainder of this article is organized as follows. Section Performance analysis of multi-hop Aloha gives a brief overview of the string topology network, and identifies the modified analytical model of Aloha for string multi-hop UASNs. Section Experiments validates our model via simulations and analyzes the differences between the results obtained from our analytical model and the simulation results. Finally, Section Conclusion concludes the study.
Performance analysis of multi-hop Aloha
In this section, we first briefly describe the string topology network . Based on the string multi-hop topology, we then present an analytical model of Aloha protocol in string multi-hop UASNs. After that, we consider the analytical model in another way, and prove that the two models are equivalent. At the end of this section, the performance expressions for string multi-hop UASNs are derived from our model.
String topology network
We notice the fact that a generated packet cannot be transmitted when the node is busy with sending. Our analytical model considers this while it is ignored by STNM. A packet sent out by each node may not follow a Poisson distribution since a packet may not be transmitted. In simulation, the packet will be dropped when it cannot be transmitted. As a result, the packet transmit rate is less than the aggregate traffic rate for each node.
As mentioned in , the string topology shown in Figure 1 favors the downstream traffic over the upstream traffic in underwater acoustic channels, as the packet from the downstream will be dropped only if it collides with other packets at a node further downstream.
Improved analytical model
However, there are three disadvantages in STNM. First, the packet transmitting rate of O i is equal to λ i in STNM. But in fact the former is less than the latter, because some packets may not be sent out. Second, we consider the reception of a packet from O i at node Oi+ 1. The duration that O i takes to transmit a packet is equal to the duration Oi+ 1 takes to receive the packet in STNM. Due to O i cannot transmit two packets at the same time, there should be no collision at Oi+ 1 between the packets from O i . That is, the probability of successful reception has nothing to do with whether or not O i is sending packets when Oi+ 1 is receiving a packet from O i . Therefore, in STNM, the collision probability of a packet reception must be higher than the actual one, since the model includes the corresponding probability. At last, STNM is not validated by the simulations or experiments.
The successful reception of a packet from O i at node Oi+ 1 depends on the state of Oi+ 1. The reception of a packet will fail while Oi+ 1 is currently overhearing the transmission of a packet by its downstream neighbor Oi+ 2, or currently sending a packet to Oi+ 2. And the reception of a packet will succeed only if Oi+ 1 is idle in twice the packet’s reception time, i.e., 2T. These constraints are independent.
where Λ = (λ transmit (1) λ transmit (2) … λ transmit (n)), and is calculated by iterative computation using Equation (5).
The Nelder-Mead simplex method has been quite effective to solve the above minimization problems . In Section Experiments, we will calculate above equations and obtain the analytical results using this method in Matlab.
Equivalent modification analytical model
We can see that this analytical model is equivalent to the one described in Section Improved analytical model.
Network performance expressions
where λtransmit (n) and P n are calculated by Equations (5), (7), and (8), respectively; L is the average packet size in bits; and α is the average fraction of data bits in each packet received by the gateway.
where c is the speed of acoustic waves in water; T is the packet transmission time; and Distance(i) is the distance from O i to Oi+ 1.
In this section, we first calculate the analytical results obtained from STNM (“the original results” for short) using Equations  and the ones obtained from our model (“the improved results” for short) using Equations (5) and (7). Then, we perform simulation with the same parameter setting using NS-3. After that, we compare STNM with the modification model, as well as validate them with the simulation results.
The NS-3 UAN module offers accurate modeling of the underwater acoustic channel and a model of the WHOI acoustic modem. Both the attenuation and noise are known to be strong functions of frequency. In our simulation, the acoustic channel model adopts Thorp attenuation , which is used for the calculation of the SNR at the receiver with the consideration of the ambient noise.
Total node number
190 dB re 1 uPα
The position of each node
(45,000i, 0, 100)
Figure 6b shows the sum of the squared differences between the original P i and the P i measured by simulation, and the sum of the squared differences between the improved P i and the P i measured by simulation versus the λ. We can observe that our improved results are always more coincident with the simulation results than the original ones. Considering P n significantly impacts results, we compute the sum of the squared differences of P i except P n , again. From Figure 6c, we can observe that the bias of our improved results still fit better than the original ones do in most cases. The above results show that our analytical model is more precise.
In the following, we explore the utilization of the string topology network. Gibson et al.  provide a method for computing the expected network utilization. Since STNM in  does not fit the simulation result well, we reconsider the utilization of the network using Equation (13).
From Figure 8, we can also observe that the utilization obtained from our model and STNM first increases with the load. After it has reached the maximum, it starts decreasing. However, the utilization obtained from simulation is monotonically non-decreasing and the maximum utilization is 1. When the load is very heavy, only the data from the last node can reach the gateway. Thus, the bias between analytical model and simulation results increases as the load goes up. This also indicates that the packet transmitted by each node cannot be approximated by a Poisson process when λ is high.
Although there is a bias between analytical model and simulation results, our analytical model is still reasonable, since λ is less than 1 in most cases for underwater scenario. To further improve the analytical model’s accuracy, the relationship between the bias and the load should be investigated. We would like to explore this topic in our future work.
In this article, we identified and validated the analytical model of Aloha in multi-hop UASNs. The simulation results justify that our modified analytical model is more accurate than STNM. Based on our model, we provide the expected network throughput and average end-to-end delay in string topology underwater networks.
The above analytical models are based on pure Aloha protocol which the node’s transmission has higher priority than the node’s reception. It is very inefficient, since a node will simply transmit a packet whenever it has anything to send, regardless of whether it is currently receiving a packet.
In the future, we would like to investigate the relationship between the bias and the load for our analytical model as well as further improve the accuracy of our analytical model. And we would also investigate other Aloha-based protocols such as slotted-Aloha protocol and Aloha with half-duplex protocol for string topology multi-hop network.
This study was supported by the National Natural Science Foundation of China under Grant no. 61073047; Fundamental Research Funds for the Central Universities: HEUCFT1202 and Harbin Special funds for Technological Innovation Talents: 2012RFLXG023.
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