Multi-hop Ad Hoc Networks

Many analytical studies have appeared in the literature investigating the performance of wireless single hop ad hoc networks with a random access MAC protocol, as discussed in Section ‎2.1. However, because performance modelling and analysis of multi-hop ad hoc networks is much more challenging, few papers addressed this issue [31-41].

The first attempt studied the performance of wireless multi-hop ad hoc network with a random access MAC protocol [31]. To analyse the saturation throughput in wireless multi-hop ad hoc networks, a simple analytical model was proposed. The transmission probability for a single hop was derived which was used to investigate multi-hop scenarios. To simplify the analysis, nodes were distributed in the network according to the Poisson distribution. Moreover, the status of the channel and backoff behaviour of the MAC protocol were simplified into limiting probabilities.

The performance of the IEEE 802.11 DCF protocol in multi-hop network scenario was investigated in [32] using an analytical model. The proposed model used a two- dimension Markov Chain model introduced in [48] to derive an expression for the transmission probability which was used to compute the packet collision probability

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taken into account the impact of the hidden node problem. Although the proposed model takes into account the effects of hidden and interfering nodes, the nodes in the network were regularly placed in a grid topology in order to simplify the analysis. In [33], an approximate analytical model for the performance analysis of a single hop and multi-hop ad hoc network was presented. The behaviour of the DCF MAC layer protocol was modelled using the Markov chain model introduced in [48]. For single hop scenarios, to derive an expression for the queuing delay, and distribution function and first moment of the service time, the M/G/1 queuing system has been adopted. The authors extended the analytical model for a single hop network to model a multi- hop network. They derived expressions for the probabilities of collision occurrence due to the hidden node problem. However, in multi-hop scenarios, they only addressed the approximate throughput and the end-to-end delay has not been considered.

In [34] Wang et al presented an analytical model for the performance analysis of wireless ad hoc network with the 802.11 DCF MAC protocol under finite load conditions in terms of the network throughput and delay. The model is limited for a chain network topology and hidden node problem was not considered. A model called Traffic-Analysis-Based (TAB) for the throughput analysis of wireless ad hoc networks with a chain topology was proposed in [35]. The TAB model is used to analyse the state transition process of the wireless nodes with increasing traffic load. The backoff states of wireless nodes have been presented using the approximate model introduced in [48].

Ali et al [36] presented approximate analytical models to estimate the throughput and delay per node in wireless multi-hop ad hoc networks. They used the Markov chain model introduced in [48] to model the channel access and backoff behaviour of the MAC protocol. In addition, the random network topologies are generated using a two-dimension Poisson distribution for the node location in the network. The authors did not derive an expression for either delay or throughput per path. Also, they did not consider the traffic load induced by the routed packets received from neighbour

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nodes. Kumar et al [37] proposed an analytical model for estimating the average end- to-end delay of multi-hop ad hoc networks in which the IEEE 802.11 DCF protocol are used at the MAC layer. This work has not considered the packet queuing delay and has not been validated using random network topologies.

An analytical model for random access MAC based wireless ad hoc networks using open G/G/1 queuing networks has been introduced in [38]. The performance of single and multi hop scenarios were investigated in terms of the throughput and end-to-end delay. The proposed model is used to derive a closed form expressions for the maximum achievable throughput and end-to-end delay. The single hop communication was modelled as an open queuing network which is used to evaluate the mean and second moment of the packet service time per hop. Then, to derive expression for end-to-end delay, the diffusion approximation was adopted to solve the open queuing network. Also, the average service time per hop was used to obtain the expression for the maximum achievable throughput. However, although the main target of the proposed queuing model was gaining insights into the queuing delay, dropping of packets due to the buffer overflow has not been considered. In addition, effects of hidden and interfering nodes which increase in multi-hop networks have not been taken into account.

In [39], Ghadimi et al extended the work introduced in [33] to address the end-to-end delay analysis in multi-hop wireless ad hoc network under unsaturated traffic condition considering the hidden and exposed terminal problem. Each single wireless node was modelled as an M/G/1 queue which is used to compute service time distribution function. Using the service time distribution function for a single hop, the probability distribution function of a single hop delay and its first and second moment were obtained. In addition, the probabilities of collisions in both hidden and exposed node conditions were calculated using the single node media access delay distribution, which was used to extend the modelling approach to investigate the delay in multi-hop scenarios. This work used the Markov chain model introduced in [48] to model the transmission state of each node that follows the 802.11 DCF MAC protocol. This model deviates from the standard because it much simplifies the IEEE

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802.11 MAC protocol [49]. Moreover, in multi-hop scenarios, the method used to compute the expected number of hops is not accurate.

An approximate stochastic Petri net model for ad hoc network was presented in [40]. The proposed model tried to exploit the symmetry between nodes by describing the behaviour of one node under a workload that is generated by the whole network. The SPN model consists of two subnets; incoming and outgoing subnets. The incoming subnet represents the processing of packets received from other nodes, whereas the outgoing subnet models the transmission of packets generated in the current node. Fixed point iteration was used to solve the proposed model. Lin et al [41] modified the work introduced in [40] to be suitable for a heavily loaded network. To model the sending and receiving process in ad hoc network, they adopted independent and receiving buffers. Also, they introduced a more accurate method for calculating the packet dropping probability. The main drawbacks of the work introduced in [40] and [41] are (1) although the MAC protocol plays a prominent role in the performance of ad hoc networks, the proposed SPN models in both [40] and [41] did not capture the behaviour of any MAC protocol, (2) the effects of hidden and interfering nodes on the performance of the network have not been considered.