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Maximum throughput serves as a fundamental metric for evaluating the performance of mobile ad hoc networks. However, the actual maximum throughput still remains significantly unknown in such networks. This paper studies the actual maximum throughput of mobile ad hoc networks under a general routing scheme with reed-solomon coding, where a source node first encodes a group of

Mobile ad hoc networks represent a class of self-configurable wireless networks, where mobile nodes can communicate with each other freely through peer-to-peer wireless links without infrastructure support [

There have been several studies on the maximum throughput of mobile ad hoc networks in the literature. However, most of efforts focused on the study of asymptotic maximum throughput. For example, in a seminal work [

Notice that all the aforementioned work on the maximum throughput of mobile ad hoc networks focused on the asymptotic results, which could not indicate the actual achievable maximum throughput of such networks. In practice, the actual maximum throughput is significantly important for network designers. Some researchers have made efforts to explore the actual maximum throughput of mobile ad hoc networks and obtained some initial results. Neely et al. [

In this paper, we study the actual maximum throughput of mobile ad hoc networks under two-hop relay routing with reed-solomon coding. Under this routing scheme, source node first encodes a group of

The main contributions of this paper are summarized as follows:

We first establish two Markov chain models to capture the fastest packet sending and receiving processes at source and destination nodes under the routing scheme in the considered mobile ad hoc network.

Based on these two Markov chain models, we then derive a closed-form expression for the maximum throughput in such network.

Finally, extensive simulations are presented to validate the accuracy of theoretical maximum throughput analysis and numerical results are also presented to illustrate how network parameters influence the maximum throughput performance.

This paper is organized as follows. We introduce system models and performance metric in Section

In this section we introduce the system models and the definition of maximum throughput adopted in this paper.

We consider a mobile ad hoc network composed of

Network model and MAC protocol.

The node movements in the network follow the independent and identically distributed (i.i.d.) mobility model widely adopted in [

We adopt a commonly used

Similar to [

A traffic arrival rate

In this section, we first introduce MAC protocol and then present a general routing scheme with reed-solomon coding.

To ensure as many simultaneous data transmissions as possible over a shared channel without interfering with each other, we adopt an equivalent-class based MAC protocol [

The parameter

We consider a general two-hop relay routing with reed-solomon coding, where a group of

Without loss of generality, we study a specific traffic flow and denote its source and destination by

We now introduce the two-hop relay routing with reed-solomon coding. When

For the case where

For another case where

It is notable that, under the routing scheme, the destination node

In this section, we first establish two Markov chain models to depict the fastest packet sending and receiving processes at source and destination nodes and provide some basic results. Based on them we then derive a closed-form expression for the maximum throughput.

For the specific traffic flow and a given packet group, under our routing scheme, the two independent processes, that is, the fastest packet sending process at source

Two absorbing Markov chains. For each state, the transition back to itself is not plotted for simplicity.

Absorbing Markov chain for the fastest packet sending process at source

Absorbing Markov chain for the fastest packet receiving process at destination

As shown in Figure

As shown in Figure

Suppose that, for the Markov chain shown in Figure

For the considered traffic flow and a given time slot, let

For the considered traffic flow and a given packet group, in some time slot, suppose that the source node

The derivations of these probabilities in Lemmas

For the Markov chain in Figure

It is notable that, for the

Let

For the considered mobile ad hoc network, the network can stably support any packet arrival rate

For the considered traffic flow, if the network is stable (i.e., the queue length at each node does not grow to infinity as the time tends to infinity) under the packet arrival rate

This is because, in a stable network, the long-term average rate of the input traffic is equal to that of the output one.

We use

Based on (

Since

To determine

Based on Markov chain theory, we know that

We now derive

We can see from Figure

We notice that if the Markov chain of Figure

By substituting

This finishes the proof of Theorem

In this section, we first provide simulation results to validate the accuracy of the theoretical model for the maximum throughput and then apply the theoretical model to explore the maximum throughput performance of mobile ad hoc networks.

To validate the accuracy of theoretical maximum throughput, a simulator was designed to simulate the packet delivery process under the considered routing scheme. The guard factor

Extensive simulations were performed to validate the accuracy of theoretical model for maximum throughput. We presented the simulation results here under two network scenarios (

Throughput versus system load

The throughput for network scenario (

The throughput for network scenario (

Another interesting observation from Figures

Based on our theoretical model for maximum throughput, we first explore the impact of number of code blocks

To understand the impact of number of original packets

Finally, we explore the impact of number of nodes

This paper studied the actual maximum throughput performance in mobile ad hoc network under a general routing scheme with reed-solomon coding. The closed-form expression of maximum throughput was derived with the help of the two Markov chain models, which were established to depict the fastest packet sending and receiving processes at source and destination nodes under the routing scheme. Extensive simulations show that our theoretical model can accurately predict the maximum throughput performance in the considered networks. Our findings are that reed-solomon coding technique could increase the maximum throughput of mobile ad hoc networks through sending limited number of code blocks, and also for each considered network, there exists an optimal network size to maximize the maximum throughput of such network.

The authors declare no conflict of interests regarding the publication of this paper.

This work was supported by NSF of Anhui Education Department under Grants KJ2013B188, KJ2014A179, KJ2015A285, and KJ2015A190, by NSF of Anhui Province under Grant 1508085MF123, by NSF of Chuzhou University under Grant 2012kj002Z, by Chuzhou University Excellent Young Talents Fund Project under Grant 2013RC005, and by Chuzhou University Talented Team of Computer System Architecture.