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Transmission power control (TPC) leads to heterogeneous transmission power levels of the nodes in multi-hop wireless ad hoc networks. This eventually results in a quite complicated collision scenario due to hidden and exposed terminal problems, and brings a big challenge for analyzing the saturation throughput of the flows. This paper presents a saturation throughput model for IEEE 802.11 multi-hop ad hoc networks with heterogeneous transmission powers. In the model, one tagged node goes through with three processes, i.e., backoff, freezing and transmission, and each of which is composed of a certain number of continuous fixed length time slots. We put forward a four-dimensional Markov chain model for the behavior of the tagged node in each fixed-length time slot. Under the condition of heterogeneous transmission powers, we consider two types of collisions, i.e., the instantaneous and persistent collisions. Their probabilities are characterized by the one-step transition probability matrix of the Markov chain. The per-flow saturation throughput of the flow is eventually derived through an iterative way. Finally, the accuracy of our model is validated by comparing the analytical values and the simulation results, and the impact of the heterogeneous power levels on the performance of the wireless multi-hop ad hoc networks is effectively analyzed.

In this paper, we focus on the per-flow throughput analysis of IEEE 802.11 multi-hop ad hoc networks. The importance of an accurate saturation throughput model lies in establishing the theoretical foundation for effective protocol performance improvements. We argue that the challenge in modeling the per-flow throughput in IEEE 802.11 multi-hop ad hoc networks lies in the analysis of the freezing process and probability of collisions. We first classify collisions occurring in the whole transmission process into instantaneous collisions and persistent collisions. Then we present a four-dimensional Markov chain model based on the notion of the fixed length channel slot to model the Binary Exponential Backoff (BEB) algorithm performed by a tagged node. We further adopt a continuous time Markov model to analyze the freezing process. Through an iterative way, we derive the per-flow throughput of the network. Finally, we validate the accuracy of our model by comparing the analytical results with that obtained by simulations. [ABSTRACT FROM AUTHOR]