In recent years, a significant amount of research has been conducted to explore the benefits of network coding in different scenarios, from both theoretical and simulation perspectives. In this paper, we utilize queueing theory to propose an analytical framework for bidirectional unicast flows in multi-hop wireless mesh networks, and study throughput of inter-flow network coding. We analytically determine performance metrics such as the probability of successful transmission in terms of collision probability, and feedback mechanism and retransmission. Regarding the coding process, our model uses a multi-class queueing network where coded packets are separated from native packets and have a non-preemptive higher priority over native packets, and both queues are in a stable state. Finally, we use simulations to verify the accuracy of our analytical model.
In a similar theoretical-based approach for multicast sessions, @cite_4 derive throughput for multi-hop wireless networks. However, in the coding process, they assume the decoding probability is equal to one and also they postpone transmission of the native packet at a node until receiving a packet from another flow to be combined with the first packet, and thus, causing a long delay.
@cite_4
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This paper presents an analytical study of the stable throughput for multiple broadcast sessions in a multi-hop wireless tandem network with random access. Intermediate nodes leverage on the broadcast nature of wireless medium access to perform inter-session network coding among different flows. This problem is challenging due to the interaction among nodes, and has been addressed so far only in the saturated mode where all nodes always have packet to send, which results in infinite packet delay. In this paper, we provide a novel model based on multi-class queueing networks to investigate the problem in unsaturated mode. We devise a theoretical framework for computing maximum stable throughput of network coding for a slotted ALOHA-based random access system. Using our formulation, we compare the performance of network coding and traditional routing. Our results show that network coding leads to high throughput gain over traditional routing. We also define a new metric, network unbalance ratio (NUR), that indicates the unbalance status of the utilization factors at different nodes. We show that although the throughput gain of the network coding compared to the traditional routing decreases when the number of nodes tends to infinity, NUR of the former outperforms the latter. We carry out simulations to confirm our theoretical analysis. We develop a new metric for quantifying end-to-end throughput in multihop wireless networks, which we term random access transport capacity, since the interference model presumes uncoordinated transmissions. The metric quantifies the average maximum rate of successful end-to-end transmissions, multiplied by the communication distance, and normalized by the network area. We show that a simple upper bound on this quantity is computable in closed-form in terms of key network parameters when the number of retransmissions is not restricted and the hops are assumed to be equally spaced on a line between the source and destination. We also derive the optimum number of hops and optimal per hop success probability and show that our result follows the well-known square root scaling law while providing exact expressions for the preconstants, which contain most of the design-relevant network parameters. Numerical results demonstrate that the upper bound is accurate for the purpose of determining the optimal hop count and success (or outage) probability. Throughput and per-packet delay can present strong trade-offs that are important in the cases of delay sensitive applications.We investigate such trade-offs using a random linear network coding scheme for one or more receivers in single hop wireless packet erasure broadcast channels. We capture the delay sensitivities across different types of network applications using a class of delay metrics based on the norms of packet arrival times. With these delay metrics, we establish a unified framework to characterize the rate and delay requirements of applications and optimize system parameters. In the single receiver case, we demonstrate the trade-off between average packet delay, which we view as the inverse of throughput, and maximum ordered inter-arrival delay for various system parameters. For a single broadcast channel with multiple receivers having different delay constraints and feedback delays, we jointly optimize the coding parameters and time-division scheduling parameters at the transmitters. We formulate the optimization problem as a Generalized Geometric Program (GGP). This approach allows the transmitters to adjust adaptively the coding and scheduling parameters for efficient allocation of network resources under varying delay constraints. In the case where the receivers are served by multiple non-interfering wireless broadcast channels, the same optimization problem is formulated as a Signomial Program, which is NP-hard in general. We provide approximation methods using successive formulation of geometric programs and show the convergence of approximations. We propose an adaptive coding technique for delay constrained simple wireless multi-hop line networks. We study the joint optimization of coding and scheduling with one sender and one receiver, with delay sensitive flows consisting of packets. We analyze the trade-off between delay and throughput for single path multi-hop wireless erasure links for different encoding and feedback acknowledgment schemes. To do so, we devise an p- norm delay cost metric where p models the sensitivity of the receiver. We show that with adaptively adjusting the coding bucket size based on p and the feedback delay, recoded multi-hop transmissions can increase the throughput of the end-to-end coded transmissions by 30 .