This paper analyzes the connection between the protocol and physical interference models in the setting of Poisson wireless networks. A transmission is successful under the protocol model if there are no interferers within a parameterized guard zone around the receiver, while a transmission is successful under the physical model if the signal to interference plus noise ratio (SINR) at the receiver is above a threshold. The parameterized protocol model forms a family of decision rules for predicting the success or failure of the same transmission attempt under the physical model. For Poisson wireless networks, we employ stochastic geometry to determine the prior, evidence, and posterior distributions associated with this estimation problem. With this in hand, we proceed to develop five sets of results: i) the maximum correlation of protocol and physical model success indicators, ii) the minimum Bayes risk in estimating physical success from a protocol observation, iii) the receiver operating characteristic (ROC) of false rejection (Type I) and false acceptance (Type II) probabilities, iv) the impact of Rayleigh fading vs. no fading on the correlation and ROC, and v) the impact of multiple prior protocol model observations in the setting of a wireless network with a fixed set of nodes in which the nodes employ the slotted Aloha protocol in each time slot.
Several works have explored how to employ the protocol model within the context of scheduling @cite_3 @cite_2 @cite_0 . Hasan and Andrews @cite_3 study the protocol model as a scheduling algorithm in CDMA-based wireless ad hoc networks. They comment that a guard zone around each transmitter induces a natural tradeoff between interference and spatial reuse, affecting higher layer performance metrics such as transmission capacity, and they employ stochastic geometry to derive a guard zone that maximizes transmission capacity. Shi @cite_5 examine the use of the protocol model within a cross-layer optimization framework and provide a strategy for correcting infeasible schedules generated under the protocol model by allowing transmission rate-adaptation to physical model SINR. Zhang @cite_1 analyze the effectiveness of protocol model scheduling using a variety of analytical, simulation, and testbed measurements. This body of work on the protocol model as a scheduling paradigm is distinct from our focus on the protocol model as an interference model of the success or failure of attempted transmissions. Iyer @cite_6 compares several interference models via simulation and qualitatively discusses the sacrifices in accuracy associated with abstracted interference models, including the protocol model.
@cite_1 @cite_3 @cite_6 @cite_0 @cite_2 @cite_5
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Accurate analytical expressions of delay and packet reception probabilities, and energy consumption of duty-cycled wireless sensor networks with random medium access control (MAC) are instrumental for the efficient design and optimization of these resource-constrained networks. Given a clustered network topology with unslotted IEEE 802.15.4 and preamble sampling MAC, a novel approach to the modeling of the delay, reliability, and energy consumption is proposed. The challenging part in such a modeling is the random MAC and sleep policy of the receivers, which prevents to establish the exact time of data packet transmission. The analysis gives expressions as function of sleep time, listening time, traffic rate and MAC parameters. The analytical results are then used to optimize the duty cycle of the nodes and MAC protocol parameters. The approach provides a significant reduction of the energy consumption compared to existing solutions in the literature. Monte Carlo simulations by ns2 assess the validity of the analysis. Interference model is the basis of MAC protocol design in wireless networked sensing and control, and it directly affects the efficiency and predictability of wireless messaging. To exploit the strengths of both the physical and the protocol interference models, we analyze how network traffic, link length, and wireless signal attenuation affect the optimal instantiation of the protocol model. We also identify the inherent trade-off between reliability and throughput in the model instantiation. Our analysis sheds light on the open problem of efficiently optimizing the protocol model instantiation. Based on the analytical results, we propose the physical-ratio-K (PRK) interference model as a reliability-oriented instantiation of the protocol model. Via analysis, simulation, and testbed-based measurement, we show that PRK-based scheduling achieves a network throughput very close to (e.g., 95p) what is enabled by physical-model-based scheduling while ensuring the required packet delivery reliability. The PRK model inherits both the high fidelity of the physical model and the locality of the protocol model, thus it is expected to be suitable for distributed protocol design. These findings shed new light on wireless interference models; they also suggest new approaches to MAC protocol design in the presence of uncertainties in network and environmental conditions as well as application QoS requirements. Many published algorithms used for scheduling transmissions in packet radio networks are based on finding maximal independent sets in an underlying graph. Such algorithms are developed under the assumptions of variations of the protocol interference model, which does not take the aggregated effect of interference into consideration. We provide a probabilistic analysis for the throughput performance of such graph based scheduling algorithms under the physical interference model. We show that in many scenarios a significant portion of transmissions scheduled based on the protocol interference model result in unacceptable signal-to-interference and noise ratio (SINR) at intended receivers. Our analytical as well as simulation results indicate that, counter intuitively, maximization of the cardinality of independent sets does not necessarily increase the throughput of a network. We introduce the truncated graph based scheduling algorithm (TGSA) that provides probabilistic guarantees for the throughput performance of the network. We consider the scheduling of arbitrary wireless links in the physical model of interference to minimize the time for satisfying all requests. We study here the combined problem of scheduling and power control, where we seek both an assignment of power settings and a partition of the links so that each set satisfies the signal-to-interference-plus-noise (SINR) constraints. We give an algorithm that attains an approximation ratio of O(log n ċ log log Δ), where n is the number of links and Δ is the ratio between the longest and the shortest link length. Under the natural assumption that lengths are represented in binary, this gives the first approximation ratio that is polylogarithmic in the size of the input. The algorithm has the desirable property of using an oblivious power assignment, where the power assigned to a sender depends only on the length of the link. We give evidence that this dependence on Δ is unavoidable, showing that any reasonably behaving oblivious power assignment results in a Ω(log log Δ)-approximation. These results hold also for the (weighted) capacity problem of finding a maximum (weighted) subset of links that can be scheduled in a single time slot. In addition, we obtain improved approximation for a bidirectional variant of the scheduling problem, give partial answers to questions about the utility of graphs for modeling physical interference, and generalize the setting from the standard 2-dimensional Euclidean plane to doubling metrics. Finally, we explore the utility of graph models in capturing wireless interference.