Abstract:In this paper we analyze synthetic mobility traces generated for three-lane unidirectional motorway traffic to find that the locations of vehicles along a lane are better modeled by a hardcore point process instead of the widely-accepted Poisson point process (PPP). In order to capture the repulsion between successive vehicles while maintaining a level of analytical tractability, we make a simple extension to PPP: We model the inter-vehicle distance along a lane equal to the sum of a constant hardcore distance… Show more
“…In Fig. 5, it is illustrated that the approximations in (22) and (23) are good also for realistic activity values, e.g., up to ξ = 0.2. For ξ = 0.5 we obtain θ = 1 for T = 0.5, and the approximations in (22), (23) break down.…”
Section: Properties Of the Meta Distributionmentioning
confidence: 87%
“…3 for example illustrations. (22) and (23) in Lemma 3 estimate accurately the moments due to the simulated hardcore process. The model M2 fails.…”
Section: Properties Of the Meta Distributionmentioning
confidence: 91%
“…The PPP becomes more problematic for the left lane because due to the high speeds over there, the drivers maintain large safety distances. We have illustrated that the envelope of the J-function for the fitted hardcore process Φ c can capture the J-function of the real snapshot, see [23,Sec. IV] for a detailed description of the fitting method.…”
Section: Validation With Real Tracesmentioning
confidence: 93%
“…The extension of the discretization model to multiple lanes is straightforward by discretizing with lane-specific parameter c. Due to directionality, only vehicles behind some distance r 0 from the receiver may contribute to other-lane interference, see [23,Section VI]. The interference originated from other lanes does not require to constrain the location of any of the points of the processes.…”
Section: Validation With Real Tracesmentioning
confidence: 99%
“…Unlike the urban scenario in [22], we would like to shed some light on the meta distribution of the SIR along motorways. Naturally, the drivers maintain large safety distances in motorways, and the PPP may not model accurately the locations of vehicles [23]. In order to maintain some degree of analytical tractability while introducing more realistic deployment, we have adopted the shifted-exponential distribution for the inter-vehicle distance in [23]- [25].…”
The meta distribution of the signal-to-interferenceratio (SIR) is an important performance indicator for wireless networks because, for ergodic point processes, it describes the fraction of scheduled links that achieve certain reliability, conditionally on the point process. In this paper, we calculate the moments of the meta distribution in vehicular ad hoc networks (VANETs) along high-speed motorways. Due to the high speeds, the drivers maintain large safety distances, and the Poisson point process (PPP) becomes a poor deployment model. Because of that, we model the distribution of inter-vehicle distance equal to the sum of a constant hardcore distance and an exponentially distributed random variable. We design a novel discretization model for the locations of vehicles which can be used to approximate well the meta distribution of the SIR due to the hardcore process. We validate the model against synthetic motorway traces. On the other hand, the PPP overestimates significantly the coefficient-of-variation of the meta distribution due to the hardcore process, and its predictions fail. In addition, we show that the calculation of the meta distribution becomes especially meaningful in the upper tail of the SIR distribution.
“…In Fig. 5, it is illustrated that the approximations in (22) and (23) are good also for realistic activity values, e.g., up to ξ = 0.2. For ξ = 0.5 we obtain θ = 1 for T = 0.5, and the approximations in (22), (23) break down.…”
Section: Properties Of the Meta Distributionmentioning
confidence: 87%
“…3 for example illustrations. (22) and (23) in Lemma 3 estimate accurately the moments due to the simulated hardcore process. The model M2 fails.…”
Section: Properties Of the Meta Distributionmentioning
confidence: 91%
“…The PPP becomes more problematic for the left lane because due to the high speeds over there, the drivers maintain large safety distances. We have illustrated that the envelope of the J-function for the fitted hardcore process Φ c can capture the J-function of the real snapshot, see [23,Sec. IV] for a detailed description of the fitting method.…”
Section: Validation With Real Tracesmentioning
confidence: 93%
“…The extension of the discretization model to multiple lanes is straightforward by discretizing with lane-specific parameter c. Due to directionality, only vehicles behind some distance r 0 from the receiver may contribute to other-lane interference, see [23,Section VI]. The interference originated from other lanes does not require to constrain the location of any of the points of the processes.…”
Section: Validation With Real Tracesmentioning
confidence: 99%
“…Unlike the urban scenario in [22], we would like to shed some light on the meta distribution of the SIR along motorways. Naturally, the drivers maintain large safety distances in motorways, and the PPP may not model accurately the locations of vehicles [23]. In order to maintain some degree of analytical tractability while introducing more realistic deployment, we have adopted the shifted-exponential distribution for the inter-vehicle distance in [23]- [25].…”
The meta distribution of the signal-to-interferenceratio (SIR) is an important performance indicator for wireless networks because, for ergodic point processes, it describes the fraction of scheduled links that achieve certain reliability, conditionally on the point process. In this paper, we calculate the moments of the meta distribution in vehicular ad hoc networks (VANETs) along high-speed motorways. Due to the high speeds, the drivers maintain large safety distances, and the Poisson point process (PPP) becomes a poor deployment model. Because of that, we model the distribution of inter-vehicle distance equal to the sum of a constant hardcore distance and an exponentially distributed random variable. We design a novel discretization model for the locations of vehicles which can be used to approximate well the meta distribution of the SIR due to the hardcore process. We validate the model against synthetic motorway traces. On the other hand, the PPP overestimates significantly the coefficient-of-variation of the meta distribution due to the hardcore process, and its predictions fail. In addition, we show that the calculation of the meta distribution becomes especially meaningful in the upper tail of the SIR distribution.
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