Outage in Motorway Multi-Lane VANETs With Hardcore Headway Distance Using Synthetic Traces

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 and an exponentially distributed random variable. We calculate the J-function and the Ripley's Kfunction for this hardcore point process. We fit its parameters to the available traces, and we illustrate that the higher the average speed along a lane, the more prominent the hardcore component becomes. In addition, we consider a transmitter-receiver link on the same lane, and we generate simple formulae for the moments of interference under reduced Palm measure for that lane, and without conditioning for other lanes. We illustrate that under Rayleigh fading a shifted-gamma approximation for the distribution of interference per lane provides a very good fit to the simulated outage probability using the synthetic traces, while the fit using the PPP is poor.

The Meta Distribution of the SIR in Linear Motorway VANETs

“…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.…”

“…3 for example illustrations. (22) and (23) in Lemma 3 estimate accurately the moments due to the simulated hardcore process. The model M2 fails.…”

“…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.…”

“…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.…”

“…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].…”