Sanjoy Kumar Jhawar

Gourab Ghatak, Sanjoy Kumar Jhawar, Martin Haenggi

We study street-constrained ($\ell_1$) shortest paths in a Poisson line Cox process (PLCP), where Poisson points of linear intensity $μ$ lie on the lines of an underlying Poisson line process (PLP) of density $λ$. Under a one-turn restriction, we derive closed-form expressions for the distribution of the nearest-neighbor path length from (i) the typical PLCP point and (ii) the typical PLP intersection, by explicitly evaluating the relevant void probabilities via a geometric decomposition of the feasible path-length set. For the intersection case, we further provide analytically tractable upper and lower bounds that capture the impact of $λ$ and $μ$. Allowing two turns from the typical point, we obtain a computable upper bound using a feasible-set shrinking argument and identify regimes in which it is tight. We also delineate parameter ranges where a one-turn route from a typical intersection can outperform a two-turn route from a typical point. Finally, we discuss how the results enable statistical performance characterization of ride-hailing services in terms of service guarantee, trip time, and consequently, derive dimensioning insights. We also illustrate qualitatively, how the results can be employed to study vehicle-to-vehicle communication broadcast messages near intersections.

Sanjoy Kumar Jhawar, François Baccelli

In this work we consider a dynamical cellular communication network in which mobile BSs are modeled as a homogeneous Poisson point process on $\mathbb R^2$. Each base station moves at a constant speed in a random direction. A typical user connects to the nearest base station and it experiences variable signal and interference powers depending on the distance of all the stations. Along the motion of the stations, the user swaps its serving station, and such an event is called a handover. We are interested in the performance evaluation of the system under some classical and tropical metrics of interest at different time of events, inducing handovers, maximal proximity of serving station, nearest interferer at closest or farthest distance with respect to the user or at any typical time epoch. A comparison study of quality of service and Shannon capacity at these epochs is also provided, among the recurrence of such ``good'' or ``bad'' scenarios. We can make an analogy with seasons based on the fluctuations of signal and interference power. Strong or mild signal or interference power correspond to different seasons of Shannon capacity along the evolution of the system.