Scattered thoughts from applied probability: networks, security queues and prediction tournaments

A sample of topics that have caught my eye in recent years.

(a) Prediction tournaments are like sports in that a higher-ranked player will likely score better than a lower-ranked one. But paradoxically, under a reasonable model the winner of a tournament is relatively less likely to be a top-ranked player, maybe clouding the interpretation of multimillion dollar IARPA-sponsored projects.

(b) At the back of a long queue at airport security, you stand still until a wave of motion reaches you; a non-standard model gives quantitative predictions for such waves.

(c) Spatial networks give rise to intriguing questions. For instance, suppose (as a bizarre fantasy) that an eccentric multi-billionaire proposes to solve traffic congestion in a huge metropolitan region by digging underground tunnels through which cars can move very fast; where to dig the tunnels?

(d) As a hard technical question, epidemic models combine a model for a contact network with a model for transmission between contacts, with various parameters including an infectiousness parameter $\rho$. Intuitively, there is always a critical value $\rho_c$ such that, starting with a sprinkling of $o(n)$ infectives, there will w.h.p. be a pandemic if $\rho > \rho_c$ but w,h,p. not if $\rho < \rho_c$. This is true in familiar specific models for the contact network, but can we prove this for all contact networks?