[Paper Review] Urban sensing as a random search process

Kevin O’Keeffe, Paolo Santi+2 more|arXiv (Cornell University)|Jan 24, 2019

Diffusion and Search DynamicsBiochemistry, Genetics and Molecular Biology2 references3 citations

TL;DR

This paper introduces the 'taxi drive' as a novel random search process that combines random destination selection with deterministic shortest-path routing in urban street networks. It demonstrates through numerical simulations that this hybrid motion reduces cover times compared to standard random walks and persistent random walks on various graph topologies, making it highly effective for urban sensing applications.

ABSTRACT

We study a new random search process: the extit{taxi-drive}. The motivation for this process comes from urban sensing, in which sensors are mounted on moving vehicles such as taxis, allowing urban environments to be opportunistically monitored. Inspired by the movements of real taxis, the taxi-drive is composed of both random and regular parts; passengers are brought to randomly chosen locations via deterministic (i.e. shortest paths) routes. We show through a numerical study that this hybrid motion endows the taxi-drive with advantageous spreading properties. In particular, on certain graph topologies it offers reduced cover times compared to persistent random walks.

Motivation & Objective

• To model and analyze a new random search process inspired by taxi movements in urban environments.
• To investigate the spreading properties of the taxi drive process on real-world and synthetic street network topologies.
• To compare the cover time of the taxi drive with classical random walk and persistent random walk processes.
• To understand how the interplay between randomness and regularity in taxi motion affects coverage efficiency in urban sensing.
• To establish theoretical foundations for the taxi drive as a stochastic process with potential applications in urban sensing and network monitoring.

Proposed method

• The taxi drive process is defined on a street network represented as a graph, with nodes as intersections and edges as street segments.
• At each step, a taxi picks up a passenger at a random node and travels along the shortest path to a randomly selected destination node.
• In cases of multiple shortest paths between origin and destination, one is selected uniformly at random.
• The process is simulated over time to compute segment visit frequencies and cover times on various graph topologies.
• Cover time is measured as the expected time for all street segments to be visited at least once.
• The performance of the taxi drive is compared numerically against ordinary random walks and persistent random walks on identical network structures.

Experimental results

Research questions

• RQ1 How does the cover time of the taxi drive process compare to that of standard random walks on urban street networks?
• RQ2 What role does the combination of random destination selection and deterministic routing play in enhancing coverage efficiency?
• RQ3 Does the taxi drive process exhibit a stationary distribution of segment visit frequencies, and does it align with real-world data patterns such as Zipf's law?
• RQ4 How does the scaling of cover time with network size compare between the taxi drive and other random walk variants?
• RQ5 Can the taxi drive process be generalized to include memory effects or preferential destination selection, and does it maintain favorable spreading properties?

Key findings

• The taxi drive process achieves significantly reduced cover times compared to ordinary random walks and persistent random walks on various graph topologies.
• On real-world street networks such as Manhattan, the taxi drive's segment popularity distribution closely follows Zipf's law, matching empirical data from nine global cities.
• The stationary distribution of the taxi drive process converges to a power-law form, indicating that a few high-traffic segments dominate, which is consistent with real taxi data.
• The process exhibits a well-defined stationary limit for node visit frequencies, even with dynamic destination selection based on past visits (β > 0), confirming its long-term stability.
• The hybrid nature of the taxi drive—combining randomness in destination choice with determinism in routing—leads to superior spreading properties compared to purely stochastic processes.
• Numerical results show that the ratio of average cover times (taxi drive to random walk) scales sublinearly with network size, indicating increasing efficiency as networks grow.