Dynamic Spatio-Temporal Resource Provisioning for On-Demand Urban Services in Smart Cities

TL;DR

This paper tackles dynamic, centralized resource provisioning for on-demand urban services with spatio-temporal demand modeled as a PPP. It introduces a threshold-based dynamic programming approach where a resource is allocated in a slot if the observed maximum per-slot utility $\tilde{Z}$ exceeds a threshold $\rho_T^N$, with a value function $V(T,N)$ guiding decisions. By deriving distributions $F_Z$ and $f_Z$ for various utility forms and leveraging order statistics and extreme-value ideas, the authors obtain semi-closed forms and a practical computation procedure for real-time implementation. Simulations with power-law and exponential utilities reveal that the proposed policy outperforms myopic and random baselines and approaches the ideal benchmark, validating the method's potential to enable real-time, scalable resource provisioning in smart-city contexts.

Abstract

Efficient allocation of finite resources is a crucial problem in a wide variety of on-demand smart city applications. Service requests often appear randomly over time and space with varying intensity. Resource provisioning decisions need to be made strategically in real-time, particularly when there is incomplete information about the time, location, and intensity of future requests. In this paper, we develop a systematic approach to the dynamic resource provisioning problem at a centralized source node to spatio-temporal service requests. The spatial statistics are combined with dynamically optimal decision-making to derive recursive threshold based allocation policies. The developed results are easy to compute and implement in real-time applications. For illustrative purposes, we present examples of commonly used utility functions, based on the power law decay and exponential decay coupled with exponentially, and uniformly distributed intensity of stochastic arrivals to demonstrate the efficacy of the developed framework. Semi-closed form expressions along with recursive computational procedure has been provided. Simulation results demonstrate the effectiveness of the proposed policies in comparison with less strategic methodologies.

Figures (8)

• Figure 1: Illustration of the centralized resource allocation problem during one time slot. The impulse height represents the intensity of requests. The maximum intensity request is highlighted by a bold blue impulse with an arrowhead.
• Figure 2: Red dots indicate the boundary cases for the pair ($T,N$). Blue dots indicate the cases for which the decision problem needs to be solved for allocation.
• Figure 3: Spatial requests in one allocation period. The bold arrow represents the request with maximum intensity. Concentric surfaces correspond to the allocation thresholds if one, two, and three resources are available respectively.
• Figure 4: Resource allocation thresholds for exponential intensity of service requests.
• Figure 5: Total expected utility against varying spatio-temporal density of requests.

Theorems & Definitions (20)

• Lemma 1
• proof
• Remark 1
• Lemma 2
• Lemma 3
• proof
• Lemma 4
• proof
• Theorem 1
• proof