Online Dynamic Pricing for Electric Vehicle Charging Stations with Reservations

TL;DR

This work tackles online dynamic pricing for EV charging by pricing a full reservation bundle (charging, parking, and reservation) at a single high-demand station. It models reservation arrivals as a continuous-time Poisson process and embeds them into a discrete-time MDP, introducing a discretization that can be controlled by timesteps $k$ and quantified via a discretization-error metric. A Monte-Carlo Tree Search (MCTS) heuristic with a UCT-based tree policy and rollout is proposed to compute pricing decisions, with implementation details and parameter choices provided. Experiments on synthetic instances show the MCTS approach rivals the optimal VI baseline when feasible and consistently outperforms a flat-rate benchmark, while also offering scalable performance insights for larger problems. The results demonstrate the practicality of fully bundled dynamic pricing and provide a framework for analyzing discretization error in continuous-time demand models.

Abstract

This paper introduces a novel model for online dynamic pricing of electric vehicle charging services that integrates reservation, parking, and charging into a comprehensive bundle priced as a whole. Our approach focuses on the individual high-demand, fast-charging location, employing a Poisson process as a model of charging reservation arrivals, and develops an online dynamic pricing strategy optimized through a Markov Decision Process (MDP). A key contribution is the novel analysis of discretization error introduced when incorporating the continuous-time Poisson process into the discrete MDP framework. The MDP model's feasibility is demonstrated with a heuristic dynamic pricing method based on Monte-Carlo tree search, offering a viable path for real-world applications.

Figures (13)

• Figure 1: Structure of the literature survey.
• Figure 2: Illustration of the online dynamic pricing of charging. The charging products being priced are vertical columns in the resource matrix on top. For example, product $[1,1,0]$ represents consecutive charging in the first time slot (resource) and second time slot out of the three. In the charging problem, we assume each product contains every resource (the charging slot capacity in a time interval) only once and that products contain only consecutive time intervals (i.e., there is no product $[1,0,1]$). Below the matrix, the request arrivals and budgets show customers requesting different products at different times and their budgets ($b_1$ to $b_7$). The next line below shows pricing actions$a_1$ to $a_7$ taken by the seller. When a customer accepts the price (i.e., when $b_i \ge a_i$, shown as green ✓), the seller accumulates a reward $r_i$, and his resource capacity is reduced by the product requirements, this is shown on the two bottom lines.
• Figure 3: Illustration of the states for the dynamic pricing of charging. Unlike \ref{['dynamic_pricing_model']}, this figure illustrates the expiration of resources after their selling period ends (grey in the capacity and product vectors). The blue squares represent the states. At timestep $t$, the capacity of the CS is expressed by the capacity vector $\boldsymbol{c}_t$. Elements of the vector represent available charging capacity in corresponding timeslots (time ranges in the green square). Possible charging session reservation requests arriving since the previous timestep is expressed by the vector $\boldsymbol{p}_t$, with ones representing the requested timeslots. Based on the three state variables $\boldsymbol{c}_t, t, \boldsymbol{p}_t$, the pricing policy provides an action $a$, the price for charging, that the user either accepts (the first two states at the bottom) or rejects (the state on the right). The state then transitions into the next timestep (details of the transition function are illustrated by \ref{['fig:decision_tree']}). The accepted charging request leads to reduced capacity values. The next charging session reservation is entered into the new state. Note that the timesteps must have much finer resolution than the charging timeslots. The gray color shows past information regarding the charging capacity and session vectors $\boldsymbol{c}_t$ and $\boldsymbol{p}_t$, respectively.
• Figure 4: The structure of the transition function $\mathcal{T}$. Given state $s_t$, the probability of getting to the next state $s_{t+1}$ is given by multiplying the probabilities along the edges. States are the decision nodes (in red), and chance states are in blue and contain the definition of the probability used along the edge.
• Figure 5: Visualization of the error term $\varepsilon_{2}(k,\lambda)$ (left) and the relative error $\varepsilon_{2}(k, \lambda)/\lambda$ (right) for different values of $k$ and $\lambda$. $\varepsilon_{2}$ is defined in \ref{['prop:err_formula']} and represents the number of ignored events caused by the discretization of the Poisson process. With the number of timesteps $k$ approaching $0$, the number of ignored events approaches the expected number of events $\lambda$. The relative error term $\varepsilon_{2}(k, \lambda)/\lambda$ (\ref{['eq:relative_error']}) represents the number of ignored events relative to the expected number of events.

Theorems & Definitions (4)

• Proposition 1
• proof
• Proposition 2
• proof