I investigate how a public charging station should allocate its scarce service capacity when users of electric car charging services can either arrive immediately or reserve a future charging window. The central object of my analysis is a coexisting reservation mechanism in which reservation users and walk-in users are both admitted, rather than a fully reservation-based system or a pure priority system. This distinction matters for electric car charging because public charging demand is spatially concentrated, temporally volatile, and strongly affected by queue uncertainty. A driver of an electric car who observes a long queue may leave the station and search elsewhere; a reservation option can retain part of that demand, but it can also lock capacity and create no-show or late-cancellation losses. I therefore compare three service capacity allocation mechanisms under a common simulation sample: first-come, first-served service, a static coexisting reservation mechanism, and a dynamic coexisting reservation mechanism. The first mechanism represents conventional operation. The second uses a fixed reservation quota throughout the day. The third adjusts the reservation quota according to real-time waiting pressure, predicted future load, and currently available charging guns. I evaluate revenue, completed service, user exits, actual waiting time, fulfillment outcomes, and the boundary conditions under which reservation creates value for electric car charging stations.
The motivation for this study is straightforward. Public charging infrastructure for electric cars has expanded rapidly, but additional charging guns are not always the most immediate lever available to an operator. In many urban stations, the operational question is how to use existing charging capacity more intelligently. Service capacity allocation between reservation users and walk-in users is one such lever. If the station reserves too little capacity, some electric car users who would have accepted a future appointment leave the system. If the station reserves too much capacity, immediate users are crowded out, and accepted reservations may fail to materialize because of late cancellation or no-show. The coexistence of reservation and immediate arrival therefore creates a trade-off between demand retention, service loss, and fulfillment loss. I build a model that makes this trade-off explicit and then use numerical experiments to identify when a coexisting reservation mechanism is worthwhile for electric car charging service providers.
Research Positioning and Contribution
Existing work on electric car charging reservations can be grouped into three broad streams. The first stream studies how reservation information enters pre-trip decisions, including route choice, station choice, and charging time selection. The second stream focuses on within-station scheduling and capacity assignment, including charging order, waiting time estimation, and time-slot allocation. The third stream examines pricing, refunds, deposit design, and cancellation penalties for electric car charging reservations. These streams provide useful foundations, but they often treat reservation as a fully reserved system or as a priority rule. They also tend to focus on either user routing or station scheduling rather than on the combined revenue, service completion, and waiting consequences of a coexisting reservation mechanism. My study fills this gap by modeling a public charging station in which reservation users and walk-in users coexist, and by comparing static and dynamic reservation quotas under a common set of electric car demand scenarios.
My contribution is threefold. First, I formulate a coexisting reservation mechanism for electric car charging that protects accepted reservations while still allowing immediate users to enter the station. Second, I develop a decomposition that separates the revenue effect of reservation into demand retention, service loss, and fulfillment loss. This decomposition allows me to identify not only whether reservation increases revenue but also why it does so. Third, I build a scenario-based simulation framework that covers different average load levels, intraday peak profiles, fulfillment environments, charging-duration distributions, supply disturbances, demand shocks, and user behavior parameters. The framework identifies the boundary conditions for static and dynamic reservation in electric car charging service capacity allocation. The managerial implication is that reservation is not a universal remedy; it is a mechanism whose value depends on load pressure, demand volatility, fulfillment quality, and the station’s ability to observe and respond to real-time states.
Model Setting
I consider a single public charging station that serves electric car users over one operating day. The day is divided into equal-length service periods. Let the set of periods be
$$T=\{0,1,\ldots,H-1\}$$
where each period represents fifteen minutes and the main experiment uses ninety-six periods. The station has a number of available charging guns in period t, denoted by X_t. In the main analysis, the station has fifteen charging guns, so X_t equals fifteen for all periods. In an extension, I allow X_t to vary to represent local equipment failure and supply-side disturbance. An electric car user arrives in period a_i and requires d_i consecutive service periods for charging. The service duration satisfies one period at minimum and a maximum d_max. The user obtains a total value v_i from completing the charging service, and the station charges a price r per service period. The payment for a completed charging service is therefore r d_i. Users differ in their per-period waiting cost c_i, their maximum acceptable waiting time w_i^max, and their reservation friction phi_i. The reservation friction captures the additional planning and transaction burden of booking a future electric car charging slot.
I assume that a user observes the current queue information and the system’s expected waiting time at arrival, and then chooses among immediate service, reservation service, and exit. If the user accepts immediate service and enters the first-come, first-served queue, the user does not subsequently exit. In the coexisting reservation mechanism, an accepted reservation locks future service capacity. This lock can delay the immediate queue that has not yet started service, but it does not interrupt charging that has already begun. Within the same period, the system first processes early cancellations and releases the corresponding reserved capacity, and then processes new user decisions. This sequence reflects a practical operating rule for electric car charging stations: cancellation information should be updated before new reservations and walk-in admissions are evaluated.
To make mechanism comparisons meaningful, I use the same simulation sample for arrival times, service durations, user preferences, and fulfillment states across all mechanisms. Differences in outcomes therefore come only from the service capacity allocation rule. All service occupancy, queue waiting, reservation windows, cancellation lead time, and mechanism decomposition are measured in service periods. Four service periods correspond to one hour. I use operating revenue as the performance proxy. I do not include electricity purchase cost, equipment depreciation, platform maintenance, or credit-management cost. Therefore, the revenue quantities reported below are operating revenue and revenue increments, not profit increments.
First-Come, First-Served Mechanism
Under the first-come, first-served mechanism, the station does not open reservations, and all service capacity is assigned according to arrival order. Let n_t^{mu_F} be the number of service units already planned for period t by accepted immediate-service users under mechanism mu_F. For a user i who arrives in period a_i and seeks immediate service starting in period s, the feasibility condition is
$$n_t^{\mu_F}+1 \le X_t,\quad t=s,s+1,\ldots,s+d_i-1.$$
The earliest feasible start period is
$$s_i^{\mu_F}=\min\{s\ge a_i:\ n_t^{\mu_F}+1 \le X_t,\ t=s,\ldots,s+d_i-1\}.$$
If this set is nonempty, the waiting time is w_i^{mu_F}=s_i^{mu_F}-a_i, and the net utility of immediate service is
$$U_i^{I,\mu_F}=v_i-r d_i-c_i w_i^{\mu_F}.$$
If no feasible start period exists, or if the waiting time exceeds the user’s maximum acceptable waiting time, the user treats immediate service as unavailable. The user accepts immediate service only when the net utility is nonnegative. Otherwise, the user exits. In this mechanism, the electric car user has only two relevant options: accept the earliest feasible immediate service or leave the station. The first-come, first-served mechanism is therefore a useful benchmark because it represents conventional operation without any reservation-based service capacity allocation.
Coexisting Reservation Mechanism
Under a coexisting reservation mechanism, the station admits both reservation users and immediate users. For any reservation mechanism mu, let m_{a_i}^{mu} be the reservation quota observed by user i at arrival period a_i. Let b_{t|a_i}^{mu} be the number of accepted reservations that have locked capacity in future period t as of period a_i. To avoid crowding out existing reservation commitments when the quota is adjusted downward, the mechanism protects service capacity in period t according to
$$p_{t\mid a_i}^{\mu}=\max\{m_{a_i}^{\mu},b_{t\mid a_i}^{\mu}\}.$$
This protection rule is important for electric car charging reservations because users who have already received a confirmed appointment should not be displaced by later quota changes. The rule creates a form of commitment protection while still allowing the station to reserve additional capacity when the current reservation quota is higher than existing commitments.
For a user who seeks immediate service starting in period s, the feasibility condition under the coexisting reservation mechanism is
$$n_t^{\mu}+1 \le X_t-p_{t\mid a_i}^{\mu},\quad t=s,s+1,\ldots,s+d_i-1.$$
The earliest feasible immediate start period is
$$s_i^{I,\mu}=\min\{s\ge a_i:\ n_t^{\mu}+1 \le X_t-p_{t\mid a_i}^{\mu},\ t=s,\ldots,s+d_i-1\}.$$
If the feasible set is nonempty and the waiting time does not exceed the user’s maximum acceptable waiting time, the net utility of immediate service is
$$U_i^{I,\mu}=v_i-r d_i-c_i(s_i^{I,\mu}-a_i).$$
If no feasible start period exists, or if the waiting time exceeds the user’s limit, the immediate-service utility is treated as negative infinity. For a reservation option, the reservation window length is W. In the main experiment, W equals eight service periods, corresponding to two hours. The set of feasible reservation start periods for user i is
$$A_i^{R,\mu}=\{s:\ a_i+1 \le s \le \min(a_i+W,H-d_i),\ b_{t\mid a_i}^{\mu}+1 \le m_{a_i}^{\mu},\ t=s,\ldots,s+d_i-1\}.$$
If the user chooses a reservation starting in period s within this set, the net reservation utility is
$$U_i^{R,\mu}(s)=v_i-r d_i-\alpha(s-a_i)-\phi_i,$$
where alpha is the inconvenience cost of shifting the charging start to a later period and phi_i is the user-specific reservation friction. The user’s choice under mechanism mu is
$$\max\left\{0,\ U_i^{I,\mu},\ \max_{s\in A_i^{R,\mu}}U_i^{R,\mu}(s)\right\}.$$
If the maximum is zero, the user exits. Otherwise, the user chooses the option with the highest net utility. The coexisting reservation mechanism does not change user preferences. It changes the relative availability of immediate service and reservation service by altering the reservation quota. This altered availability is precisely the service capacity allocation decision that I study for electric car charging.
Static Coexisting Reservation Mechanism
The static coexisting reservation mechanism is denoted by mu_S(m), where m belongs to the set M of integers from zero to X. The parameter m is a fixed reservation reserve level. The static mechanism uses the same reservation quota throughout the operating day:
$$m_t^{\mu_S(m)}=m,\quad t\in T.$$
Under this rule, the current reservation quota is constant, so the immediate waiting time and the feasible reservation set are determined by the same fixed reserve level in every period. The static mechanism is a natural benchmark for electric car charging stations that want to introduce reservations without investing in real-time state monitoring or short-term demand prediction. It balances demand retention, service loss, and fulfillment loss through a single fixed parameter. A low reserve level protects immediate users but may fail to retain electric car users who would have accepted a future slot. A high reserve level retains more reservation demand but may crowd out immediate users and increase the consequences of no-shows and late cancellations.
Dynamic Coexisting Reservation Mechanism
The dynamic coexisting reservation mechanism is denoted by mu_D(theta). The dynamic parameter vector is
$$\theta=(m_1,m_2,m_3,\eta_1,\eta_2,\zeta),$$
where m_1, m_2, and m_3 are low, medium, and high reservation reserve levels with
$$0 \le m_1 \le m_2 \le m_3 \le X.$$
The thresholds eta_1 and eta_2 are waiting-pressure triggers with eta_1 less than eta_2, and zeta is a future-load threshold. The dynamic mechanism uses three real-time state variables: current waiting pressure w_t^{mu}, average predicted future load rho_t^{pred}, and currently available charging guns x_t^{idle,mu}. The reservation quota is determined by a state-dependent mapping:
$$m_t^{\mu_D(\theta)}=g_\theta(w_t^{\mu},\rho_t^{pred},x_t^{idle,\mu}),$$
where the mapping takes values in the set of three reserve levels. The state response rule follows a fixed priority order, which I summarize in the table below. The rule is designed so that the station increases reservation capacity when waiting pressure is high but future load remains acceptable, and reduces reservation capacity when future load is high or when currently available charging guns are scarce. This logic is consistent with the operational reality of electric car charging: reservation can smooth demand when the station is congested, but it should not lock too much capacity when the station is already constrained.
| Priority | State condition | Reservation quota |
|---|---|---|
| 1 | Current waiting pressure is high and future load is not high | High level m3 |
| 2 | Current waiting pressure is even higher | High level m3 |
| 3 | Current waiting pressure reaches the low threshold, or available guns are insufficient | Medium level m2 |
| 4 | Waiting pressure is low, future load is high, and available guns are sufficient | Low level m1 |
| 5 | All other states | Medium level m2 |
I can express the dynamic rule more compactly as a piecewise mapping. The rule first checks whether waiting pressure is at least the high threshold and future load is at most the future-load threshold plus a small relaxation margin. If so, the high reserve level is used. If waiting pressure is at least the high threshold plus one, the high reserve level is also used even if the future-load condition is not fully satisfied. If waiting pressure is at least the low threshold, or if currently available guns are at or below a minimum level, the medium reserve level is used. If waiting pressure is below the low threshold, future load is above the future-load threshold, and available guns are above the minimum, the low reserve level is used. Otherwise, the mechanism returns to the medium reserve level. This ordered rule avoids conflicting state signals and keeps the dynamic electric car charging reservation policy interpretable.
$$m_t^{\mu_D(\theta)}=\begin{cases}
m_3, & w_t^{\mu}\ge \eta_2 \text{ and } \rho_t^{pred}\le \zeta+0.1,\\
m_3, & w_t^{\mu}\ge \eta_2+1,\\
m_2, & w_t^{\mu}\ge \eta_1 \text{ or } x_t^{idle,\mu}\le x_{\min},\\
m_1, & w_t^{\mu}\lt \eta_1,\ \rho_t^{pred}\gt \zeta,\ x_t^{idle,\mu}\gt x_{\min},\\
m_2, & \text{otherwise}.
\end{cases}$$
For parameter identification, I search over the finite set of reserve levels and the finite grid of state thresholds. I first identify the best static reserve level in each scenario. I then construct candidate triples of low, medium, and high reserve levels around the best static level. The dynamic candidate set explicitly includes the static optimal rule as a special case. Therefore, if state information does not provide additional value, the dynamic mechanism can collapse to the static mechanism. This nesting property is important for electric car charging operators because it prevents the dynamic rule from being selected merely because it is more complex. When training-period revenue differences among candidate rules are very small, I favor the simpler and smoother rule. Frequent quota switching can increase implementation complexity and platform management cost in electric car charging operations. If the revenue improvement is limited, a more complex state response rule is not justified.
Fulfillment States and Revenue Decomposition
After a reservation request is accepted, the system locks the corresponding service periods. The reservation execution state can be on-time arrival, early cancellation, late cancellation, or no-show. On-time users enter the reserved electric car charging service. Early cancellation requires notification at least K periods in advance. In the main experiment, K equals four periods. Early cancellation releases the committed capacity, and the released capacity may be absorbed by later demand. Late cancellation and no-show do not provide effective completed service, and I treat them as fulfillment loss. Let C_mu be the total number of completed service periods under mechanism mu. To identify the mechanism effect relative to first-come, first-served, I decompose the difference into three net effects and also record a capacity backfill recovery measure.
The first effect is demand retention, denoted by R_mu. It measures the number of service periods that are completed under mechanism mu but would have been lost under first-come, first-served. This term reflects the additional completed electric car charging service generated by improved service availability and reduced waiting uncertainty. The second effect is service loss, denoted by O_mu. It measures the number of service periods that would have been completed under first-come, first-served but are not completed under mechanism mu, excluding losses caused by late cancellation or no-show. This term mainly corresponds to immediate-service crowding out and scheduling mismatch. The third effect is fulfillment loss, denoted by F_mu. It measures the number of service periods that would have been completed under first-come, first-served but are not completed under mechanism mu because of late cancellation or no-show. This term captures the effective service loss caused by failed reservation fulfillment. In addition, capacity backfill recovery, denoted by Q_mu, measures the number of service periods released by early cancellation that are subsequently re-locked by other accepted reservations.
Let r be the revenue per effective service period. The operating revenue under mechanism mu is
$$\Pi_{\mu}=r C_{\mu}.$$
The revenue increment relative to first-come, first-served is
$$\Delta\Pi_{\mu}=\Pi_{\mu}-\Pi_{\mu_F}.$$
Because the revenue per effective service period is constant, the revenue increment depends only on the change in completed service periods. By the definitions above, I obtain the following decomposition for electric car charging service capacity allocation:
$$\Delta\Pi_{\mu}=r(R_{\mu}-O_{\mu}-F_{\mu}).$$
Taking expectations over the simulation sample gives
$$\mathbb{E}[\Delta\Pi_{\mu}]=r\mathbb{E}[R_{\mu}-O_{\mu}-F_{\mu}].$$
This decomposition is central to my analysis. It states that a coexisting reservation mechanism creates revenue only through three channels: demand retention increases revenue, while service loss and fulfillment loss decrease revenue. The mechanism is beneficial when the retained electric car charging demand is large enough to cover the service loss and fulfillment loss. The decomposition also clarifies why the same reservation quota can perform well in one station and poorly in another. In a station with strong demand volatility and moderate fulfillment quality, reservation may retain many electric car users who would otherwise exit. In a station with weak fulfillment quality, the same quota may create large no-show losses and reduce effective service completion.
Theoretical Implications
The static mechanism chooses a fixed reserve level to maximize expected revenue increment:
$$m^{\star}\in\arg\max_{m\in M}\mathbb{E}[\Delta\Pi_{\mu_S(m)}].$$
Because the reserve-level set is finite, at least one optimal static reserve level exists. The marginal revenue effect of increasing the reserve level from m minus one to m is
$$\mathbb{E}[\Delta\Pi_{\mu_S(m)}]-\mathbb{E}[\Delta\Pi_{\mu_S(m-1)}].$$
This marginal effect can be expressed as the change in demand retention minus the changes in service loss and fulfillment loss, all multiplied by the unit revenue. Therefore, the static mechanism should not simply maximize the reservation quota. It should find a moderate reserve level that balances demand retention against immediate-service crowding out and failed fulfillment. When the reserve level is low, an additional unit of reservation capacity is more likely to retain electric car demand that would otherwise exit. When the reserve level is high, an additional unit is more likely to crowd out immediate users and amplify no-show losses. The optimal static configuration usually appears as a moderate reserve level, and its exact position depends on load, peak shape, and fulfillment quality.
The dynamic mechanism has a nesting advantage. Because the dynamic candidate set contains the static optimal rule, the best dynamic rule cannot perform worse than the static optimal rule on the training sample. The additional value of the dynamic mechanism comes from state heterogeneity. If two reachable states have different marginal values of reservation capacity, and if the dynamic rule can choose different reserve levels in those states, then the dynamic mechanism can improve on a fixed quota. For electric car charging, such state heterogeneity is common. When current waiting pressure is high but future load is still acceptable, a higher reservation quota can retain more electric car demand. When future load is high or available guns are scarce, a higher reservation quota can create service loss and fulfillment loss. A static rule must compromise across these states. A dynamic rule can raise the quota when retention value is high and lower it when service-loss risk is high.
Simulation Design
I use a training-and-evaluation design. In the training stage, I run fifty simulation replications per scenario to search for the static optimal reserve level and to construct and screen dynamic candidate rules. In the evaluation stage, I use another one hundred independent simulation replications to compare first-come, first-served, the static mechanism, and the dynamic mechanism. Confidence intervals for revenue increments are based on the evaluation replications. For the aggregate results across nine scenarios, I first average within each evaluation replication across scenarios with equal weights, and then compute the mean and confidence interval across the one hundred evaluation replications. This design reduces the risk that the dynamic rule is overfitted to a particular simulation sample.
The main experiment considers a city-level public charging station with fifteen charging guns. The service day has ninety-six fifteen-minute periods. The service duration set is two to eight periods, corresponding to thirty to one hundred twenty minutes. The average service duration is 3.21 periods, or 48.15 minutes. The unit service price and the unit service-period revenue are both 7.87 yuan. In the normal fulfillment environment, the on-time arrival rate, early cancellation rate, late cancellation rate, and no-show rate are 0.82, 0.08, 0.05, and 0.05, respectively. Early cancellation requires at least four periods of advance notice. I summarize the main parameters in the table below.
| Parameter | Value | Interpretation |
|---|---|---|
| H | 96 periods | One operating day in fifteen-minute periods |
| X | 15 charging guns | Main station capacity |
| Service duration support | 2 to 8 periods | Thirty to one hundred twenty minutes |
| Mean service duration | 3.21 periods | Approximately 48.15 minutes |
| Unit service revenue r | 7.87 yuan per period | Revenue per effective service period |
| Unit value center | 12.75 yuan per period | Pre-truncation center of user value distribution |
| Waiting cost | 1.42 or 4.88 yuan per period | Low and high waiting sensitivity |
| Reservation friction | 0.24 to 1.42 yuan | Additional cost of booking an electric car charging slot |
| Reservation window W | 8 periods | Two-hour search window for future charging |
| Prediction window | 8 periods | Two-hour average future load |
| Load levels | 0.55, 0.75, 0.90 | Light, medium, and high load |
| Normal fulfillment | 0.82, 0.08, 0.05, 0.05 | On-time, early cancel, late cancel, no-show |
Arrivals follow a nonhomogeneous Poisson process. I set average load to 0.55, 0.75, and 0.90, corresponding to light, medium, and high load. I also set the intraday peak profile to flat, bimodal, or spike. The nine load-peak combinations form the main scenario matrix. This matrix covers capacity-relaxed daily operation, clearly tight operation, and strongly congested peak operation. It therefore provides a stable identification boundary for comparing service capacity allocation mechanisms for electric car charging.
| Load | Flat peak | Bimodal peak | Spike peak |
|---|---|---|---|
| Light load | S11: light-flat | S12: light-bimodal | S13: light-spike |
| Medium load | S21: medium-flat | S22: medium-bimodal | S23: medium-spike |
| High load | S31: high-flat | S32: high-bimodal | S33: high-spike |
For the arrival process, I construct a normalized intraday weight function for each peak profile. The total expected number of electric car arrivals is
$$N_{\rho,X}=\frac{\rho H X}{\mathbb{E}[D]},$$
and the arrival rate in period t is
$$\lambda_{\rho,p}(t)=N_{\rho,X}w_p(t),$$
where w_p(t) is the normalized peak-profile weight. The actual number of arrivals is drawn from a Poisson distribution with this rate. This construction ensures that, for a given average load and station size, different peak profiles have the same total expected electric car charging demand. Differences in outcomes therefore come from the intraday distribution of demand, not from a different total demand level. The flat profile has a broad transition, the bimodal profile has two clear peaks, and the spike profile has a narrow high-intensity main peak with secondary peaks and a negative correction term. Negative values are truncated at zero before normalization.
Main Results
The main results show that the revenue gains from coexisting reservation are scenario-dependent. The static mechanism never produces a negative average revenue increment across the nine scenarios, and its nine-scenario average revenue increment is 37.97 yuan per day. The dynamic mechanism produces a nine-scenario average revenue increment of 102.68 yuan per day. The average additional revenue of the dynamic mechanism relative to the static mechanism is 64.71 yuan per day. Except in the light-flat scenario S11, where the dynamic mechanism collapses to the static mechanism, the additional revenue of the dynamic mechanism is positive in the other eight scenarios, and the lower bound of the ninety-five percent confidence interval is above zero. In S11, the revenue increment of both the static and dynamic mechanisms is only 0.87 yuan per day, and the confidence interval includes zero. This result means that when average load is low and intraday demand fluctuation is weak, the value of reservation for electric car charging is close to zero and may not form a stable positive return.
The dynamic-static additional revenue is highly uneven across scenarios. The largest gains appear in spike and bimodal scenarios with medium or high load, especially S33, S23, and S13. S32 and S22 also show substantial dynamic gains. By contrast, S12 and S21 have small dynamic additional revenue, indicating that when demand fluctuation is weak or state differences are not pronounced, the improvement space of the dynamic mechanism over the static mechanism is limited. An electric car charging operator should compare the expected implementation cost of dynamic monitoring and short-term prediction with the scenario-specific additional revenue before deploying a dynamic reservation rule.
| Scenario | Dynamic minus static mean revenue increment (yuan per day) | 95 percent confidence interval | Significantly positive |
|---|---|---|---|
| S11 | 0.00 | [0.00, 0.00] | Collapses to static |
| S12 | 8.34 | [4.48, 12.21] | Yes |
| S13 | 89.88 | [78.98, 100.77] | Yes |
| S21 | 11.49 | [0.79, 22.19] | Yes |
| S22 | 87.83 | [74.83, 100.83] | Yes |
| S23 | 115.61 | [102.19, 129.04] | Yes |
| S31 | 61.39 | [47.06, 75.71] | Yes |
| S32 | 89.48 | [77.86, 101.10] | Yes |
| S33 | 118.36 | [103.21, 133.52] | Yes |
The static reserve boundary is also informative. The optimal static reserve level is one charging gun in S11, S12, S22, and S32; two charging guns in S21, S23, S31, and S33; and four charging guns in S13. In the light-flat scenario S11, a small reservation quota already covers most of the marginal electric car demand that can be retained. Further reservation reduces immediate-service capacity, and the marginal revenue becomes close to zero or negative. In the light-spike scenario S13, the point at which marginal revenue turns negative moves to a higher reserve level. Even though average load is not high, local demand concentration means that a moderate increase in reservation capacity can absorb electric car users who would otherwise exit. In the high-spike scenario S33, the static optimum remains around two charging guns, but the decline in marginal revenue is flatter. This pattern indicates that in a system with high overall load and local congestion, a very low reserve level misses demand retention opportunities, while a very high reserve level crowds out immediate electric car charging and amplifies fulfillment risk.
| Scenario | Optimal static reserve level | Interpretation |
|---|---|---|
| S11 | 1 | Small reserve covers marginal retention |
| S12 | 1 | Weak state differences |
| S13 | 4 | Local spike justifies a larger reserve |
| S21 | 2 | Moderate reserve under medium load |
| S22 | 1 | Bimodal demand but moderate pressure |
| S23 | 2 | Spike pressure requires reserve |
| S31 | 2 | High load with flat profile |
| S32 | 1 | Reserve must protect immediate capacity |
| S33 | 2 | Balance retention and service loss |
The dynamic quota structure also reveals how the mechanism works. In S11, the best dynamic parameters are 1, 1, and 1, so the three reserve levels are identical. The dynamic mechanism therefore collapses to the static mechanism, and the quota change range is zero. By contrast, S13, S22, S23, S32, and S33 form clearer multi-level quota structures. The differences between the highest and lowest reserve levels are 4, 4, 4, 3, and 4 in these scenarios. These are also the scenarios with high dynamic additional revenue. The result shows that the value of the dynamic mechanism comes from observable state differences. When the suitable reserve level differs across states, a state response rule can create additional value for electric car charging service capacity allocation. When state differences are negligible, the dynamic rule should collapse to a simpler static rule.
| Scenario | Static optimum | Final low, medium, high reserve levels | Waiting thresholds | Future-load threshold |
|---|---|---|---|---|
| S11 | 1 | 1/1/1 | 0/1 | 0.55 |
| S12 | 1 | 0/1/3 | 1/2 | 0.55 |
| S13 | 4 | 2/4/6 | 1/2 | 0.65 |
| S21 | 2 | 1/2/4 | 1/2 | 0.65 |
| S22 | 1 | 0/2/4 | 1/2 | 0.85 |
| S23 | 2 | 1/3/5 | 1/3 | 0.85 |
| S31 | 2 | 1/2/4 | 1/2 | 0.80 |
| S32 | 1 | 0/1/3 | 1/2 | 0.95 |
| S33 | 2 | 1/3/5 | 1/3 | 0.90 |
From the perspective of quota usage, most scenarios other than S11 use at least two reserve levels in the evaluation sample. S13, S22, S23, S31, S32, and S33 use close to three levels on average, and the share of non-medium quota usage is between 22 and 42 percent. This pattern confirms that the dynamic mechanism actually switches quotas according to operating states rather than remaining at a single level. The switching pattern is consistent with the theoretical explanation: the dynamic mechanism raises the reservation quota when waiting pressure is high and future load is acceptable, thereby retaining more electric car charging demand, and lowers the quota when waiting pressure is low, future load is high, and available guns are sufficient, thereby reducing service capacity allocation risk.
Mechanism Decomposition and Service Outcomes
The revenue decomposition confirms that demand retention is the main source of value. On average, the dynamic mechanism retains 11.56 additional electric car users, corresponding to 36.44 service periods of demand retention, and generates 3.44 service periods of backfill recovery. It also incurs 12.22 service periods of service loss and 11.11 service periods of fulfillment loss. The static mechanism retains 7.22 additional users, corresponding to 22.78 service periods of demand retention, and generates 2.22 service periods of backfill recovery. In representative scenarios such as S13, S22, S23, and S33, the dynamic demand retention reaches 40, 39, 50, and 62 service periods, respectively. The corresponding service loss and fulfillment loss also rise, but their magnitudes are generally lower than demand retention. The dynamic mechanism in S22, S23, and S33 retains 23, 25, and 28 more service periods than the static mechanism. This result shows that state-dependent response can convert more electric car demand that would otherwise exit into future completed service. At the same time, capacity backfill recovery in S13, S22, S23, and S33 is 4, 4, 4, and 6 service periods, reflecting that early-cancelled reservation capacity is sometimes re-locked by other electric car reservations.
| Metric | Static mechanism | Dynamic mechanism |
|---|---|---|
| Additional retained users | 7.22 | 11.56 |
| Demand retention in service periods | 22.78 | 36.44 |
| Capacity backfill recovery | 2.22 | 3.44 |
| Service loss in service periods | Not separately reported here | 12.22 |
| Fulfillment loss in service periods | Not separately reported here | 11.11 |
The service outcomes show that the revenue improvement is mainly associated with more completed electric car charging services and fewer exits, rather than with a pure reordering of existing demand. Across the nine scenarios, the average number of completed users is 288.36 under first-come, first-served, 289.75 under the static mechanism, and 292.44 under the dynamic mechanism. The average number of exits is 40.09, 34.71, and 29.65, respectively. The dynamic mechanism reduces daily exits by 10.44 relative to first-come, first-served. This reduction is consistent with the demand retention channel in the decomposition.
The three mechanisms also differ in final actual waiting time. The average final actual waiting time is 0.427 service periods under first-come, first-served, 0.416 under the static mechanism, and 0.475 under the dynamic mechanism. The dynamic mechanism increases waiting by about 0.049 periods relative to first-come, first-served, or about 0.73 minutes, and by about 0.059 periods relative to the static mechanism, or about 0.89 minutes. Therefore, the dynamic mechanism improves revenue, increases completed electric car charging service, and reduces exits, but it also produces a small increase in final actual waiting. This pattern reflects a trade-off among revenue, service completion, and user waiting. In the model, accepted reservations are protected in their committed periods, so a user who arrives on time can enter the reserved electric car charging service. Fulfillment loss mainly comes from late cancellation or no-show. The user-side reservation non-fulfillment rate in the main dynamic experiments is roughly between 13.1 and 19.3 percent. This result implies that an electric car charging operator should pair reservation with reminders, cancellation constraints, and credit management to reduce the adverse effect of failed fulfillment.
| Outcome | First-come, first-served | Static mechanism | Dynamic mechanism |
|---|---|---|---|
| Average completed users | 288.36 | 289.75 | 292.44 |
| Average exits | 40.09 | 34.71 | 29.65 |
| Average final actual waiting in periods | 0.427 | 0.416 | 0.475 |
| Average revenue increment in yuan per day | 0.00 | 37.97 | 102.68 |
Boundary Analysis
The main results establish the value of coexisting reservation under a normal fulfillment environment. I next examine whether the conclusion depends on fulfillment quality, charging duration distribution, supply-demand prediction, and user behavior parameters. These extensions correspond to the fulfillment loss, demand retention, service loss, and state-response value channels in the decomposition. The purpose is to identify the boundary sources of the mechanism rather than to claim universal superiority.
Fulfillment Environment
Fulfillment quality affects whether accepted reservations become completed electric car charging service. I consider a high-quality fulfillment environment and a low-quality fulfillment environment. In each environment, I examine two cases: keeping the mechanism parameters identified in the main experiment, and re-training the parameters in the new environment. The first case tests the extrapolation of existing parameters, while the second case identifies the boundary after parameter adaptation.
The results show that fulfillment quality strongly affects the revenue boundary. Under high fulfillment with fixed parameters, the nine-scenario average revenue increments of the static and dynamic mechanisms rise from 37.97 and 102.68 yuan per day in the main experiment to 69.19 and 155.38 yuan per day. After re-training, they rise further to 92.39 and 169.36 yuan per day. Under low fulfillment with fixed parameters, the static mechanism maintains a positive average revenue increment in only three scenarios, and its nine-scenario average falls to negative 5.19 yuan per day, with a ninety-five percent confidence interval that includes zero. The dynamic mechanism also falls substantially but remains positive in eight scenarios, with an average of 33.44 yuan per day. After re-training, the static average recovers to 5.93 yuan per day, and the dynamic average rises to 44.51 yuan per day. These results are consistent with the fulfillment-loss channel: when late cancellation and no-show increase, the same reservation commitment is less likely to be converted into completed electric car charging service. A station with weak fulfillment should not simply expand reservation volume. It should first use reminders, cancellation constraints, and credit management to reduce failed fulfillment, and then re-identify the appropriate reserve level and dynamic thresholds.
| Boundary case | Static mean (yuan per day) | Dynamic mean (yuan per day) | Dynamic minus static |
|---|---|---|---|
| High fulfillment, fixed | 69.19 | 155.38 | 86.19 |
| High fulfillment, retrained | 92.39 | 169.36 | 76.98 |
| Low fulfillment, fixed | -5.19 | 33.44 | 38.62 |
| Low fulfillment, retrained | 5.93 | 44.51 | 38.58 |
Fast-Charging Era
Fast-charging technology changes the distribution of electric car charging duration and affects both demand retention and service loss. I shift the baseline duration distribution forward to one to eight service periods, with a mean of about 2.77 periods. This represents an environment in which more electric car users complete charging within fifteen to forty-five minutes while a small long-tail demand remains. The results show that the duration shift changes the revenue level and the optimal parameter position, but it does not eliminate the relative value of reservation, especially dynamic reservation. With fixed main-experiment parameters, the average revenue increments of the static and dynamic mechanisms in the fast-charging environment are 36.76 and 97.75 yuan per day, and the average dynamic additional revenue is 60.98 yuan per day. After re-training, the static and dynamic averages are 33.76 and 95.42 yuan per day, and the dynamic additional revenue is 61.66 yuan per day. The ranking of mechanisms is consistent across the fixed and retrained cases.
Because average service duration shortens, the number of electric car arrivals must increase to maintain the same load level. As a result, completed users and exits can both rise. In the fast-charging environment, the dynamic mechanism completes about 331.60 to 331.75 users on average, higher than the 292.44 in the main experiment. Average exits are about 41.94 to 42.75, also higher than the 29.65 in the main experiment. Nevertheless, the dynamic mechanism still reduces exits by 8.64 to 9.46 relative to first-come, first-served. The average revenue increment per reduced exit is about 9.63 to 10.18 yuan. This result shows that reservation continues to work through exit reduction and effective service completion in the fast-charging era.
| Fast-charging case | Static mean | Dynamic mean | Dynamic minus static |
|---|---|---|---|
| Fixed parameters | 36.76 | 97.75 | 60.98 |
| Retrained parameters | 33.76 | 95.42 | 61.66 |
Supply Faults, Demand Peak Mismatch, and User Behavior
The value of the dynamic mechanism may come from prediction or from real-time state response. To distinguish these sources, I introduce three disturbances while keeping the main parameters fixed: a sudden single-gun failure during the evening peak window, a local evening demand increase, and a local evening demand decrease. The supply fault reduces available capacity from fifteen to fourteen guns for two hours. The demand shocks raise or lower the local arrival rate by thirty-five percent at the peak window. For each disturbance, I consider three information states: unknown, partial warning, and fully known.
The results show that, under the assumed disturbance size, fixed parameters, and state response rule, the relative advantage of the dynamic mechanism does not disappear because of imperfect prediction. For the supply fault, the average revenue increments of the dynamic mechanism under unknown, partial-warning, and fully-known states are 107.47, 107.94, and 107.97 yuan per day. The dynamic additional revenues relative to the static mechanism are 67.10, 67.57, and 67.59 yuan per day. The differences are very small. Under the new peak, the average daily revenue increment of the dynamic mechanism rises to about 135 yuan, and the dynamic additional revenue reaches more than 85 yuan per day. Under the cancellation peak, the average revenue increment remains around 93 yuan per day, and the dynamic additional revenue is about 61 yuan per day. Therefore, under the current disturbance scale and rule structure, the value of the dynamic mechanism does not rely entirely on perfect prediction. It also relies on real-time response to current congestion, future load, and available charging guns.
User waiting cost and reservation friction also affect the choice among immediate service, reservation service, and exit. When waiting cost rises by twenty percent, the average revenue increments of the static and dynamic mechanisms fall to 32.90 and 95.52 yuan per day, and the dynamic additional revenue is 62.62 yuan per day. When reservation friction rises by twenty percent, the average revenue increments of the static and dynamic mechanisms are 40.90 and 105.17 yuan per day, slightly above the main experiment average. A possible explanation is that, in the current parameter range, higher reservation friction suppresses some marginal electric car reservation demand whose net utility is close to zero, and this suppression can alleviate excessive quota pressure in some scenarios. This does not mean that higher reservation friction is desirable. It means that, within the local disturbance range, the ranking of the three mechanisms remains unchanged.
| Boundary case | Static mean | Dynamic mean | Dynamic minus static |
|---|---|---|---|
| Supply fault, unknown | 40.37 | 107.47 | 67.10 |
| Supply fault, partial warning | 40.37 | 107.94 | 67.57 |
| Supply fault, fully known | 40.37 | 107.97 | 67.59 |
| New peak, unknown | 49.69 | 135.53 | 85.84 |
| New peak, partial warning | 49.69 | 135.57 | 85.89 |
| New peak, fully known | 49.69 | 135.09 | 85.41 |
| Cancellation peak, unknown | 32.30 | 93.78 | 61.47 |
| Cancellation peak, partial warning | 32.30 | 92.83 | 60.53 |
| Cancellation peak, fully known | 32.30 | 92.95 | 60.65 |
| Waiting cost plus twenty percent | 32.90 | 95.52 | 62.62 |
| Reservation friction plus twenty percent | 40.90 | 105.17 | 64.27 |
I also change the station size to ten, twenty, and thirty charging guns while keeping average load and peak structure consistent. The results show that station size does not change the main ranking of the dynamic mechanism relative to the static mechanism. For ten guns, the static and dynamic averages are 23.99 and 88.24 yuan per day, and the dynamic-static difference is 64.25. For fifteen guns, the corresponding values are 37.97, 102.68, and 64.71. For twenty guns, the values are 60.45, 127.92, and 67.47. For thirty guns, the values are 88.76, 163.75, and 74.98. In all four cases, the dynamic advantage is significant in eight of nine scenarios. I further change the center parameter of the truncated normal distribution of user unit-period value by plus or minus ten and twenty percent. The overall ranking remains unchanged, but when the unit-period service value is low, the dynamic additional revenue falls noticeably. In some light-load scenarios, the paired confidence interval of the dynamic-static difference includes zero. This result shows that the applicability of the dynamic mechanism still has parameter and scenario boundaries.
| Station size | Static mean | Dynamic mean | Dynamic minus static | Significant scenarios |
|---|---|---|---|---|
| 10 guns | 23.99 | 88.24 | 64.25 | 8 of 9 |
| 15 guns | 37.97 | 102.68 | 64.71 | 8 of 9 |
| 20 guns | 60.45 | 127.92 | 67.47 | 8 of 9 |
| 30 guns | 88.76 | 163.75 | 74.98 | 8 of 9 |
| Value center change | Static mean | Dynamic mean | Dynamic minus static | Significant scenarios |
|---|---|---|---|---|
| Minus twenty percent | 12.53 | 42.80 | 30.27 | 7 of 9 |
| Minus ten percent | 29.35 | 85.91 | 56.56 | 7 of 9 |
| Baseline | 37.97 | 102.68 | 64.71 | 8 of 9 |
| Plus ten percent | 46.82 | 112.67 | 65.85 | 7 of 9 |
| Plus twenty percent | 46.56 | 115.69 | 69.12 | 8 of 9 |
Managerial Implications for Electric Car Charging
The results lead to several practical implications for electric car charging service capacity allocation. First, a station should not treat reservation as a binary choice. The relevant decision is the reserve level and the state response rule. For a light-load station with a flat peak profile, a low reserve static mechanism is often sufficient. The dynamic mechanism may collapse to the static rule, and the revenue gain may be statistically indistinguishable from zero. In such a station, the main value of reservation is user convenience rather than revenue improvement. The operator should weigh the service experience benefit against the implementation cost.
Second, for stations with bimodal or spike profiles and medium or high load, the dynamic mechanism is more attractive. The additional value comes from state heterogeneity. When current waiting pressure is high and future load is acceptable, a higher reserve level can retain more electric car charging demand. When future load is high or available guns are scarce, a lower reserve level can protect immediate users and reduce fulfillment risk. An electric car charging operator with real-time queue monitoring and short-term load prediction can therefore use the dynamic rule to improve service capacity allocation without adding charging guns.
Third, fulfillment quality is a precondition for reservation value. In a low-fulfillment environment, the static mechanism may lose money on average, and the dynamic mechanism can only partially buffer the loss. The operator should first reduce late cancellation and no-show through reminders, cancellation constraints, and credit management. Only after fulfillment quality improves should the operator increase the reservation quota or adopt a more active dynamic rule. This sequence is important for electric car charging because a failed reservation not only wastes reserved capacity but also delays immediate users and weakens trust in the reservation channel.
Fourth, the value of the dynamic mechanism does not require perfect prediction. Under supply faults and demand shocks, the dynamic rule performs similarly under unknown, partial-warning, and fully-known information states. The reason is that the rule responds to current congestion, future load, and available guns. This finding is useful for electric car charging operators who may not have a sophisticated forecasting system. A simple state response rule based on observable queue pressure and capacity availability can still create value, as long as the station monitors the relevant state variables and updates the rule periodically.
Fifth, the station should avoid a fixed reservation rule that is never updated. The fast-charging era changes the duration distribution and the optimal parameter position. Although the relative value of reservation remains, the specific reserve levels and thresholds should be re-identified when the charging technology, user composition, or demand pattern changes. An electric car charging station that mechanically keeps a historical quota may miss demand retention opportunities or create unnecessary service loss.
Conclusion
I study service capacity allocation for electric car charging when reservation users and immediate users coexist. I formulate a first-come, first-served mechanism, a static coexisting reservation mechanism, and a dynamic coexisting reservation mechanism. The theoretical analysis shows that the revenue increment of reservation relative to first-come, first-served can be decomposed into demand retention, service loss, and fulfillment loss. The static mechanism should choose a moderate reserve level that balances retention against crowding out and failed fulfillment. The dynamic mechanism can improve on the static rule when different operating states have different marginal values of reservation capacity. The dynamic candidate set includes the static optimal rule, so the dynamic mechanism can collapse to the static mechanism when state information is not valuable.
The main experiments show that, in a fifteen-gun public electric car charging station under normal fulfillment and nine load-peak scenarios, the average revenue increment is 37.97 yuan per day for the static mechanism and 102.68 yuan per day for the dynamic mechanism. The average dynamic additional revenue is 64.71 yuan per day. Both reservation mechanisms avoid negative average revenue increments across the nine scenarios, but the light-flat scenario has a revenue increment of only 0.87 yuan per day with a confidence interval that includes zero. The dynamic mechanism increases completed users and reduces exits relative to first-come, first-served, with a small increase in final actual waiting. The decomposition shows that demand retention is the main source of value, while service loss and fulfillment loss are the main mechanism costs.
The boundary analysis shows that the conclusion is robust in direction but conditional in magnitude. Higher fulfillment quality raises the revenue boundary. Lower fulfillment quality compresses the static mechanism’s feasible space and only partially buffers the dynamic mechanism. Fast charging changes the duration distribution and parameter position but does not eliminate the relative value of dynamic reservation. Supply faults and demand peak mismatches show that the dynamic advantage does not rely entirely on perfect prediction. Waiting cost and reservation friction change revenue levels but do not reverse the mechanism ranking within the studied range. Station size and user value sensitivity also preserve the main ranking, although low-value and light-load scenarios have weaker dynamic advantages.
For electric car charging practice, the central message is that coexisting reservation is a service capacity allocation tool, not a universal solution. A light-load flat station may need only a simple static rule or no reservation at all. A medium- or high-load station with bimodal or spike demand can benefit from a dynamic rule that responds to waiting pressure, future load, and available guns. A low-fulfillment station should prioritize reminder systems, cancellation constraints, and credit management before expanding reservation. A station facing fast charging, supply faults, or volatile demand should retain real-time response capability and update its parameters regularly. These conclusions provide a basis for electric car charging operators to design reservation quotas and dynamic response rules that improve service completion and operating revenue without necessarily adding new charging infrastructure.