I study how a public electric vehicle charging station should allocate limited service capacity when reservation users and walk-in users coexist. My starting point is practical rather than purely theoretical: electric vehicle charging demand is growing quickly, yet many public stations already face local congestion, uncertain waiting times, and heterogeneous user patience. Instead of assuming a fully reservation-based system or a purely first-come, first-served system, I model a coexisting reservation mechanism in which a station keeps part of its capacity available for immediate arrivals while also accepting advance reservations. I compare three mechanisms under identical simulated demand samples: a first-come, first-served mechanism, a static coexisting reservation mechanism, and a dynamic coexisting reservation mechanism. The comparison is based on operating revenue, completed electric vehicle charging services, user exits, realized waiting time, and a decomposition into demand retention, service loss, and no-show or late-cancellation loss.
The central question I address is whether a coexisting reservation mechanism can improve the service performance of an electric vehicle charging station without adding chargers. I also ask when a static reservation quota is sufficient and when a state-dependent dynamic quota creates additional value. My analysis is organized around a single station with fixed prices and fixed physical capacity, but the logic extends to parking, healthcare, tourism, and other service systems in which reservation users and walk-in users share capacity. Throughout the analysis, I use the term electric vehicle deliberately because the charging context combines long service durations, limited physical plugs, and user impatience in a way that makes capacity allocation especially consequential.
Modeling framework. I consider one operating day divided into H equal-length slots. In the baseline, H = 96 and each slot lasts 15 minutes. The station has X charging guns in slot t, and the baseline uses X = 15. An electric vehicle user i arrives in slot a_i and requires d_i consecutive slots of charging service, with 1 ≤ d_i ≤ d_i^max. The user obtains value v_i from completing the charge and pays r d_i when the charge is completed. The user also bears a waiting cost c_i per slot and has a maximum acceptable waiting time w_i^max. A reservation option imposes an additional friction cost φ_i and a time inconvenience α for each slot between arrival and the reserved start time. I compare mechanisms using the same simulated arrival times, service durations, user preferences, and fulfillment states, so differences come only from the allocation rules.
For the first-come, first-served mechanism, I define n_t^μ as the number of accepted immediate users already scheduled to occupy capacity in slot t under mechanism μ. If a user wants to start immediate service in slot s, the feasibility condition is that adding one more electric vehicle user does not exceed capacity in any slot of the required service window. The earliest feasible start time and the resulting utility can be written as follows.
$$s_i^{\mu_F}=\min\left\{s\ge a_i:\ n_\tau^{\mu_F}+1\le X_\tau,\ \tau=s,\ldots,s+d_i-1\right\}$$
$$U_i^{I,\mu_F}=v_i-r d_i-c_i\left(s_i^{\mu_F}-a_i\right)$$
If no feasible start time exists, or if the resulting wait exceeds the user’s maximum acceptable waiting time, the user exits. In this mechanism, an electric vehicle user chooses only between immediate service and exit. This benchmark is useful because it represents the common operating logic of many public charging stations before reservation is introduced.
Under a coexisting reservation mechanism, the station protects some capacity for reservation users while still serving immediate arrivals. Let m_{a_i}^μ be the reservation quota observed by a user arriving in slot a_i, and let b_{t|a_i}^μ be the number of accepted reservations already locking capacity in future slot t. To avoid harming accepted reservations when the quota is adjusted downward, the protected capacity is the maximum of the current quota and the existing reservation commitment.
$$p_{t|a_i}^{\mu}=\max\left\{m_{a_i}^{\mu},b_{t|a_i}^{\mu}\right\}$$
For immediate service under mechanism μ, the feasibility condition becomes that the station must have enough capacity after protecting reservation commitments. The earliest feasible immediate start time and the corresponding utility are given below.
$$s_i^{I,\mu}=\min\left\{s\ge a_i:\ n_\tau^{\mu}+1\le X_\tau-p_{\tau|a_i}^{\mu},\ \tau=s,\ldots,s+d_i-1\right\}$$
$$U_i^{I,\mu}=v_i-r d_i-c_i\left(s_i^{I,\mu}-a_i\right),\quad s_i^{I,\mu}-a_i\le w_i^{\max}$$
If the user prefers a reservation, the feasible reservation start times must lie inside the reservation window and must not exceed the quota in any required slot. I write the feasible reservation set and the reservation utility as follows.
$$A_i^{R,\mu}=\left\{s:\ a_i+1\le s\le \min\left(a_i+W,H-d_i\right),\ b_{\tau|a_i}^{\mu}+1\le m_{a_i}^{\mu},\ \tau=s,\ldots,s+d_i-1\right\}$$
$$U_i^{R,\mu}(s)=v_i-r d_i-\alpha\left(s-a_i\right)-\phi_i$$
The user then selects the option with the highest nonnegative utility among exit, immediate service, and the best feasible reservation. This choice structure is important for electric vehicle charging because a user who faces a long immediate queue may accept a later reservation, but only if the reservation is feasible and the inconvenience is not too large.
$$ \max\left\{0,\ U_i^{I,\mu},\ \max_{s\in A_i^{R,\mu}}U_i^{R,\mu}(s)\right\} $$
I distinguish two coexisting reservation mechanisms. The static mechanism uses a fixed reservation quota m throughout the day, where m belongs to the integer set from 0 to X. The dynamic mechanism allows the quota to depend on real-time state information: current waiting pressure, predicted average load in a future window, and currently idle charging guns. The dynamic quota rule can be summarized as a mapping from state to one of three quota levels.
$$m_t^{\mu_D(\theta)}=g_\theta\left(w_t^{\mu},\rho_t^{pred},x_t^{idle,\mu}\right),\quad g_\theta(\cdot)\in\{m_1,m_2,m_3\}$$
I use a finite ordered rule. First, if current waiting pressure is high and future load is not too high, the station uses the high quota. Second, if waiting pressure is even higher, the station also uses the high quota. Third, if waiting pressure reaches a lower threshold or if currently planned available guns are insufficient, the station uses the medium quota. Fourth, if waiting pressure is low, future load is high, and available guns are sufficient, the station uses the low quota. Otherwise, the station uses the medium quota. This design allows the dynamic mechanism to give more capacity to reservations when immediate congestion is high but future capacity is still manageable, and to protect immediate users when future load or capacity constraints are more severe.
| Order | State condition | Quota |
|---|---|---|
| 1 | High waiting pressure and future load not high | m3 |
| 2 | Waiting pressure further increases | m3 |
| 3 | Low waiting threshold reached or planned idle guns insufficient | m2 |
| 4 | Low waiting pressure, high future load, and sufficient idle guns | m1 |
| 5 | All other states | m2 |
Revenue decomposition. Because I hold the unit revenue per effective service slot constant, the revenue difference between mechanisms comes only from differences in completed electric vehicle charging service slots. I define the revenue of mechanism μ as the product of the unit revenue r and the total number of completed service slots C^μ. The revenue increment relative to first-come, first-served is then written as follows.
$$\Delta\Pi^{\mu}=\Pi^{\mu}-\Pi^{\mu_F}=r\left(C^{\mu}-C^{\mu_F}\right)$$
I decompose the difference in completed service slots into three net effects. Demand retention R^μ is the number of service slots completed under mechanism μ that would have been lost under first-come, first-served because the electric vehicle user would have exited. Service loss O^μ is the number of service slots that would have been completed under first-come, first-served but are not completed under mechanism μ for reasons other than late cancellation or no-show, such as immediate-service crowding or scheduling mismatch. No-show loss F^μ is the number of service slots that would have been completed under first-come, first-served but are lost because a reservation user cancels late or does not arrive. The revenue decomposition follows directly.
$$\Delta\Pi^{\mu}=r\left(R^{\mu}-O^{\mu}-F^{\mu}\right)$$
$$\mathbb{E}\left[\Delta\Pi^{\mu}\right]=r\,\mathbb{E}\left[R^{\mu}-O^{\mu}-F^{\mu}\right]$$
This decomposition is the analytical core of my evaluation. A coexisting reservation mechanism is not automatically beneficial for electric vehicle charging. It creates value only when the demand retention gained by reducing waiting uncertainty and preserving access is large enough to cover the service loss from crowding out immediate users and the no-show loss from unfulfilled reservations. I also track capacity backfill, which is the number of reservation slots released by early cancellation and subsequently locked by other accepted reservations. Backfill is not a separate revenue term in the decomposition, but it helps explain how early cancellation can be partially absorbed by the system.
Static optimum and dynamic value. For the static mechanism, I choose the fixed reservation quota that maximizes expected revenue increment over the finite set of feasible quotas. Because the set is finite, an optimum exists. The marginal effect of increasing the quota by one unit is the change in expected demand retention minus the changes in expected service loss and expected no-show loss.
$$m^{*}\in\arg\max_{m\in\{0,1,\ldots,X\}}\mathbb{E}\left[\Delta\Pi^{\mu_S(m)}\right]$$
$$\mathbb{E}\left[\Delta\Pi^{\mu_S(m)}\right]-\mathbb{E}\left[\Delta\Pi^{\mu_S(m-1)}\right]=r\,\mathbb{E}\left[\left(R^{\mu_S(m)}-R^{\mu_S(m-1)}\right)-\left(O^{\mu_S(m)}-O^{\mu_S(m-1)}\right)-\left(F^{\mu_S(m)}-F^{\mu_S(m-1)}\right)\right]$$
The static mechanism therefore should not simply maximize the number of reservations. A low quota may fail to retain electric vehicle demand that would otherwise exit, while a high quota may crowd out immediate users and amplify no-show risk. The optimal static quota is usually moderate. For the dynamic mechanism, I include the static optimum as a special constant rule in the dynamic candidate set. Therefore, the best dynamic rule cannot perform worse than the best static rule on the training sample. Dynamic value arises only when different states have different marginal values of reservation capacity and when the state signal is informative enough to act on that difference.
Simulation design. I use a training-and-evaluation design. In the training stage, I run 50 simulation replications per scenario to identify the best static quota and then to search over dynamic candidate rules around that static optimum. In the evaluation stage, I use 100 independent replications to compare first-come, first-served, static reservation, and dynamic reservation. Confidence intervals are based on the evaluation replications. Arrivals follow a nonhomogeneous Poisson process. I consider three average load levels, 0.55, 0.75, and 0.90, and three within-day peak profiles: flat, two-peak, and sharp. The resulting nine load–peak scenarios allow me to examine both loose and tight capacity conditions for electric vehicle charging.
The arrival rate in each slot is constructed from a normalized within-day weight function. The total expected number of arriving electric vehicle users is proportional to average load, the number of slots, the number of charging guns, and the inverse of average service duration. The within-day weights are normalized so that different peak profiles have the same total expected demand for a given load and station size. This gives a clean comparison of how the timing of electric vehicle demand affects the value of reservations.
$$\lambda_{\rho,p}(t)=N_{\rho,X}w_p(t),\qquad N_{\rho,X}=\frac{\rho H X}{\mathbb{E}[D]}$$
$$\sum_{t=1}^{H}w_p(t)=1$$
| Scenario | Load | Peak profile | Interpretation |
|---|---|---|---|
| S11 | Light | Flat | Loose capacity and weak within-day variation |
| S12 | Light | Two-peak | Loose average capacity but local electric vehicle demand peaks |
| S13 | Light | Sharp | Low average load with concentrated congestion |
| S21 | Medium | Flat | Moderate pressure with smooth demand |
| S22 | Medium | Two-peak | Moderate pressure with repeated congestion episodes |
| S23 | Medium | Sharp | Moderate average load with severe local peaks |
| S31 | High | Flat | Persistent capacity pressure |
| S32 | High | Two-peak | High load with repeated peaks |
| S33 | High | Sharp | High load and concentrated congestion |
In the baseline, the service duration distribution over 2 to 8 slots has mean 3.21 slots, or 48.15 minutes. This aligns with public fast-charging behavior in which many electric vehicle users complete a charge within roughly 30 to 60 minutes while a right tail remains. The unit revenue per effective service slot is 7.87. The baseline fulfillment environment has an effective arrival rate of 0.82, an early cancellation rate of 0.08, a late cancellation rate of 0.05, and a no-show rate of 0.05. Early cancellation must occur at least four slots before the reserved start time. I also test high and low fulfillment environments. The reservation window is eight slots, or two hours, and the future-load prediction window is also eight slots.
| Parameter | Baseline value | Role in the electric vehicle charging model |
|---|---|---|
| H | 96 slots | One day in 15-minute intervals |
| X | 15 guns | Station charging capacity |
| Service duration set | 2 to 8 slots | 30 to 120 minutes of charging |
| Mean service duration | 3.21 slots | About 48 minutes |
| Unit revenue | 7.87 per slot | Revenue per effective charging slot |
| Average load | 0.55, 0.75, 0.90 | Light, medium, and high electric vehicle demand pressure |
| Reservation window | 8 slots | Two-hour advance reservation horizon |
| Prediction window | 8 slots | Short-window future load signal |
| Early cancellation lead | 4 slots | Minimum notice for capacity release |
| Baseline fulfillment | 0.82 / 0.08 / 0.05 / 0.05 | Arrival, early cancel, late cancel, no-show |
Main results. Across the nine scenarios, the static mechanism produces a positive average revenue increment in all nine scenarios, with a nine-scenario average of 37.97 per day. The dynamic mechanism produces a nine-scenario average revenue increment of 102.68 per day, and the average dynamic advantage over the static mechanism is 64.71 per day. The dynamic mechanism does not create a positive additional advantage in the light-load flat scenario, where it collapses to the static rule. In the other eight scenarios, the dynamic advantage is positive, and the lower bound of the 95 percent confidence interval is above zero in each case. The largest dynamic advantages appear in sharp-peak and two-peak scenarios with medium or high load, especially S33, S23, and S13.
| Scenario | Static revenue increment | Dynamic revenue increment | Dynamic minus static | Dynamic advantage statistically positive |
|---|---|---|---|---|
| S11 | 0.87 | 0.87 | 0.00 | No; dynamic collapses to static |
| S12 | 14.56 | 22.90 | 8.34 | Yes |
| S13 | 75.55 | 165.43 | 89.88 | Yes |
| S21 | 49.03 | 60.52 | 11.49 | Yes |
| S22 | 32.58 | 120.41 | 87.83 | Yes |
| S23 | 32.35 | 147.96 | 115.61 | Yes |
| S31 | 61.70 | 123.09 | 61.39 | Yes |
| S32 | 37.93 | 127.42 | 89.48 | Yes |
| S33 | 37.15 | 155.51 | 118.36 | Yes |
The pattern is intuitive for electric vehicle charging. When demand is light and flat, a small reservation quota is enough to capture most of the available retention benefit, and further state dependence does not add much. When demand has sharp peaks or two-peak structure, a fixed quota must compromise across states. The dynamic rule can raise the quota when immediate waiting pressure is high and future load remains tolerable, and it can lower the quota when future load is high or idle capacity is scarce. This state dependence is the source of the dynamic advantage.
| Mechanism | Average completed electric vehicle users | Average exits | Average final realized wait in slots |
|---|---|---|---|
| First-come, first-served | 288.36 | 40.09 | 0.427 |
| Static coexisting reservation | 289.75 | 34.71 | 0.416 |
| Dynamic coexisting reservation | 292.44 | 29.65 | 0.475 |
The service outcomes show that the revenue improvement is not merely a reshuffling of the same electric vehicle demand. The dynamic mechanism increases completed users and reduces exits relative to first-come, first-served. At the same time, it increases final realized waiting by about 0.049 slots, or roughly 0.73 minutes, relative to first-come, first-served, and by about 0.059 slots, or roughly 0.89 minutes, relative to the static mechanism. This is a meaningful trade-off: the reservation mechanism improves completed electric vehicle charging services and reduces exits, but it does so with a modest increase in realized waiting for accepted immediate users.
Mechanism decomposition. On average, the dynamic mechanism yields 11.56 retained electric vehicle users, 36.44 service slots of demand retention, and 3.44 service slots of capacity backfill. It also incurs 12.22 service slots of service loss and 11.11 service slots of no-show loss. The static mechanism yields 7.22 retained users, 22.78 service slots of demand retention, and 2.22 service slots of backfill. The dynamic mechanism therefore generates more retention but also more loss than the static mechanism. Its net advantage comes from the fact that the additional retention is larger than the additional losses in most scenarios.
| Decomposition term | Static mechanism | Dynamic mechanism |
|---|---|---|
| Retained electric vehicle users | 7.22 | 11.56 |
| Demand retention in service slots | 22.78 | 36.44 |
| Capacity backfill in service slots | 2.22 | 3.44 |
| Service loss in service slots | Not separately averaged in the same table | 12.22 |
| No-show loss in service slots | Not separately averaged in the same table | 11.11 |
The decomposition clarifies the economics of reservation in electric vehicle charging. The main benefit is not higher price or extra capacity. The main benefit is that some electric vehicle users who would otherwise exit because of uncertain or long waiting are converted into completed charging services. The main costs are service loss from crowding out immediate users and no-show loss from reservations that are cancelled late or not honored. This is why reservation design must be paired with reminder systems, cancellation constraints, and user credit management when fulfillment quality is weak.
Static quota boundaries. The optimal static quota varies by scenario. In S11, S12, S22, and S32, the static optimum is one gun. In S21, S23, S31, and S33, it is two guns. In S13, it rises to four guns. The light-load flat scenario has very little room for reservation value because the immediate queue is already short; a small quota captures the marginal retention benefit, and further reservation capacity mainly crowds out immediate users. The light-load sharp scenario is different: although average load is low, local congestion is severe, so a larger reservation quota can absorb electric vehicle users who would otherwise exit. In the high-load sharp scenario, the optimum remains near two guns, but the marginal revenue curve is flatter, indicating that both under-reservation and over-reservation are costly.
| Scenario | Static optimal quota | Final dynamic tiers m1/m2/m3 | 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 |
The dynamic rule uses multiple quota tiers in most scenarios. In S11, all three tiers are equal, so the dynamic mechanism degenerates to the static mechanism. In S13, S22, S23, S32, and S33, the gap between the highest and lowest tiers is three or four guns. These are also the scenarios with the largest dynamic revenue advantage. The average number of actually used tiers is close to three in several medium- and high-load scenarios, and the share of non-medium quota use is between 22 and 42 percent. This confirms that the dynamic value comes from observable state differences rather than from a mechanical increase in the average reservation quota.
Fulfillment environment. Fulfillment quality changes the boundary of the mechanism because it directly affects no-show loss. In a high-fulfillment environment, the static and dynamic mechanisms with fixed baseline parameters raise their nine-scenario average revenue increments to 69.19 and 155.38 per day, respectively. After retraining in the new environment, the averages rise further to 92.39 and 169.36. In a low-fulfillment environment with fixed baseline parameters, the static mechanism has a positive average revenue increment in only three scenarios, and its nine-scenario average becomes negative at -5.19, with a 95 percent confidence interval that includes zero. The dynamic mechanism remains positive in eight scenarios, with an average of 33.44 and a confidence interval from 27.14 to 39.74. After retraining, the static average recovers to 5.93 and the dynamic average rises to 44.51.
| Fulfillment environment | Static average | Dynamic average | Dynamic minus static |
|---|---|---|---|
| High fulfillment, fixed parameters | 69.19 | 155.38 | 86.19 |
| High fulfillment, retrained | 92.39 | 169.36 | 76.98 |
| Low fulfillment, fixed parameters | -5.19 | 33.44 | 38.62 |
| Low fulfillment, retrained | 5.93 | 44.51 | 38.58 |
This result has a clear managerial meaning for electric vehicle charging operators. When users are reliable, reservation capacity is more likely to convert into completed charging services, so the revenue boundary is higher. When fulfillment is weak, simply expanding reservation availability is risky. The station should first improve reminders, cancellation rules, and credit management, and then re-estimate the appropriate quota and dynamic thresholds. Otherwise, the station may accept many electric vehicle reservations that later become no-show losses.
Fast charging and duration shifts. Faster charging changes the distribution of service duration and therefore the number of electric vehicle users who can be served in a day. I shift the baseline duration distribution forward so that the mean is about 2.77 slots, while retaining a right tail. With fixed baseline parameters, the static and dynamic averages become 36.76 and 97.75 per day, and the dynamic advantage is 60.98. After retraining, the static and dynamic averages are 33.76 and 95.42, and the dynamic advantage is 61.66. The ranking of mechanisms does not change. The total number of completed users rises because shorter charging durations allow more electric vehicle users to be processed, but exits also rise because the number of arrivals is scaled up to maintain the same load. The dynamic mechanism still reduces exits relative to first-come, first-served by about 8.64 to 9.46 users per day.
| Fast-charging variant | Static average | Dynamic average | Dynamic minus static |
|---|---|---|---|
| Fixed baseline parameters | 36.76 | 97.75 | 60.98 |
| Retrained parameters | 33.76 | 95.42 | 61.66 |
Supply and demand disturbances. I also test whether the dynamic advantage depends on perfect prediction. I introduce a two-hour local capacity failure in which available guns fall from 15 to 14, a local evening demand increase of up to 35 percent, and a local evening demand decrease of up to 35 percent. For each disturbance, I distinguish unknown, partially anticipated, and fully known information states. Under the tested disturbance scale and fixed state-response rule, the dynamic advantage remains. In the supply-failure case, the dynamic average revenue increment is 107.47, 107.94, and 107.97 under unknown, partial, and full information, respectively. The dynamic advantage over static is 67.10, 67.57, and 67.59. The differences are very small. In the added-peak case, the dynamic average rises to about 135, and the dynamic advantage is above 85. In the cancelled-peak case, the dynamic average remains around 93, and the dynamic advantage is about 61. This indicates that the dynamic value in electric vehicle charging comes largely from real-time state response rather than from perfect foresight.
| Disturbance | Information state | Static average | Dynamic average | Dynamic minus static |
|---|---|---|---|---|
| Supply failure | Unknown | 40.37 | 107.47 | 67.10 |
| Supply failure | Partial warning | 40.37 | 107.94 | 67.57 |
| Supply failure | Fully known | 40.37 | 107.97 | 67.59 |
| Added peak | Unknown | 49.69 | 135.53 | 85.84 |
| Added peak | Partial warning | 49.69 | 135.57 | 85.89 |
| Added peak | Fully known | 49.69 | 135.09 | 85.41 |
| Cancelled peak | Unknown | 32.30 | 93.78 | 61.47 |
| Cancelled peak | Partial warning | 32.30 | 92.83 | 60.53 |
| Cancelled peak | Fully known | 32.30 | 92.95 | 60.65 |
Behavioral sensitivity and station scale. A 20 percent increase in waiting cost lowers the static and dynamic averages to 32.90 and 95.52, while the dynamic advantage remains 62.62. A 20 percent increase in reservation friction raises the static and dynamic averages to 40.90 and 105.17. This may occur because higher friction suppresses marginal reservation demand that has near-zero net utility, which can ease over-quota pressure in some scenarios. This does not mean that higher friction is desirable; it simply shows that the mechanism ranking is robust within the tested range. I also test station sizes of 10, 20, and 30 charging guns. The dynamic advantage remains positive in eight of nine scenarios, and the overall ranking is unchanged.
| Station size X | Static average and 95% CI | Dynamic average and 95% CI | Dynamic minus static and 95% CI | Significant scenarios |
|---|---|---|---|---|
| 10 | 23.99 [20.27, 27.72] | 88.24 [83.26, 93.23] | 64.25 [60.65, 67.84] | 8 of 9 |
| 15 | 37.97 [33.25, 42.68] | 102.68 [96.97, 108.38] | 64.71 [60.91, 68.50] | 8 of 9 |
| 20 | 60.45 [55.46, 65.44] | 127.92 [121.91, 133.94] | 67.47 [63.26, 71.69] | 8 of 9 |
| 30 | 88.76 [82.55, 94.98] | 163.75 [156.82, 170.68] | 74.98 [71.16, 78.81] | 8 of 9 |
I further test the sensitivity of user service value. When the pre-truncation center of the value distribution is reduced by 20 percent, the static and dynamic averages fall to 12.53 and 42.80, and the dynamic advantage falls to 30.27. When the center is increased by 20 percent, the static and dynamic averages rise to 46.56 and 115.69, and the dynamic advantage rises to 69.12. The overall mechanism ranking remains, but the dynamic advantage is weaker when electric vehicle users place low value on charging service. This indicates a genuine boundary: dynamic reservation is most useful when demand pressure is meaningful and when the value of completed electric vehicle charging is high enough to justify the additional service loss and no-show risk.
| Value center shift | Static average and 95% CI | Dynamic average and 95% CI | Dynamic minus static and 95% CI | Significant scenarios |
|---|---|---|---|---|
| -20% | 12.53 [9.67, 15.40] | 42.80 [39.11, 46.50] | 30.27 [27.82, 32.73] | 7 of 9 |
| -10% | 29.35 [25.22, 33.47] | 85.91 [81.06, 90.75] | 56.56 [52.94, 60.17] | 7 of 9 |
| Baseline | 37.97 [33.25, 42.68] | 102.68 [96.97, 108.38] | 64.71 [60.91, 68.50] | 8 of 9 |
| +10% | 46.82 [41.37, 52.26] | 112.67 [106.69, 118.65] | 65.85 [61.88, 69.83] | 7 of 9 |
| +20% | 46.56 [42.29, 50.83] | 115.69 [109.72, 121.65] | 69.12 [65.07, 73.18] | 8 of 9 |
Interpretation for electric vehicle charging operations. The results support a practical rule for public charging stations. For a light-load station with a flat electric vehicle demand profile, a small static reservation quota is likely to capture most of the available benefit. A dynamic mechanism may collapse to the static rule, so deploying a complex state-dependent system is not justified unless implementation costs are very low. For stations with two-peak or sharp-peak electric vehicle demand, and for stations with medium or high average load, the dynamic mechanism is more attractive. The extra value comes from using real-time congestion, future load, and idle capacity to adjust the reservation quota. For stations with weak fulfillment, the priority should be to improve reservation reliability before expanding reservation capacity. For stations facing fast charging, supply failures, or volatile demand profiles, the station should retain a real-time response capability and update parameters periodically rather than relying on a fixed quota indefinitely.
I also emphasize that the revenue results are operating revenue increments, not profit increments. I do not subtract electricity purchase costs, equipment depreciation, platform maintenance, or the cost of implementing the reservation system. This is why the managerial interpretation should be conditional. A dynamic mechanism with an average advantage of 64.71 per day may be valuable for a large station with a low-cost digital platform, but it may not be worthwhile for a small station with high implementation and monitoring costs. The right question is not whether dynamic reservation is always better, but whether the expected gain in a specific electric vehicle charging environment exceeds the cost of state monitoring, prediction, and rule maintenance.
Limitations and extensions. Several limitations remain. First, I do not explicitly model the fixed and variable costs of the reservation platform, user reminder systems, or credit management. Second, although I test imperfect prediction, I do not fully characterize arbitrary prediction error distributions or control errors. Third, I treat price, deposit, and refund rules as exogenous. Fourth, I focus on a single station rather than a network of stations with electric vehicle users choosing among sites. These limitations suggest natural extensions: a multi-station network with cross-site electric vehicle choice, joint optimization of price and capacity, reservation deposits and refunds, and more detailed prediction-error analysis. Such extensions would make the mechanism design closer to a platform-level electric vehicle charging service.
Conclusion. I have developed and evaluated a coexisting reservation mechanism for electric vehicle charging in which reservation users and walk-in users share a fixed service capacity. The analytical decomposition shows that reservation value comes from demand retention minus service loss and no-show loss. The static mechanism can improve operating revenue when the reservation quota is moderate, but its performance depends on load, peak shape, and fulfillment quality. The dynamic mechanism generally dominates the static mechanism in scenarios with stronger state heterogeneity, especially two-peak and sharp-peak scenarios with medium or high load. In the baseline, the static mechanism raises average revenue by 37.97 per day, the dynamic mechanism raises it by 102.68 per day, and the dynamic advantage over static is 64.71 per day. The service results show that the revenue gain is accompanied by more completed electric vehicle charging services and fewer exits, with a modest increase in realized waiting. The mechanism is therefore a capacity-allocation tool rather than a substitute for new electric vehicle charging infrastructure. Its sensible use requires attention to scenario type, fulfillment quality, implementation cost, and the trade-off among revenue, service completion, and user waiting.