An Evaluation of Temporal- and Spatial-Based Dynamic Parking Pricing for Commercial Establishments

All smart parking management systems (SPMS) have incorporated the dynamic pricing into its features and capabilities. The collection of parking fees on a corresponding spot has been dependent on either its time- or space-value, with most SPMS utilizing temporal-based parking fee collection. However, little to no study has been conducted to assess or evaluate these pricing schemes according to its friendliness and economics towards both parkers and business operators. In this work, we evaluate two current temporal- and three proposed spatiotemporal-based dynamic parking pricing methods by computing their social optimum range and economic effects to both users and parking management entities. Our extensive analysis utilizing both empirical mobility traces and driver parking duration behavior provide important insights in the current pricing setups and present necessary adjustments in improving parking fee collection that contribute to societal benefits.

vacant and available parking lots, appropriate and dynamic 23 pricing fees are applied to discriminate parkers and allow 24 congestion control. For example, commercial establishments 25 offer self-service, valet, and online reservation parking [4]. 26 In the collection of appropriate parking dues, some previous 27 studies included the walking distance covered, reservation, 28 The associate editor coordinating the review of this manuscript and approving it for publication was Ajit Khosla . and estimated time of arrival in their parking payment [5] and 29 cruising time and parking limitations [6]. 30 With the advent of sensor electronics, wireless technolo-31 gies, and cloud computing, there has been an abundance of 32 published smart parking management systems (SPMS) aimed 33 in pollution reduction and user convenience in their smart 34 parking management system [7]. Most of all, SPMS should 35 maximize profit and optimize vacant space usage [8]. In max- 36 imizing parking revenues, dynamic pricing has been imple-37 mented that considers both the temporal and spatial values of 38 a parking slot, such as peak and off-peak hours, and street and 39 covered parking areas [9]. 40 While these SPMS provide optimal solution to their respec-41 tive objectives, pricing has always been biased towards busi-42 ness operators, which, understandably be the case since they 43 can dictate the price of their own properties. However, there 44 is no existing study yet that evaluates and analyzes the vari-45 ous parking price friendliness to parking users, or how can 46 it be sustainable to the parkers. Empirically, land proper-47 ties appreciate in value, therefore, parking fees will defi-48 nitely increase as time goes on. Given this land appreciation, 49  Since we do not present any 'smart' features, this work is 74 fitted for parking businesses and commercial centers unwill-75 ing to upgrade their car park infrastructures and simply rely 76 on optimal fee collection that is beneficial also to park-77 ers. The major contributions of this paper are enumerated 78 below.  In order to gauge the effects of these prices on both 85 users and businesses, the social optimum range for each 86 pricing is calculated, and the bias of the average earning 87 is checked. For a given set of parking rate constants, 88 if the observed social optimum is less than the average, 89 then we conclude that the established parking rate is 90 parker-friendly, otherwise, business-friendly. 91 2) Through an online survey, we present a lognormal 92 distribution of the parking duration behavior from 93 246 respondents. To the best of our knowledge, this 94 is the first research work to provide an empirical 95 parking duration behavior from commercial establish-96 ment users that can serve as a benchmark for further 97 understanding and studying parking duration behavior. 98 3) Extensive simulations employing empirical mobility 99 traces and parking duration have been implemented to 100 compare and evaluate the proposed pricing schemes. 101 We also incorporated a synthetic human behavior of 102 long-duration parking to foresee its effects to business 103 and user. 104 The paper is outlined as follows: Section II discusses the 105 published works related to dynamic pricing involved in park-106 ing management. We also state here that while these papers 107 discussed dynamic pricing, there is no literature that com-108 pares the friendliness of such methods to the users. To allow 109 realistic vehicular parking traces, we utilized the taxi GPS 110 traces in Section III. In Section IV, we present the dynamic 111 parking pricing schemes that will be evaluated in this study. 112 We also present here two alternative pricing based on spatial 113 and temporal values. To provide a common ground of com-114 parison, we derived the social optimum range for each park-115 ing pricing scheme. This is presented in Section V. We then 116 present the results of our extensive simulations in Section VI. 117 Finally, we conclude our work in Section VII.

119
In this section, we provide a brief literature review of papers 120 discussing how parking management systems determine their 121 pricing method. In these previous studies, it is accepted that 122 the number of available spaces that can be used by parkers 123 are always static and scarce, thus, there is a need to dynam-124 ically allocate these fixed resources. It is in this line that 125 most research papers have focused their work and based their 126 pricing policies.

127
In [11], a demand-driven dynamic parking pricing has been 128 studied on the street parking slots in Beijing. The pricing 129 scheme was based on traffic performance and current parking 130 demand. Ref.
[12] included additional charges in collecting 131 parking fees such as, vehicle type and miscellaneous. The 132 work presented seven dynamic pricing schemes but were only 133 differentiated by its introduced price adjustment and occu-134 pancy rates. On the other hand, pricing schemes in [13] are 135 based on linear and exponential reservation demands, and 136 not on walk-in customers, aimed at maximizing revenues and 137 minimizing cruising cost.

138
Three pricing schemes, based on space occupancy, were 139 assessed in [14], where the proposed new scheme focused 140 on price variation based on peak periods. This was also the 141 criterion employed in [15] in developing their reactive and 142 proactive pricing schemes. In [16] and [17], a bidding pro-143 cess took place when the number of parkers was more than 144 the number of available parking slots. The maximum rev-145 enue was chosen from these requesting parkers. Similar to 146 this process was found in [18], except that parking own-147 ers were the ones proposing time-differentiated parking fee 148 rates to surrounding customers. In [19], parking fees were 149 based on the cumulative effect of many factors, such as 150 distance-to-slot, remaining free slots, traffic density, and 151 parking duration. This was also the case considered in [20].

152
Instead of these factors, [21], determined their parking fees 153 based on the parking status and utilization rate of mem-154 ber establishments. Accordingly, the price can increase or 155 decrease depending on the parking system losses.

156
The parking pricing fees in [22] implemented a linear 157 rate collection for both autonomous and regular vehicles by 158 considering both parking duration and location. In another 159 work, [23], the parking fees were recalculated daily based on 160 the parker's travel information and focused more on driver 161 benefits rather than establishment revenue. Different from 162 these research works, the pricing policy in [24] was based 163 on a regional distribution of parking lots and fine-grained  demands. Finally, [26] incorporated game theory in obtaining 169 its parking fee with government agencies, drivers, and park-170 ing firms as the players involved.

171
Machine learning was used in determining occupancy-172 based parking prices for various parking lots in Seattle. Com-173 pared to two benchmarks, this pricing method provided the 174 largest city revenue [27], [28]. 175 We differentiate our work from these papers in three ways. 176 Firstly, we focus only on the evaluation of current parking

206
In evaluating the current and proposed dynamic pricing sche 207 -mes, we utilize empirical mobility taxi datasets roaming an 208 urban city from [29] to mimic vehicles looking for a parking 209 space, while at the same time, disregard traffic modeling. 210 The parking buildings are set to be located at the intersec-211 tions, for simplicity of evaluation, but can easily be adjusted 212 once participating parking businesses have been identified. 213 This method of assuming parking locations is applicable to 214 places where empirical parking data from commercial estab-215 lishments and buildings are inaccessible or difficult to obtain, 216 e.g., in the Philippines.

217
The Beijing City taxi mobility traces are arranged per taxi 218 ID and sampled every 10 seconds for seven days. A taxi 219 ID has many trajectories, τ ID , composed of GPS coordinate 220 points, λ e , such that τ ID = λ S , λ 2 , . . . , λ e , . . . , λ E . λ S 221 and λ E are denoted as the start and end points, respectively, 222 λ e ∈ R 2 is a duple {lat, lon} where lat and lon are the latitude 223 and longitude coordinates of the taxi's instantaneous position, 224 respectively [30].

225
In Figure 2, a parking business, P n , n ∈ {1, 2, . . . , N }, 226 has n maximum available slots, where a vehicle can select 227 a space that can be leased with an hourly rate. At time 228 t = kT S , k = 0, 1, . . . , κ, there are m nearby (within R r of 229 P n ) vehicles, V m , looking for a possible parking space with 230 reasonable fees. The parking business displays its available 231 number of vacant slots and its dynamic pricing.

232
Upon entry, time T entry starts, and based on the dynamic 233 pricing scheme, the vehicle is alloted a free space. For spa-234 tiotemporal methods, available parking slots are categorized 235 into regular and special spaces. Regular categories are those 236 with equal probability, regardless of its proximity to mall 237 entrance/exit, elevators, PWD spots, and other important 238 landmarks. However, regular spaces can be classified into 239 indoor or outdoor (street) parking. The rest is classified under 240 special categories where the location matters and it adds value 241 to the dynamic price. The parking duration ends, T exit , when 242 the vehicle is already exiting the parking center. Effectively, 243 the parking duration, PD, PD = T exit − T entry .

244
One may argue that the traces utilized in this study are 245 those with no parking intentions, however, employing these 246 mobility traces will help understand, and even predict, the 247 worst case scenario when there are many vehicles looking 248 for a possible parking space. Therefore, by allowing these 249 vehicular movements to mimic parking vehicles is justified, 250 more specifically, in comparing and evaluating the different 251 applied and proposed dynamic parking pricing schemes given 252 a huge amount of customers.

254
In this section, we evaluate temporal-and spatiotemporal-255 based dynamic parking pricing schemes, F xx (m), considering 256 temporal and spatial values of a car garage up for lease by 257 a vehicle V m . The proposed parking fees take into account 258 salient variables and features of an available parking space, 259 e.g., land value, entry time, demand value, unique services, 260   [14], [15], [16], [19], The fee utilizing the linear rate parking pricing [13], [33] 282 for user m, F LR (m), is an adjusted fixed rate pricing and is 283 governed by (3).
In (3), a user has to pay a fixed parking fee, denoted

292
In linear rate pricing, parking users are advised to park 293 only for a certain duration to provide other incoming vehicles 294 available parking slots and avoid the additional penalty equal 295 to K adj t LR .

296
Note that when T def = 24 hours, t LR = 0, effectively, 297 The fee using min-max [10] rate parking pricing for user m, 300 F MM (m), is described by (4), where charged fees, K h , are 301 based on parking duration value,

311
If T min = T def and K min = K , then the lower bounds of 312 Linear and Min-Max Rate Pricing schemes are equal, i.e., 313 Two spatiotemporal dynamic parking pricing schemes are 319 presented in this subsection. The parking duration is still a 320 vital component of the proposed pricing methods, however, 321 the spatial value of the parking slot has now been considered. 322

323
The adaptive rate parking pricing for user m, F AR (m), allows 324 parking price movement based on both temporal and spatial 325 conditions. It is shown in (5).
where T j > 0 assigns the parking slot premium value at the 328 j th time interval the car entered, stayed, and left the parking 329 premise. T j assigns the temporal weight of the vacant parking 330 slot and considers peak and off-peak scenarios.

331
On the other hand, y = y K − n −|PS nocc | entry n +1 is the 332 normalized occupancy of the parking lot, upon vehicle entry, 333 and it can be defined as the spatial value of the parking slot. 334 If |PS n occ | entry (the number of occupied parking spaces upon 335 VOLUME 10, 2022 entry) approaches n , the parking slot should be valued at a higher price, else, vehicles will be charged less. y K ≥ 337 1 increases the parking lot's spatial value.

338
In adaptive rate pricing, parking users can avail of the 339 parking slot at a lower cost especially, during off-peak hours. 340 One may argue that the adaptive rate pricing is not realistic,

353
where a (t) and b γ (s) are time-and space-dependent coef-

363
We define F γ (s) below in (7), where 's and 's are the asso-364 ciated parking land dues (similar to real estate property tax) 365 and maximum vacancies in each classification, respectively.

366
The coefficient α denotes which car park category will the 367 vehicle be parked. where K res > K for having the convenience of a reserved 384 parking slot and δT as the time difference between arrival and 385 reservation, normally dictated by the reservist. In practice, 386 this is automatically deductible from the parker. Any excess 387 charges will just be subtracted from the actual parking pay-388 ment upon checkout. 390 We define the user and business social optimum range, S xx , 391 in (9), for a parking pricing scheme as the ratio of parking 392 charges and duration to gauge business profitability and mon- For user m, S xx can be defined as the parking pricing 401 impact, i.e., effective parking fee rate. This value should be 402 minimized to denote the value of their money for the service 403 rendered, i.e., lease of a parking space. On the other hand, for 404 businesses, S, means how much can they effectively profit 405 per parker m multiplied by the total available parking slots 406 n . The limits of S xx are determined by getting the minimum 407 and maximum values of (9) in each of the dynamic parking 408 pricing schemes.

409
In general, we assume that a parking business is operational 410 24 hours a day and the parker is charged on an hourly rate. 411 Note that a fraction of an hour is already considered as one 412 hour. Also, we do not consider parking durations with over-413 lapping days.

414
In Fixed Rate Pricing, the social optimum range, S FR is 415 given below in (10). As an example, the S xx lower is computed 416 by dividing K with the maximum allowable PD = 24 hours, 417 while S xx higher is obtained by dividing K by PD = 1 hour.
For Linear Rate Pricing, assuming that K is only applicable 420 for the first t LR = 3 hours and K adj = K β , β > 3, is charged 421 for each succeeding hour or a fraction of it, we have (11). 422 From simulations, 1 ≤ β ≤ 3, the Linear rate pricing scheme 423 becomes unreasonable and less competitive.

455
In this section, we present our extensive simulation results 456 using empirical mobility traces from Beijing City where the 457 characteristics are described in Table 1.

TABLE 1. Simulation and dataset attributes/parameters.
We use the GPS coordinates of nearby taxis to act like vehi-459 cles that will be utilizing the parking space of a commercial  The values of T j (for the Adaptive Rate Pricing) are 471 assumed and shown in Table 3. Later on, T j can be derived 472 from empirical situations and is highly dependent on the 473 establishment. In our example, we placed the highest pre-474 mium on the 10:00 AM -2:00 PM time interval since these 475 are rush/peak hours when people tend to meet up for lunch 476 and meetings. Note that an exact value for these assumptions 477 can be derived per each parking building. If T j = 1 for all 478 time intervals, then F AR (m) charges the parker based on the 479 spatial value of the parking slot only.

480
Note that the constant values selected here are chosen such 481 that the discrepancies between temporal and spatiotemporal 482 pricing schemes do not have a big discrepancy. In reality, 483 however, premium establishments can charge their customers 484 a fee equivalent to the parking lot's high value and demand 485 VOLUME 10, 2022  availability. Also, commercial establishments will also con-  3) To simulate the situation where long-duration parkers 512 are using the car garages, a Weibull distribution with 513 scale value of 18.4009 and shape value of 3.5211 fit-514 ted over a set of synthetic parking duration samples is 515 simulated. This is shown in Figure 4(b).

518
We performed a set of extensive simulations composed 519 of 1000 runs for each parking duration scenario over the 520 seven-day mobility dataset. We limit our cost evaluation to 521 those given values in Table 2 only.

523
Given the three parking duration characteristics and with a 524 sampling time of 10 minutes, the average cumulative distri-525 butions parked and unparked (those who do not have any 526 available parking slot upon arrival) vehicles are shown in 527 Figure 5. We note that as sampling time is decreased, these 528 numbers increase as there are more available vehicular GPS 529 traces to consider.

530
Given an allotted n = 1000 available slots for each com-531 mercial building, for a short-duration parking behavior, the 532 number of unparked vehicles is negligible since they will have 533 available spaces to leave their cars, as shown in Figure 5(a). 534 However, when the duration of a parked car is increased, 535 the establishments are overwhelmed by incoming vehicles, 536 starting at 11:00 AM, since there are already parked vehicles 537 with no intention of vacating their spaces. This is exhibited 538 by Figure 5(b) and Figure 5(c). This scenario is exempli-539 fied by office employees leaving their vehicles parked in an 540 establishment near their work places. From the standpoint of 541

581
The Min-Max pricing offers the intermediate price 582 between the Fixed and Linear rate dynamic pricing schemes. 583 From its definition in (4), short-, mid-, and long-duration 584 parkers can easily be discriminated by various fixed pricing 585 rates, K h . The more fixed prices involved in Min-Max is, 586 the better it is to understand the parking behaviors of cus-587 tomers. From the extensive simulation results, the Min-Max 588 Rate dynamic pricing method allows a compromise for both 589 businesses and users.

590
The Adaptive Rate pricing offers a relatively low price 591 offering to nearby parkers. This is so because the time interval 592 value T j has values less than one. However, the adaptive rate 593 can easily be more expensive when the spatial value, y K , 594 or the temporal value, T j , is increased unjustifiably. This vari-595 able is left to the parking managers to place the appropriate 596 values that will not discourage its customers.

597
Finally, the Complementary rate pricing is advantageous 598 to establishments that offers special types of parking lots 599 and services, e.g., valet or PWD assistance. These supports 600 are charged based on service rendered by the driver taking 601 over the vehicle and/or the premium (e.g., security) loca-602 tion where the car is parked. The coefficients a (t) and 603 b γ (s) can easily be adjusted accordingly too to provide 604 which of the time-value or space-value is prioritized. Com-605 pared to the other four pricing schemes, a customer must be 606 well-informed about the convenience this pricing scheme is 607 offering.

609
Given the values in Tables 2 and 3, the social optimum value 610 range, S xx for each of the dynamic pricing is shown in Table 4 611 below. The midpoint of S xx , S xx ave , is also given in the fourth 612 column. 613 We evaluate the user-or business-friendliness of each 614 dynamic parking pricing scheme. Recall that if the average 615 is near the lower S xx , then the pricing model is user-friendly, 616 otherwise, it is business-friendly. 617 VOLUME 10, 2022

627
In general, the Fixed rate pricing is really customer-friendly 628 and encourages its customers to avail its facility since only 629 one value needs to be paid. The parker does not need to 630 worry about its time and the varying cost. In most commercial 631 establishments, e.g., malls and restaurants, that are located 632 within the vicinity of each other, this kind of parking pricing 633 is implemented.

634
On the other hand, the Linear rate pricing is mostly utilized 635 by commercial establishments which are near offices. Under-636 standably, since there is a lower vehicular parking arrival, 637 getting the target revenue is difficult to achieve under this 638 circumstance, thus, implementing this method instead of the 639 fixed pricing.

640
The Min-Max pricing is between the Fixed and Linear 641 rate methods. It addresses both the short-and long-duration 642 parkers by having their respective parking fees. However, 643 under the empirical distribution, the Min-Max behaves like 644 the Fixed rate pricing.

645
In the simulations, 0 < T j < ∞ and those off-peak hours 646 have weights less than one. However, setting T j > 1 can 647 easily turn the Adaptive rate pricing business-friendly. Also, 648 setting y K > 2 will automatically increase the parking fee 649 that will make it lean towards the business side.   has the lower number of parking vehicles, but utilizing the 663 appropriate pricing method can yield a better parking revenue 664 when compared to PB34, i.e., implementing the Adaptive rate 665 parking pricing. One reason here is that the parking vehicles 666 happened during the time interval from 10:00 AM to 3:00 PM 667 where T j = 1.5. Given this finding, the Adaptive rate pricing 668 can be utilized by establishments with the majority of its cus-669 tomers using their facility during peak hours. From Figure 9 670 below, we can see the monthly consumer rental for each of 671 the pricing scheme. Therefore, depending on the location of 672 the commercial establishment, any of these studied dynamic 673 pricing schemes can be implemented in order to address target 674 parking revenue. However, one difficult thing, is explaining 675   Figure 9 also illustrates the monthly expenditure of a vehi-678 cle owner when he/she parks on a facility given the dynamic 679 parking pricing. Realistically, the Linear rate price is too 680 much for a middle class customer and will still settle with 681 the Fixed rate pricing.

683
In this research work, we evaluated five different spatiotem-684 poral dynamic parking pricing schemes according to its social 685 optimum measure based on value for money. Parking fees 686 based on the temporal value are highly dependent on the 687 parking duration of a parker, while spatial value considers 688 the number of available parking spaces upon entry of a vehi-689 cle and its land valuation. The assessment of these pricing 690 schemes provides the impacts of such parking fee rate to 691 the income generation of business owners and effects to the 692 daily parking expenditures of frequent parkers. Our eval-693 uation results reveal that the most commonly used Fixed 694 and Linear parking pricing schemes are benefiting users and 695 business entities for varying parking customer distribution, 696 respectively. This means that commercial establishments earn 697 from a group of parkers by employing Fixed rate, however, 698 on the other hand, they acquire income from small groups 699 of parkers when using Linear Rate. Also, Fixed rate pricing