An Algorithm and Software for Establishing Heterogeneous Parking Prices Nir Fulman, Itzhak Benenson Geosimulation Lab, Department of Geography and Human Environment, Tel Aviv University, Israel
[email protected],
[email protected] Abstract Parking prices in cities often do not reflect the heterogeneity of parking supply and demand. Underpricing results in high parking occupancy and long cruising time, whereas overpricing leads to low occupancy and hampered economic vitality. We present PARKFIT2, a spatially explicit algorithm for establishing a heterogeneous in space pattern of parking prices that preserve a predetermined level of occupation. PARKFIT2 generates this pattern based on the GIS layers representing urban parking demand and supply and on the relation between willingness to pay for parking and distance between parking place and destination. We apply PARKFIT2 for establishing heterogeneous parking prices that guarantee close to 90% parking occupancy in the Israeli city of Bat Yam.
1. From predefined and constant to adaptive and heterogeneous parking prices Parking demand is defined by the destinations’ capacity and attractiveness for drivers’ activities and is thus essentially heterogeneous in space and in time. The price of parking, and especially of curb parking, is usually constant and established for years over large urban areas. As a result, the parking supplydemand-prices triple is often unbalanced (Arnott & Inci, 2006; Shoup 2011). The problem is salient for both curb parking and the off-street parking facilities. High demand and underpriced parking result in long cruising time, and indirectly in traffic congestion and pollution. Overpricing results in underoccupancy, long cruising for parking in adjacent cheaper areas and is disadvantageous for the nearby economic activities. Researchers developed various economic models to investigate the issue of optimal curbside and garage parking pricing and regulations (See Inci, 2015 for a comprehensive review). Several studies focus on the negative effects of cruising for parking and suggest solutions to remedy it (Arnott & Inci, 2006; Calthrop & Proost, 2006; Shoup, 2006). Others examine spatial competition of parking garages and curbside parking spaces among themselves and with each other (Arnott, 2006; Anderson & de Palma (2004, 2007); Inci & Lindsey, 2014). Another strand of works links parking prices to congestion fees by embedding parking into bottleneck models (Arnott et al., 1991; Zhang et al., 2011; Fosgerau & de Palma, 2013; Verhoef et al., 1995). Although these models identify policy components that optimize average parking utilization, they pay limited attention to the spatial and stochastic aspects of the parking process. As a result, it is difficult to extend their conclusions to real-world situations. Shoup (2006) popularized the idea that on-street parking prices must be set to preserve a certain fraction of spots on every street block vacant in order to eliminate cruising. This rule-of-thumb reached 1
practitioners and stakeholders in recent years, and several cities around the world have started pilot projects of adjustment of curb-parking prices to demand. The cities of Calgary and Seattle operate a demand-responsive on-street parking policy that varies prices by city areas (CPA, 2016; SDOT, 2016), while in Los Angeles and San Francisco, parking fees are differentiated block by block, depending on the time of day (LADOT, 2016; SFMTA, 2016). Typically, in these projects parking fees for the chosen spatial units are updated repetitively, once in a period of time, until occupancy rates fall within the range of 60 – 80%. The San Francisco project, called SFpark, was reviewed by scholars who found that it achieved considerable progress toward realizing its goals. Pierce&Shoup (2013) calculate the elasticity of demand for curb parking revealed by price changes during SFpark’s first year. They find that although elasticity is far from uniform, SFpark has made a great impact in a very short period of time. Through simulations based on SFpark data, Millard-Ball et al. (2014) show that the target occupancy rates of 60-80% are slowly achieved, and that cruising for parking diminished by about 50%. Yet demand-responsive parking is not free of shortcomings. First, in order to determine the steady level of prices the projects employed expensive sensors for estimating parking occupation. As a result, the pilot projects of San Francisco and Los Angeles, for example, cost millions of dollars to set up and operate. Moreover, the projects require adjusting the prices iteratively until the target occupancies are achieved, which is costly in terms of menu costs and frustration from customers. A more efficient way of designing parking policy is to turn to demand-prediction models that establish parking prices that preserve a certain level of occupation. We thus present PARKFIT2, a novel algorithm that produces such a pattern. PARKFIT2 builds on the algorithm proposed by (Levi, Benenson, 2015) for estimating the demand/supply ratio. The equilibrium price pattern is estimated based on the highresolution GIS layers of roads, parking lots and buildings that are widely available at the municipal levels. PARKFIT2 is developed as an ArcGIS Python application and is freely available at https://www.researchgate.net/profile/Nir_Fulman.
2. PARKFIT2 algorithm 2.1. Initial settings PARKFIT2 considers demand at resolution of a separate building and parking facilities at resolution of a separate parking place and parking lot. A standard layer of buildings with height attribute, that is usually available from the municipal GIS, is used for estimating parking demand. The default size of an area necessary for parking a car is set as 5x2m. In case no additional information is available, curb parking places for parallel parking are constructed 5 meters apart from each other on both sides of the two-way streets and on the right side of the one way streets and are estimated based on the layer of road links or other areas available for parking. Information on possible perpendicular parking and on parking permissions and restrictions can easily be accounted for. Parking lots and floors of parking garages are divided into 5x2 areas and added to the overall parking supply (Figure 1). Drivers cannot be charged differently for every parking place. Typically, the minimal units for establishing parking price are street link or parking lot. Larger units, especially in case of the curb
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parking, as several street links, or all street links within an urban neighborhood can be also considered. We assume that there exists a maximum acceptable distance between a parking place and a destination. The goal of the PARKFIT2 is to establish a pattern of parking prices that keeps occupancy of each parking unit below the predefined threshold occupancy Oth.
Figure 1. GIS layers that are sufficient for applying PARKFIT2 algorithm: Buildings define demand for parking, parking lots and street segments define the supply. In case no other information is available, curb parking places along street links and in parking lots are constructed automatically. 2.2. Factors influencing behavior of drivers In order to simulate the parking behavior of drivers, it is necessary to reveal the factors that control it. This issue has received considerable attention in past decades. Feeney (1986) reviewed over 20 studies from the period of 1970-1984 that analyze the effect of parking cost and time on travel mode choice. Axhausen and Polak (1991) noted that only a few applications have previously investigated drivers’ choice between different types and locations of parking. However, in recent decades the trend is changing. Different scholars have started looking into both matters mostly through discrete choice models, based on stated and revealed preferences data. The majority of studies implement Multinomial Logit (MNL), Nested Logit (NL) and more recently also Mixed Multinomial Logit (MMNL) models. Parking prices and distance from parking place to destination are the only factors considered by almost all works in this field (Zhang & Zhou, 2016). Typically, they are found to negatively affect the probability 3
of choosing to park. For example, Teknomo and Hokao (1997) implement an MNL model based on data collected in Surabaya, Indonesia, to examine parking location choice in the CBD. They find several statistically significant factors, among them parking prices and walking time to destination, which display a negative influence on the probability to park. Hensher & King (2001) implement an NL model to examine mode and location choice in a CBD, and further derive elasticities of parking demand with respect to parking price, walking distance and other properties. They find that a 1% increase in hourly parking rates results in a reduction in the probability to park of between 0.5% and 1%, and that a similar increase in walking time would reduce the probability by 0.1% to 0.7%. Studies differ greatly in considering other attributes related to trip and parking conditions. Zhang & Zhou (2016) note that no such attribute is inspected by more than 2/5 of 23 works they review. They explain that this stems from the difference in study areas and research methods. Hess & Polak (2004) also show that the relative importance of factors differs between study areas. They analyze parking choice preferences in Birmingham, Coventry and Sutton Coldfield and reveal that the evaluation of time components (access, search and egress) varies across the areas. Clearly then, our model must be flexible enough to accommodate for the influence of various factors and their relative importance in determining the behavior of drivers. Most researchers also ignore the possible influence of driver characteristics on parking behavior. One such characteristic is income and its proxies. When considered, they are not always found significant (Zhang & Zhou, 2016) or of great importance to model adjustment to observed data (Simicevic, 2013). However, this may be the result of respondents’ reluctance to answer honestly regarding their income (Shiftan and Burd-Eden, 2001). Recent success was achieved by Ibeas et al. (2014), who examined parking behavior in a coastal town in Spain through an MMNL model. They conclude that the perception of parking charges is fairly heterogeneous, and depends both on the drivers’ income levels and whether or not they are local residents. Based on our review of the subject, formulas that control drivers’ behavior are formulated. They consider the basic factors that we believe are universally essential in determining drivers’ behavior: walking distance to destination, parking price and personal income. The formulas can be varied to express the influence of other factors. We examine the sensitivity of the model in section 3.2. 2.3. Drivers’ willingness to pay and the tradeoff between parking price and walking distance to destination Each driver c is characterized by its economic status Sc and aims at parking as close as possible to its destination. Driver’s economic status defines its maximal willingness to pay wc,max for the “best possible parking place,” nearest to the entrance to a destination and we assume that the value of wc,max monotonously grows with the increase in Sc. Basic model assumptions: -
Driver’s c willingness to pay wc(d) for a parking place at a walking distance d from the best possible one decreases monotonously with d and employ the dependency wc(d) = wc,max/d
(1)
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Below, we assume a sub-linear decrease in wc(d) with an increase in d (< 1). -
For a driver c of economic status Sc, all parking places at a distance d, which price is below wc(d), are equally attractive The attractiveness Ac(p, d), for a driver c, of a parking place p at a walk distance d ≥ 1 from the best one as Ac(p, d) = min(1, wc(d)/Fp)/d
(2)
where Fp is the price of parking place p. In what follows we consider = 0.5. Note that Ac(p, d) vary between 1 and zero. 2.4. The Nearest Pocket algorithm as a basis for the PARKFIT2 PARKFIT2 extends an algorithm proposed by Levy and Benenson in (Levy, Benenson, 2015) (Figure 2). Further on, we call the PARKFIT algorithm as Nearest Pocket Algorithm (NPA) and the algorithm applied in PARKFIT2 Nearest Pocket Algorithm for Prices (NPAP). To remind, let for each building k = 1, 2, 3, …, K the number of drivers for whom k is the destination be nk. The steps of the CP algorithm are as follows: (1) Build the list of all (driver, destination) pairs (the length of this list is n1 + n2 + n3 + … + nK) that represents total demand and randomly reorder it; (2) Assign parking places according to the list order - m-th driver is assigned nearest to its destination yet vacant parking place.
Figure 2: An illustration of NPA. (1) 5 Blue and 5 Green Drivers aim to park near destination of their color; (2) List of (driver, destination) pairs is constructed and randomly reordered; (3) 6 First drivers in a queue are parked at the places that are nearest to their destinations; (4) The remaining 4 drivers in the queue are parked at the places that are equally close to both destinations. 5
2.5. Major stages of the Nearest Pocket Algorithm for Prices NPAP consists of two stages – establishment of initial price for every parking unit and convergence to an equilibrium distribution of prices, by parking units (Figure 3).
Figure 3: Major steps of the NPAP algorithm. 2.5.1.
Stages 1 Establishing initial parking prices
Let Oth be the threshold occupation rate. Similar to the NPA, the list of (driver, destination) pairs of n1 + n2 + n3 + … + nK length is constructed, randomly reordered and m-th driver is assigned to the nearest yet vacant parking spot that is nearest to its destination, if such exists at a distance below the maximally acceptable. Different from the NPA, in NPAP an assignment is repeated M times, and for each parking unit the list of drivers who parked there and their willingness to pay for this place is stored. For each unit, drivers who parked at it in these repetitions are stored and ordered according their willingness to pay. Let Mth be the number of repetitions for which the occupancy of a parking unit is above Oth. The initial price Fu for all parking places on a parking unit u is set equal to the average willingness to pay calculated over (1 – Oth)*2 drivers with the lowest willingness to pay for parking, on unit u. 2.5.2.
Stage 2, iterative convergence to equilibrium price pattern
Starting from initial pattern of parking prices, the prices Fu of parking units vary, in iterations, until the average occupation rate at each parking unit decreases below the Oth. At this stage we have to manage scenarios where the demand/supply ratio is globally greater than 1. For this purpose, we introduce a probability gc for a driver c to skip parking entirely if there is no sufficiently
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attractive parking place at a distance below the maximal walk distance. We assume that the value of gc is positive for the places which attractiveness is below the threshold value of Ath: gc(A) =
0
if A > Ath,
1 – exp(γ*(1 - Ath/A))
if A ≤ Ath
(3)
In our computational experiments we employ Ath = 0.1 and γ = 0.1. The algorithm applied at the second stage differs from that applied at stage 1 in two respects: - The attractiveness of each parking place for a given driver is estimated according to the formula (2) that accounts for the price of a parking place. - A driver may decide to skip parking entirely, according to (3). The assignment of parking places to drivers is performed in respect to parking places’ attractiveness. It is repeated M times, and the average occupancy of each parking unit is stored. In case the occupancy is below Oth, parking price Fu on a unit does not change, Fu’ = Fu; otherwise, it is increased by x percent, Fu’ = Fu(1 + x/100), where Fu denotes a parking price on a unit u at a current, and Fu’ at a next iteration. The study of the NPAP shows that the higher is x the faster is the convergence of the pattern to the equilibrium one. However, for x that is too high, cyclic fluctuations of unit prices become possible. In our simulations below we apply the value of x = 5% that does not cause fluctuations. The number of model iterations necessary for convergence to the equilibrium pattern was less than 60, in all experiments. 2.5.3. Modified NPA as a benchmark for NPAP Slightly modified NPA can be exploited to identify the areas over which parking prices should be adjusted. The idea is simple - instead of distributing drivers over the parking units until all parking places on the unit are occupied, exclude the unit from parking when the threshold occupation rate Oth is reached. The units which occupancy reaches Oth are the candidates to become overly occupied in PARKFIT2. Their prices should be increased, then. Just as for the general NPAP, random arrivals of drivers can result in variation in different runs of the algorithm. In what follows, to recognize the units on which the parking price should be raised we apply PARKFIT with the given threshold rate Oth 20 times and consider the unit as a candidate for price adjustment if its occupation rate reached Oth in one run at least. Note that in addition to providing the candidate units for price adjustment, application of the PARKFIT with Oth < 1 provides the estimate of the excessive number of drivers, by destinations, that lack parking places in the area.
3. Study of the algorithm 3.1. Abstract scenarios We investigate NPAP in three abstract scenarios that simulate parking in a neighborhood that consists of 60 streets, 400 buildings and 2400 parking spots (Figure 4). In all scenarios, the link occupancy limit Oth is set to 85%; the number of iterations M in which all drivers attempt to park is 20. For formulas (1), (2) and (3) respectively we consider α = 0.1, = 0.5 and γ = 0.1. Let us denote N as the total number of parking places in the neighborhood, D as the total demand for parking spaces and W, as the average willingness to pay of drivers.
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We consider night parking, where cars enter and park, and not turnover. Price is set per night for the entire duration, not per hour of the night. Qualitative description of scenarios: Scenarios C1 through C3 were implemented to investigate the influence of varying global and local demand and willingness to pay of drivers on model outcomes. Scenarios C1 and C2: D < N for all, except the 16 central destinations, for which D > N. In C1 Willingness to pay W of all urban drivers is normally distributed with the same average and 20% coefficient of variation, while in C2 the drivers who aim at the central destinations have higher economic status than the rest of the drivers and their willingness to pay W is thus higher. Scenario C3: W is distributed as in C1 but total demand D is higher than the total number of parking places N.
Figure 4: Links and destinations used in scenarios
Scenarios parameters C1: Total demand D = 1792, Overall occupation rate O = 1792/2400 75% of the capacity. For 16 central destinations D = 16, which is above the supply on adjacent streets, while for all other destinations D = 4, much below the surrounding supply. All drivers belong to a population with an average willingness to pay of W = 3.3 with 20% coefficient of variation for all W, i.e. STD = 0.66 (Figure 5). C2 D = 1792, Overall occupation rate O = 1792/2400 75% of the capacity. For 16 central destinations D = 16, above the supply on adjacent streets, for all other destinations D = 4, much lower. W = 5 for central destinations while for all others W = 3 with 20% coefficient of variation for all W (Figure 5).
a
b
c
Figure 5: Distribution of willingness to pay of drivers in C1 and C3 (a) and in C2 for drivers who belong to centermost destinations (b) and to all other destinations (c). 8
In scenarios C1 and C2, the street links where parking prices increase are almost identical to those in which occupancy reaches the threshold in the benchmark model (Figure 6). In C1, 4 excessive links have their prices increased while in C2 the number is reduced to 1. This stems from a greater homogeneity of income levels, and thus of price sensitivities, in C1. Compared to C2, when the price of parking in an overly-occupied unit is increased, it is more likely that an excessive number of drivers will choose to park in other units. This results in higher occupancies and increased prices.
a
b
c
Figure 6: Street links on which price was increased above the initial rate; (a) C1; (b) C2; and street link occupancy in the benchmark model (c). In both scenarios C1 and C2, model price pattern converges to a concentric hill (Figure 7). No drivers give up on parking in either case.
a
b
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c
d
Figure 7: Distribution of demand in scenarios C1 and C2 (a); Occupancy rate for the steady parking pattern established according to the (Levy & Benenson, 2015) algorithm in either C1 or C2 (b); Final parking prices on links in scenario C1 (c) and C2 (d). As can be seen in Figure 6, the competition for parking places in the overpopulated grid center results in higher prices there in both C1 and C2 scenarios. However, in C2 the prices in the center are higher than in C1, following higher willingness to pay of the center’s residents. This results in essentially lower dispersion of the drivers of the same willingness to pay in C2 (Figure 8): The average parking distance for the drivers in C1 is close to 24 m, while in C2 it is only 16 m.
a
b
Figure 8: Willingness to pay of parked drivers, averaged by link; (a) C1; (b) C2. 10
C3: As in C1, W = 3.3 for all destinations and demand is uniform in space, but different from C1, D = 24 for 16 central destination, and D = 6 for all others. This results in D = 2688, 288 above the maximum parking capacity of the area. For the 85% occupancy this results in 2688 – 2400 * 0.85 = 648 drivers that have to give up on parking in the area. In the Nearest Pocket stage, as D/N > 1 and parking prices do not influence drivers’ decisions. Drivers park irrespective to their willingness to pay. The occupancy reaches 100% and 288 drivers fail to park. During convergence to an equilibrium distribution of prices, 741 drivers, on average, give up on parking. This is more than the minimal number of 648 because the attractiveness of essential fraction of the parking places becomes too low (e.g. they are costly but yet too distant from the destination). When the parking pattern stabilizes, links nearer to the center are occupied by drivers with higher willingness to pay (Figure 9).
a
b
c d Figure 9: Scenario C3 - Distribution of demand (a); final link prices (b); average, by link, income of parked drivers after NPA (c); average by link willingness to pay of parked drivers after NPAP.
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3.2. Sensitivity analysis Sensitivity analysis is conducted for the same grid used in section 3.1. (Figure 4). First, D/N ratio is examined for different income levels W of drivers. We start with demand = 0 for 16 centermost destinations, 3 for all others and add 3 demand to 16 centermost destinations up to a maximum of 129, for total D of 1152, 1200… 3216 or D/N ratios of 0.48, 0.5… 1.34. Each D/N ratio is examined with the average W = 2, 3 and 4 for 16 centermost destinations and average W = 3 for all other destinations, STD = 0.7 for all groups of drivers. Link occupancy threshold is set equal to a threshold value of 92%, above which driver’s cruising time starts to grow (Levy et al. 2013). We present the results using five measures: The number of links in a steady price pattern at which price has increased The number of drivers who give up on parking The prices of most and least expensive links in this pattern The ratio between most and least expensive links in this pattern The average income of drivers who give up on parking
-
For all examined average values of W, when D/N ≤ 0.5, the occupancy of all links remains below the threshold and parking prices do not increase at any of them. For the values of D/N between 0.52 and 0.86, some links become overly-occupied and their price increases. The phenomenon spreads outwards from the center of the grid with the growth of D/N between scenarios, but the grid center always remains most expensive. For D/N ≥ 0.86, the steady price of all links is higher than the minimal price (Figure 10a). Starting at the value of D/N = 0.86, which is close to the link occupancy threshold of 0.92, the number of drivers who give up on parking becomes non-zero (Figure 10b). With the further growth of D/N, the number of drivers who give up increases in parallel to an increase in number of additional drivers added to the system. The prices of all links increase with the increase in D/N (Figure 10c) and the fraction of the centermost drivers among those who give up on parking grows too (Figure 10d). However, the ratio of highest to lowest link prices always remains close to ~0.6 (Figure 10e). Fraction of Links of which Price was Increased
Number of Drivers who Give Up on Parking 1600.0
100.00
1400.0
Number of Drivers
Fraction (%)
80.00 60.00 40.00 20.00
1200.0 1000.0 800.0 600.0 400.0 200.0
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0.85
0.95
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1.15
1.25
1.35
0.45
0.55
0.65
0.75
Demand / Supply Ratio W=4
W=3
0.85
0.95
1.05
Demand / Supply Ratio
W=2
W=4
a
W=3
b
12
W=2
1.15
1.25
1.35
Fraction of Centermost Drivers Among those who Give up and Fraction of Centermost Drivers in the Population
Highest and Lowest Link Prices 20.0
105
18.0
100
% among Give up
16.0
Link Price
14.0 12.0 10.0 8.0 6.0
95 90 85 80
75 70
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W=4
W=3
53
55
57
59
61
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65
% in the Population
Demand / Supply Ratio
W=2
W=2
c
W=3
W=4
d Ratio of Highest to Lowest Link Prices 16.0 14.0 12.0
Ratio
10.0 8.0 6.0 4.0
2.0 0.0
0.45
0.55
0.65
0.75
0.85
0.95
1.05
1.15
1.25
1.35
Demand / Supply Ratio W=4
W=3
W=2
e Figure 10: Parking pattern characteristics as depending on D/N and W. Number of links for which price has increased (a); Number of drivers who give up on parking (b) highest and lowest link prices; (c) Willingness to pay for drivers who give up on parking (d); Ratio of highest to lowest link prices (e). To investigate sensitivity to α and β in formulas (1) and (2), we consider the scenario in which the overall D/N ratio is 0.9, 16 centermost destinations have D = 66 and all the rest D = 3, and W = 3 for all drivers. We vary α between 0.05 to 0.15 and β between 0.4 and 0.6. The sums of parking prices in all links for each combination of α and β are examined. Moreover, we examine the resulting parking prices averaged by distance classes along the grid from the central block, starting from a distance of 1 for the four links that enclose it (Figure 11).
Figure 11: Distance classes from the central block.
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Generally, prices are higher when α is lower and β is higher (Figure 12). Indeed, lower α means less sensitivity to higher parking prices, while higher β means less inclination to park further away from destination.
α β
0.05
0.10
0.15
0.4
199
178
152
0.5
222
193
178
0.6
246
216
191
a
b Figure 12: Steady parking prices as dependent on α and β, for α between 0.05 ÷ 0.15, β between 0.4 ÷ 0.6. (a) Sums of parking payments over the entire area; (b) prices average by distance class.
4. Establishing heterogeneous parking prices in the city of Bat Yam As our case study, we applied NPAP for establishing the night parking prices for residents, in the city of Bat Yam, Israel. In case of the overnight residential parking, destinations can be associated with residential buildings and the number of cars that aim at each destination can be estimated based on the car ownership in city’s statistical blocks. We based the estimates of demand and supply on the Bat Yam GIS for the year 2010, supplied to us by the city’s municipality. The population of Bat Yam in 2010 was 130,000, total car ownership 35,000, total number of buildings 3300 and total number of apartments 51,000. That is, the average car ownership in the city was 35,000/51,000 ≈ 0.69 car/apartment. Based on a GIS street layer, 27,000 curb parking places were constructed and the results agreed with the field survey conducted in 2010 (Levy et al, 2013). Several parking lots in Bat Yam are free for the residents and the total number of parking places on parking lots and under the residential buildings (that is, dedicated to the building’s residents) is 19,000. The average overnight demand-to-supply ratio is thus 35,000/(27,000 + 19, 000) ≈ 0.76 cars/parking place. 14
The demand for parking created by the residents of each building is estimated based on the car ownership rate as provided by the Israeli population census for 2008 for 40 Bat Yam statistical blocks. The drivers that may park on the dedicated parking places under the building were excluded. Link occupancy threshold is set to 92%, above which drivers’ cruising time starts to grow (Levy et al, 2013). Based on the information of residents’ economic status supplied per traffic analysis zone (TAZ, Figure 13), minimal parking price is set 1 NIS per night and assigned, as willingness to pay, to the residents of the poorest statistical block. For the residents of the other blocks average willingness to pay is set proportionally to the ratio of their economic status to the economic status of the residents of the poorest block, with a 20% coefficient of variation within the block. Research regarding the specific factors influencing Figure 13: Bat Yam income by TAZ mode and parking choice among the residents of Bat Yam, and their relative importance, is not conducted. This is because the purpose of the current chapter is not to formulate a parking pricing policy, but rather to explore a realistic scenario in terms of scale, heterogeneity of supply, demand and income levels of drivers, and complexity of the street network. Therefore, formulas (1), (2) and (3) are set up as in section 3.1. 4.1. Establishing parking prices for street links The model was implemented for establishing parking prices on street links. There is almost no difference in the street links where parking prices are increased above the initial rate and those in which occupancy reaches the threshold in the benchmark model (Figure 14). Although the global demand/supply in Bat Yam is far below 1, the distribution of demand, as estimated with the Nearest Pocket algorithm, is highly heterogeneous and potential overnight parking occupancy is above 0.92 in over 2/3 of the city area (Figure 15a). That is why the prices of the equilibrium pattern obtained with the PARKFIT2 algorithm reach the level of 10 – 20 NIS in the central part of the city (Figure 15b). As can be seen, high heterogeneity of demand results in high heterogeneity of parking prices.
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a
b
Figure 14: Links on which the prices increased above the initial rate (a); benchmark occupancy (b)
a
b
Figure 15: Bat Yam parking patterns. (a) Parking demand by street segments; (b) Equilibrium parking prices, in NIS, for 92% occupation threshold estimated for the street links as parking units. 16
4.2. Establishing parking prices by TAZ To establish parking prices per TAZ in Bat Yam, the price of all parking places in a TAZ is increased by the same value when the fraction of occupied parking places in the TAZ is above the threshold. Three TAZ become occupied to the threshold in the benchmark model but their prices remain unchanged in PARKFIT2’s equilibrium price pattern (Figure 16). This is because in stage 2 of PARKFIT2, the available parking places in these TAZ are highly unattractive for some of the drivers, and they prefer to avoid them and give up on parking entirely. As a result, they don’t become overly-occupied.
a
b
Figure 16: (a) TAZ on which price was increased above the initial rate; (b) TAZ occupancy in the benchmark model. Figure 17 presents TAZ model outcome compared to prices established by links and then aggregated by TAZ. Results are qualitatively similar in both cases, with prices generally lower, especially in peripheral TAZ, for the TAZ-based modeling. The D/N value in the peripheral Bat Yam TAZ is usually low and parking places on some of the links there are rarely occupied. In the TAZ-based version of the model, the average price over TAZ is established accounting for these under-used links. That is why the steady prices in the TAZ-version of the model are lower than those obtained in the link-based version.
17
a
b
Figure 17: Parking prices of TAZ in Bat Yam. (a) Direct calculations at TAZ resolution; (b) Model output by links aggregated to TAZ. 4.3. Incorporating parking lots into the model Out of 15 public or free private lots in Bat Yam, only 4 are situated in the high D/N ratio areas. Thus, their influence on the parking pattern is minor. To investigate the possible influence of parking lots we have located 10 lots with 250 parking spots each in key locations of high D/N. A constant parking price of 1 NIS is set for the parking lots. Parking fees are established for street links and TAZ and a comparison to the price patterns achieved in sections 4.1. (Figure 18a) and 4.2. (Figure 18b) is drawn. Introducing parking lots, thus effectively increasing parking supply, leads to an interesting phenomenon in the case of pricing parking on street links. In the immediate vicinity of the lots, on-street prices are lower than in the pattern achieved without parking lots, but further away they become higher. The reason is that drivers whose destinations are in the vicinity of the lots use them when no better option is available, instead of giving up on parking. However when spots closer to destination are vacant, they prefer them, and push drivers for whom the lots are too distant to park in more remote places. The pressure on these places is increased and their parking prices are adjusted.
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a
b
Figure 18: Comparison of price patterns established with and without parking lots. (a) Results achieved with parking lots for street links are compared to results from section 4.1. (b) Results achieved with parking lots for TAZ are compared to results from section 4.2. 5. Occupancy thresholds and parking units According to Shoup (2006), cities should aim at 85% occupation level, at which cruising behavior is minimized. Levy et al. (2013) show that this level can be raised to 92-93%. However in San Francisco’s SFpark experiment, the upper bound of the target average occupancy range was set to 80%. The gap is not arbitrary. As Shoup (2013) explains, if the bar is set too high, it is impossible to avoid reaching full parking capacity often, due to the stochastic variation in parking demand. The issue of stochastic variation in parking demand can be treated in PARKFIT2 by simulating the maximum expected demand, as is done in the Bat-Yam case study. But variation in occupancy also stems from the stochastic arrival order of drivers who wish to park. Occupancy of smaller parking units is more influenced by this variation than larger ones, and they are more likely to become fully occupied. Due to this, maximum occupancy of units does not necessarily imply increased cruising time, and should not be considered when determining the occupancy threshold in PAKRFIT2 More importantly, where variation of a single occupancy is higher, the average is more influenced by the number of iterations M. Thus small units and insufficient number of iterations may lead to price fluctuations that result in higher prices and to equilibrium price patterns that differ greatly from each 19
other. For this reason, parking units shouldn’t be too small. In any case PARKFIT2 should be run with an increasing number of iterations, until the parking prices converge to similar equilibrium patterns. The number of iterations may be limited due to considerations of computational performance, in which case, it is possible to increase the unit size. However note that maximum prices are higher for smaller units, as they account for the spatial distribution of demand with higher resolution. This issue is pointed out in the comparison of price patterns established for street links and TAZ in Bat Yam (section 4). 6. Conclusions The spatially explicit, high-resolution PARKFIT2 algorithm for establishing heterogeneous pattern of urban parking prices is proposed and implemented. The algorithm accounts for spatial distribution of parking demand and supply and for population distribution of willingness to pay for parking. It implements the advantages of demand-based pricing, but does not require street equipment for price adjustments. PARKFIT2 is applied for establishing heterogeneous parking prices in the Israeli city of Bat Yam. A discussion on the implications of parking unit size and occupancy threshold on model outcomes is presented. Our model study raises several issues that are relevant for the urban parking policy: What parking units should be chosen for establishing parking prices – does the block level approach used in Los Angeles and San Francisco achieve lower cruising time than the zonal pricing implemented in Calgary and Seattle? How should we preserve parking space to the weaker population groups? How can the current parking prices be substituted by the heterogeneous ones? We investigate these questions based on the outcomes of the corresponding model scenarios. 7. References Anderson, S.P., de Palma, A. (2004). The economics of pricing parking. Journal of Urban Economics, 55, 1-20. Anderson, S.P., de Palma, A. (2007). Parking in the city. Papers in Regional Science, 86, 621–632. Arnott, R. (2006). Spatial competition between parking garages and downtown parking policy. Transportation Policy 13, 458–469. Arnott, R., de Palma, A., Lindsey, C.R. (1991). A temporal and spatial equilibrium Analysis of commuter parking. Journal of Public Economics, 45, 301–335. Arnott, R., & Inci, E. (2006). An integrated model of downtown parking and traffic congestion. Journal of Urban Economics, 60(3), 418–442. Axhausen, K. W., & Polak, J. W. (1991). Choice of parking: stated preference approach. Transportation, 18(1), 59-81. Bhat, C. R., & Castelar, S. (2002). A unified mixed logit framework for modeling revealed and stated preferences: formulation and application to congestion pricing analysis in the San Francisco Bay area. Transportation Research Part B: Methodological, 36(7), 593-616. Bradley, M., Kroes, E., & Hinloopen, E. (1993). A joint model of mode/parking type choice with supplyconstrained application. In PTRC Summer Annual Meeting, 21st, 1993, University of Manchester, United Kingdom. CPA (Calgary Parking Authority). (2016). On-Street Parking Rates. Retrieved from https://www.calgaryparking.com/findparking/onstreetrates Calthrop, E., & Proost, S. (2006). Regulating on-street parking. Regional Science and Urban Economics, 36, 29–48. 20
Feeney, B. P. (1989). A review of the impact of parking policy measures on travel demand. Transportation Planning and Technology, 13(4), 229-244. Fosgerau, M., de Palma, A. (2013). The dynamics of urban traffic congestion and the price of parking. Journal of Public Economics, 105, 106–115. Hensher, D. A., & King, J. (2001). Parking demand and responsiveness to supply, pricing and location in the Sydney central business district. Transportation Research Part A: Policy and Practice, 35(3), 177196. Hess, D. (2001). Effect of free parking on commuter mode choice: Evidence from travel diary data. Transportation Research Record: Journal of the Transportation Research Board, (1753), 35-42. Hess, S., & Polak, J. W. (2004). Mixed Logit estimation of parking type choice. In 83rd Annual Meeting of the Transportation Research Board, Washington, DC (pp. 561-582). Hunt, J. D., & Teply, S. (1993). A nested logit model of parking location choice. Transportation Research Part B: Methodological, 27(4), 253-265. Ibeas, A., Dell’Olio, L., Bordagaray, M., & Ortúzar, J. D. D. (2014). Modelling parking choices considering user heterogeneity. Transportation Research Part A: Policy and Practice, 70, 41-49. Inci, E. (2015). A review of the economics of parking. Economics of Transportation, 4, 50-63. Inci, E., Lindsey, C.R. (2014). Garage and Curbside Parking Competition with Search Congestion. Regional Science and Urban Economics, 14, 49-59. LADOT (Los Angeles Department of Transportation). (2016). About LA Express Park. Retrieved from http://www.laexpresspark.org/ Levy, N., & Benenson, I. (2015). GIS-based method for assessing city parking patterns. Journal of Transport Geography, 46, 220-231. Levy, N., Martens, K., & Benenson, I. (2013). Exploring cruising using agent-based and analytical models of parking. Transportmetrica A: Transport Science, 46, 220-231. Pierce, G., & Shoup, D. (2013). Getting the prices right. Journal of the American Planning Association, 79(1), 67-81. SDOT (Seattle Department of Transportation). (2016). Parking in Seattle. Retrieved from http://www.seattle.gov/transportation/parking/ Simićević, J., Vukanović, S., & Milosavljević, N. (2013). The effect of parking charges and time limit to car usage and parking behaviour. Transport Policy, 30, 125-131. SFMTA (San Francisco Municipal Transportation Authority). (2016). SFpark: The Basics. Retrieved from http://sfpark.org/about-the-project/faq/the-basics/ Shoup, D. (2006). Cruising for parking. Transportation Policy, 13, 479–486. Shoup, D. (2011). The high cost of free parking. Chicago, IL: Planners Press. Shoup, D. (2013). Getting the prices right. Journal of the American Planning Association, 79:1, 67-81. Teknomo, K., & Hokao, K. (1997). PARKING BEHAVIOR IN CENTRAL BUSINESS DISTRICT A STUDY CASE OF SURABAYA, INDONESIA. Easts J. 2(2), 551-570. Verhoef, E., Nijkamp,P ., Rietveld,P. (1995). The economics of regulatory parking policies: The (im)possibilities of parking policies in traffic regulation. Transportation Research Part A, 29, 141–156. Zhang, R., & Zhu, L. (2016). Curbside parking pricing in a city centre using a threshold. Transport Policy, 52, 16-27.
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8. Appendix: Full Nearest Pocket for Prices algorithm Notation Let us denote ‒ Parking places as pi, i = 1, 2, … I; parking units (link/set of connected links/set of links within a certain area/parking lot) as uj, j = 1, 2, … J, the occupation threshold of a parking unit u j as xj (say, x = 0.85) and the price of parking on parking unit uj as Qj. Let Qmin > 0 be the minimal values of Qj and is common for all j ‒ Destinations as dk, k = 1, 2, …, K and destination’s k demand for parking as Dk. ‒ The economic status of a driver as S. Let the distribution of the status S of drivers whose destination is d k be normal with average mk and STD = sk. ‒ The distance between a parking place pi and destination dk, measured in numbers of parking places that the driver passes when walks from pi to dk (don’t like this definition now, regular walk distance looks me better). Let rk,max be maximal distance acceptable to drivers between the parking place and the destination d k (dk may be estimated in field studies). ‒ The number of parking spots on a parking unit u j as Hj, its occupancy rate averaged over M iterations Yj. Let the number of iterations in which uj is fully occupied be Uj ≤ M.
Initial settings 1.
Based on demand Dk at every destination dk, construct a table of drivers DRIVERSTABLE, in which each row represents a driver and each destination dk is represented Dk times. The length of DRIVERSTABLE is equal to
ΣkDk 2. 3. 4.
5. 6.
Assign economic status to every driver in DRIVERSTABLE according to the distribution of economic status of drivers for destination dk (characterized by mk and sk). Build a table L of all parking spots pi on all parking units uj. Use L to store if pi is free or occupied and, if p i is occupied, to store economic status S of a driver who parked on p i. For each destination dk, construct a list Pk of parking places at a distance less than rk,max from dk. Sort Pk by destinations and then by the distance between d k and pi. Use Vk to store, for each dk, the number of free parking places pi at a distance less than rk,max from it. Set Vk = number of parking places pi in a distance less than rk,max from it. Use Fk to store the number of drivers, for each destination d k, who aim at dk but fail to park at a distance less than rk,max from it. Set Fk = 0 For each parking unit uj, let Sj stores average economic status of drivers who parked on u j.
Stage 1: Setting initial distribution of prices 1. 2. 3. 4. 5.
6.
For all parking unit uj set Qj = Qmin In table L, mark all pi as unoccupied. Set Uj = 0 for all j Randomly reorder DRIVERSTABLE Repeat by drivers in DRIVERSTABLE until the last driver in DRIVERSTABLE is reached: For driver a from DRIVERSTABLE retrieve a’s destination d(a), economic status S(a), a list of parking places Pd(a), a number Vd(a) of free parking spots in Pd(a) and a number of drivers who aimed at d(a) but failed to find a parking place Fd(a) If Vd(a) > 0 Then Iterate by Pd(a) until a parking place p marked unoccupied in a table L is reached In table L, mark p as occupied by a and store a’s economic status S (a) Set Vd(a) = Vd(a) – 1 Else Set Fd(a) = Fd(a) + 1 For each fully occupied parking unit uj Uj = Uj + 1 and calculate the average value xxj of the economic status of Int[(1 – xj)*2] least wealthy drivers that parked on uj If Uj = 1 Then Oj = xxj Else Oj = Oj + xxj
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7. 8.
Repeat stages 3 - 7 M times, (M - parameter). If (Hj > 3) & (U > 0) Then Qj = Qj/U Else don't change Qj
Stage 2: Adjusting parking prices Additional notation ‒
‒ ‒ ‒ ‒ ‒
Let the attractiveness Ai of a parking place pi located on a parking unit uj, for a driver a of economic status S(a) be A(pi, S(a)): Ai = A(pi, S(a)) = min(1, W/Qj)/di,a = min(1, S(a)/(Qj*di,a))/di,a where di,a is the distance between the parking spot pi and a’s destination d(a) The W = S(a)/di,a can be considered as a willingness to pay (maximal acceptable hourly fees) of drivers. We use < 1 to reflect slow decrease in W with an increase in a walk distance; (0.25, 0.5) serves to control a decay of attractiveness with the increase in a walk distance. Let R be a threshold of attractiveness: for A < R a driver may decide to give up on parking. Let the probability of a driver a to give up on parking at p i because of the low attractiveness of pi be gi,a = 1 – MAX(Ai ≥ R, exp(-γ/Ai)). For each driver a, let n(a) be the number of times it gave up on parking. Let z(a) (z(a) = 0 initially) indicates whether the driver has finally gave on and sold the car (z(a) = 1). Let mk denotes, for the destination dk, the number of drivers who aim at dk but give up on parking due to low attractiveness of the parking spots that was free when they arrived to d k.
Initial setting For each dk, set Fk = 0, mk = 0 and Vk = number of pi in a distance less than rk,max from the dk.
Algorithm steps 1. 2. 3.
4. 5. 6. 7.
In table L, mark all pi as unoccupied. Randomly reorder DRIVERSTABLE. Repeat until the last driver in DRIVERSTABLE is reached: Consider driver a from DRIVERSTABLE with its z(a), d(a), Vd(a), and S(a) If z(a) = 0 Then If Vd(a) > 0 Then Iterate through list Pd(a) and find unoccupied parking place pbest in Pd(a) for which the attractiveness Ai is the highest. Calculate gi,a If RAND(0,1) < gi,a Then md(a) = md(a) + 1 n(a) = n(a) + 1 Else In table L, mark pbest as occupied Set Vd(a) = Vd(a) – 1 Else Fd(a) = Fd(a) + 1 Else md(a) = md(a) + 1 Repeat stages 2 - 3 M (parameter) times. If for driver a n(a)/M > 0.33 Then z(a) = 1 Calculate the fraction FF100 of parking units with 100% occupation and the fraction of FF intermediate of parking units with occupation rate above xj but below 100% If FF100 < 0 and FF < FFthreshold (typically, FFthreshold = 0.01) Then Stop Else Increase prices for uj for which the occupation is above the xj by setting Qj = Qj*1.05 Repeat steps 2 – 6
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