To quit or to cruise? Modeling parking search decisions based on serious games Nir Fulman1 and Itzhak Benenson1 and Eran Ben-Elia2 Abstract.1Knowing when a driver will quit cruising and either The goal of this paper is to experimentally establish models of leave the area or park at an expensive off-street facility is critical individual parking search behavior in a highly occupied area, under for modeling parking search. We employ a serious game – the dilemma of the very uncertain and cheap on-street versus PARKGAME for estimating the dynamics of drivers’ decision certain and expensive off-street parking. The models can be used to making. 49 Participants of a game experiment were involved in characterize agent-drivers in a spatially-explicit, empirically-based three scenarios where they had to arrive on time to a fictional appointment or face monetary penalties, and to choose between parking ABM, and thus improve our ability to study the collective uncertain but cheap on-street parking or a certain but costly consequences of parking policy. To this end, we study and analyze parking lot. Scenarios diverged on the time to appointment and parking behavior based on gamified lab experiments with the distance between the meeting place and parking lot locations. PARKGAME Serious Game. Players played a series of 8 or 16 computer games on a Manhattan grid road network with high on-street parking occupancy and nearby parking lot of unlimited capacity. Players’ choices to quit or 2 METHODOLOGY to continue search, as dependent on the search time, were analyzed with an accelerated-failure time (AFT) model. Results show that drivers are mostly risk-averse and quit on-street parking search 2.1 PARKGAME serious game platform very soon after potential loses begin to accumulate. The Our experiments are performed with PARKGAME – a flexible implications of game-based methods for simulation model development and sustainable parking policy are further discussed. serious game platform for studying parking search behavior and decision-making. The urban road and parking infrastructure in PARKGAME are represented by GIS layers of street links and 1 INTRODUCTION parking lots in a standard shapefile format. On-street parking spots are constructed automatically by the game software at 4m distance Future automated vehicles will definitely simplify urban from each other along the street links in line with the direction of transportation and parking [1]. Until that happens, long search for traffic. Figure 1 presents the user interface of PARKGAME: On- parking is an inherent component of a car trip to the center of the street parking spots are presented to the player as green (vacant) or city, with negative externalities including traffic congestion, and red (occupied) dots and a parking lot is represented by a larger air and noise pollution [2]. Cruising typically involves time-to- circle, and the destination is marked by a red flag. A green arrow money tradeoffs between certain but expensive parking at a paid that appears above the car, represented by a blue rectangle, and possibly distant off-street facility and uncertain yet usually functions as a virtual compass and points the driver in the direction cheaper on-street parking. Understanding driver behavior in of the destination. response to on-street and off-street parking conditions and prices is The player navigates – advances, accelerates, decelerates and a basic step on the way to sustainable parking policy. takes turns using the keyboard arrow keys. The field of view is Urban parking space is highly heterogeneous and adequate only 5 parking spaces ahead at any moment; spots further ahead representation of drivers’ parking search demands a high-resolution remain colorless until the driver approaches them. Although other and spatially-explicit representation of cruising drivers and parking cars competing with the player for free spots are currently not options. This can be achieved with Agent-Based models (ABM) included in the interface, the effect of other cruising drivers is [3]. Knowledge on individual driver parking behavior has the indirectly represented in the game by a random turnover process potential of turning ABM into a highly effective policy support whereby on-street parking spots are randomly occupied and tool. Significant efforts have been made to understand drivers’ vacated at a preset rate. reaction to parking prices [6], yet we still lack a formal description The player can only park at a vacant spot with a maximum of drivers’ reaction to prominent factors such as the occupation speed of 12 km/h, similar to real-life conditions [5]. A slider on the rate, time stress and distance between parking place and top right corner of the screen changes from green to red when the destination. speed is too high for safe parking. The player parks the car by pushing the SPACE button and this ends the game. The software 1 Department of Geography and Human Environment, School of then calculates the walking distance from the selected spot to the Geoscience, Tel Aviv University, Israel, e-mail: nirfulma@post.tau.ac.il, destination. Based on the preset walking speed, it then computes bennya@post.tau.ac.il the walking time and adds it to the total time of the game. 2 Department of Geography and Environmental Development, Ben-Gurion University of the Negev, Israel, e-mail: benelia@bgu.ac.il Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0). In the game, players are expected to attend a fictional meeting performed on a Manhattan-like city grid of 10X8 blocks. Each link in Ta minutes from the start of the game. They start the game with is considered as two-way traffic, 90m long with 20 parking spots a fixed budget B, out of which the on-street Con or lot Coff parking on each side. The on-street occupancy rate r was set very high, to r costs are deducted, based on the eventual parking choice. Lot = 99.75%, enforcing long cruising for on-street parking. Every 15 parking is always available but, to roughly reflect local conditions, seconds, several spots were assumed to be occupied by “other” at double the price of parking on-street, Coff ~ 2*Con. Players cruise drivers an identical number of randomly selected occupied spots for parking, park the car and walk to the destination at a constant were vacated. Lot parking was always available. speed of 3.6 km/h = 1m/sec. The total game time is calculated as The starting point in all games is 315 meters from destination, the sum of the search time and walk to the destination. If players equivalent to ca 1-minute drive at the maximum allowed speed of reach the destination later than Ta minutes from the start of the 30km/h (figure 2). This starting point is far enough from the game, they are fined based on a per-minute lateness rate Lminute. destination to distinguish between the start of a game and start of Thus as in reality, the goal of the player is to find parking quickly the parking search, and close enough to avoid unnecessary and close to the destination. The maximum allowed cruising time is navigation. The parking prices and lateness fee used in the Tm > Ta and the player that still cruises at Tm is considered to have experiments are presented in table 1. decided to park at a lot at a moment Tm, in which case we overlook The parking lot was always located down the road beyond the the time of driving to the lot. The on-street and lot parking costs destination from the perspective of the player’s starting position Con and Coff, as well as the remaining time until the meeting, the and direction. The maximum allowed search time Tm was 9 walking time from the current position of the car to the destination minutes in all scenarios. and the per-minute late fine Lminute, are presented to the player on Cruising behavior of drivers was tested in three scenarios the screen (figure 1). The game administrator’s UI enables (figure 2, table 2). In scenario A, the lot was located 45m from the modifying key game parameters. The output of the game includes a destination, and the time until the expected meeting was 3:00 min. detailed log of all the decisions taken by the player during the At a walking speed of 1m/sec, the walk between the parking lot game. and destination took 0:45 min. Scenarios B and C were devised for studying the influences of the parking lot’s location on cruising behavior. The distance between the destination and the lot in these 2.2 Experiment design, participants and procedure scenarios is 135m and thus Woff = 2:15 min. Players had less time In pilot experiments, it became clear that in realistic irregular to search for on-street parking in scenario B than in scenario A, street layouts, cruising is strongly affected by the network topology while in scenario C, the additional walk is seemingly neutralized and one-way traffic, resulting in confounding effects with by increasing Ta from 3:00 to 4:30 minutes. topology-enforced wayfinding. For this reason the experiment was Figure 1. Game screenshot (translated from Hebrew): The player is about to reach the destination (red flag) in a Tel Aviv street, and observes a vacancy five parking places ahead (small green circle). Details important for decision-making are presented on the screen. Table 1. Cost-related parameters used in the game experiments Parameters Derived parameters Initial Lot parking On-street Penalty for one On-street parking Off-street parking, budget price Coff parking price minute delay maximum gain Maximum gain B Con Lminute Gon,max = B - Con Goff,max = B - Coff Value (ILS) 20 15 7.5 1.5 20 - 7.5 = 12.5 20 - 12.5 = 7.5 Table 2. Description of PARGKAME scenarios and their parameter values Scenario Time of the Distance from parking lot to Safe (until fined) Walk from the lot to Number of meeting Ta destination Doff (m) cruising duration Ts destination woff (min) participants A 3:00 45 2:15 0:45 49 B 3:00 135 0:45 2:15 10 C 4:30 135 2:15 2:15 10 a b c Figure 2. View of the game area (a) and zoom to the destination (red flag) and lot (grey circle) in Scenarios A (b) and B/C (c) 49 participants (30 men and 19 women) holding a valid driving Following this they participated in a training session of 4 license between the ages of 19 to 67 (Avg. = 32, STD = 11) were consecutive games playing scenario A. The objectives of this recruited through an online ad to participate in the experiment. The session were to practice the use of the keyboard, and to get used to participants arrived at the lab after registering online and were the on-street parking availability observed in the game. Players randomly divided into game sessions of up to 4 players per session, participating in pilot sessions were debriefed and shown videos of Figure based 2. Game on their screenshot availability that (translated from Hebrew): day. The sessions Theinplayer took place the is about their to reach the destination movements in order (red flag) inthat to ensure a Telkey Avivdecisions street, andwere observes computer labaand vacancy were five parking run from places August ahead 2017 (small to May green circle). Details 2018. important correctly for decision-making represented in the game. are presented on the screen. After arriving to the computer lab, participants were provided a Following the training session, the experimental session show up fee of ILS30 and signed a mandatory consent form. They commenced. At the end of an experimental session, cumulative sat individually, each in front of the computer with 21 inch screens. rewards were tallied up and granted to players. All 49 participants played scenario A. In addition, 10 randomly chosen players also played scenario B and another 10 participants played scenario C. Five players of each of the latter groups started out with scenario A and continued with B or C and five played in 3 RESULTS – TEMPORAL DECISION an opposite order - B or C and then A. MAKING After a 10-minute oral briefing of the game mechanism and Cruising drivers make two types of decisions at junctions. The first scenarios details, players filled in a pre-test questionnaire regarding decision is whether to continue the search for the uncertain yet their parking habits as well as basic socio-demographic data. cheaper on-street parking or head to the certain but more expensive lot. The second decision is where to drive, that is whether to parking off-street and paying no fine or a minor fine. The hazard approach, remain at the same distance or recede from the rates then decrease reflecting players who take the risk of being destination and/or parking lot. In this paper we focus on the former late and continuing cruising despite the fine time. choice, and leave the latter for later examination. To assess the influence of scenario parameters on players’ Overall, players parked at the lot in 59% (231 out of 392) of the choice to quit on-street parking search we employ parametric games in scenario (A), 69% (55 of 80) in scenario (B) and 51% (41 hazard models. Namely, we fit an accelerated-failure time (AFT) of 80) in scenario (C). Every player parked at the lot at least once model, the analytical form of which is ℎ(𝑡|𝒁) = ℎ0 (𝑡)𝑒 𝜷𝒁 , where during the series of 8 games of a certain scenario. The minimal 𝒁 is a vector of covariates, ℎ0 (𝑡) is the baseline hazard that is, the number of times a player parked at the lot in a scenario is 2 and the hazard function assuming all components of 𝒁 are zero, and 𝛽 is a maximal is 8. On average, players park at the lot in 4.7 of 8 games vector of coefficients to be estimated. in scenario A, 5.5 of 8 games in scenario B and 4.1 of 8 games in We compare four parameterizations of the basic hazard function scenario C, with STDs of 1.2, 1.6 and 1.2 respectively. The ℎ0 (𝑡): Lognormal, Log-logistic, Weibull and Exponential and differences between the distributions of the number of lot choices consider the time until meeting and distance between parking lot in the three scenarios are insignificant (χ2 = 3.32, p > 0.1) and destination as covariates. Akaike’s Information Criterion according to a Kruscal-Wallis test. (AIC) is applied to compare goodness of fit for different To study the dependence of the player’s decision to quit parameterizations [7]. cruising and park at the lot we applied actuarial survival analysis As can be seen in table 3, the log-logistic and the lognormal [6], where survival means continuing cruising for on-street models provide the best and similar approximation of the parking. Formally, the survival is relevant for games where players experimental data and both generate hazard functions that fit very parked at the lot before reaching the maximal game time T m, well to those presented in figure 3b. The Weibull model and the whereas games concluding with on-street parking and the two exponential model are the worst. games where players cruised for the entire game time Tm without The analytical form of the hazard function that is based on the succeeding to park are considered as “right-censored”. best approximating log-logistic hazard is as follows Figure 3a presents the Kaplan-Meier survival curves – i.e. the 1 1 [( )−1] probability S(t) to continue cruising, in scenarios A, B and C. The 𝜆𝛾 𝑡 𝛾 ℎ(𝑡) = 1 ( ) (1) horizontal axis represents the time t in seconds, and the vertical 𝛾[1+(𝜆𝑡) 𝛾 ] axis shows the fraction of drivers still cruising at time t. The log- rank test suggests the scenarios' survival curves differ substantially, resulting in survival function of the form (χ2 = 39.98, df = 2, p < 0.001). Figure 3b presents the 1 −1 corresponding kernel-smoothed instantaneous hazard function 𝑆(𝑡) = {1 + (𝜆𝑡)𝛾 } (2) ℎ(𝑡) = 𝑑/𝑑𝑡 log(𝑆(𝑡)) for the three scenarios that reflects the instantaneous rate to park off-street at t if a player failed to park on street before. where 𝜆 = 𝑒 𝜷𝒁 = 𝑒 ∑ 𝛽𝑖 𝑍𝑖 , 𝑍𝑖 are covariates, and 𝛽𝑖 and 𝛾 are As evident, the hazard rates h(t) are non-linear in all three estimated from the data. If 1/𝛾 > 1, the conditional hazard first scenarios: They grow from the start of the game and until shortly rises and then falls, and if 1/𝛾 < 1, it declines monotonously. after the time of the meeting, and many games end with the player Figure 3. Kaplan-Meier curves (a) and kernel-smoothed hazard rates (b) scenarios A, B and C Table 3. AIC value for four parametric survival models Parameterization Log likelihood AIC Lognormal -308.8 625.5 Log-logistic -307.9 623.8 Weibull -321.9 651.7 Exponential -472.7 951.3 Table 4. Log-logistic AFT regression model output Coef. Std. Err. Z p meet_time 0.0070 0.001 6.94 < 0.001 lot_dist -0.0036 0.0007 -4.60 < 0.001 constant 3.988 0.1668 23.91 < 0.001 ln 𝛾 -1.253 0.0443 -28.52 < 0.001 Log likelihood = -307.906 Figure 4. Kaplan-Meier curves (a) and kernel-smoothed hazard rates (b) scenarios A, B and C The parameters’ estimates for the log-logistic model are presented in table 4 and Wald statistic (z), indicates that the 4 IS CRUISING FOR PARKING RISKY? influence of both covariates is highly significant (p < 0.001). Experimental data make it possible to investigate an issue critically As can be seen, 1/𝛾 = 𝑒1.25282 3.5, indicating non- monotonous unimodal hazard function, as in Figure 3b. The important for parking modeling: Do drivers decide to quit the positive value of β for the meet_time indicates longer on-street search based on the instantaneous stress of being late or is there a search when the time between the start of the game and the general search strategy that they apply? To answer this question, meeting increases, while negative β for lot_dist covariate indicates we propose a theoretically optimal model of player behavior and shorter search in case the lot is farther away from the destination. compare it to the experimental results Given the Log-logistic hazard model, the empirical equation for Consider a series of games that start at a time moment 0, of λ is, thus duration Tm and assume that the player is cruising at the speed that 𝜆 = 𝑒 −(3.99823−0.0036×𝑙𝑜𝑡_𝑑𝑖𝑠𝑡+0.00701×𝑚𝑒𝑒𝑡_𝑡𝑖𝑚𝑒) (3) is close to the maximal possible (30 km/h) and decreases the speed and the overall survival function is to the parking limit of 12 km/h immediately upon noticing a vacant on-street spot. In this case, the time necessary to traverse a 90m 𝑆(𝑡) = {1 + (𝜆𝑡)3.5 }−1 (4) street link is close to 10 seconds and the appointment time Ta and while the hazard - conditional probability to decide to quit the maximum allowed game time Tm can be considered in 10-sec time on-street search and park at the lot, is given by steps. In the model below on-street parking at t is defined as “finding a vacant parking spot by the end of time step t” and 𝜆3.5 𝑡 2.5 ℎ(𝑡) = (5) parking at a lot at t is defined as “parking at the lot at the 0.28571×[1 + (𝜆𝑡)3.5 ] beginning of time step t”. Figure 4 shows the log-logistic fitted survival curves compared to the empirical Kaplan-Meier estimates. As evident the observed Parameters of the model are as follows: initial game budget B, the fit is very good. cost of parking on street Con and on the lot Coff and fine L10 per According to (3), a marginal one-second increase in the time additional 10-second delay, L10 = Lminute/6. For the average until meeting (meet_time) increases λ by 𝑒 0.0071 ~ 0.007 while a occupation rate r, the probability to find on-street parking while marginal one-meter increase in the distance between the lot and the traversing a random link with its 20 parking spots (that takes a time destination (lot_dist) that is an additional one second walk step of 10 seconds) can be estimated as decreases λ by only half i.e. 𝑒 −0.0036 ~ 0.0035. This makes sense as the distance between the lot and the destination is important in 𝑝 = 1 − 𝑟 20 (6) case of parking at the lot only, while the time until meeting always The accumulated late fine for arriving at the destination is denoted affects the game’s outcome. below as L(t), and counts down starting from the Ta. For the driver arriving at the destination at time-step t, it is 0 𝑖𝑓 𝑡 ≤ 𝑇𝑎 interval [0, t], t < Tm. The average gain K(t, Δt), Δt  1, t + Δt ≤ 𝐿(𝑡) = { 𝐿10 × (𝑡 − 𝑇𝑎 ) 𝑖𝑓 𝑡 > 𝑇𝑎 Tm, from the decision, at t, to cruise until t + Δt, and park at the lot (7) at t + Δt + 1, is equal to: 𝜏= ∆𝑡−1 We assume that a player that cruises until the end of the game (T m) 𝐾(𝑡, ∆𝑡) = (∑ 𝑝 × (1 − 𝑝)𝜏 × 𝐺𝑜𝑛 (𝜏 + 1)) + (1 − 𝑝)∆𝑡 and fails to park on-street, parks at the lot at the beginning of time 𝜏= 0 step Tm + 1, pays the lot cost, walks to the destination from the lot × 𝐺𝑜𝑓𝑓 (𝑡 + ∆𝑡 + 1) and pays the maximal late fine calculated as L(Tm + 1 + woff). (12) The probability of failing to find a vacant on-street parking spot Dependence of 𝐾(𝑡, ∆𝑡) on t and Δt for the scenario A is presented during the time interval [0, t] is: in figure 5, and is similar for scenarios B and C. (1 − 𝑝)𝑡 (8) In figure 5, each curve starts at a different t and represents The gain of a player who parked on-street, if cruised during the 𝐾(𝑡, ∆𝑡) - the gain of a player, searching unsuccessfully until t, if time interval [0, t] and parked by the end of a time step t is: they continue searching for additional time Δt. For each t, the entire curve 𝐾(𝑡 + 1, ∆𝑡) is below the curve 𝐾(𝑡, ∆𝑡) and 𝐺𝑜𝑛 (𝑡) = 𝐵 − 𝐶𝑜𝑛 − 𝐿(𝑡 + 𝑤𝑜𝑛 ) (9) eventually 𝐾(𝑡, 0) becomes negative. In addition, for the values of t for which 𝐾(𝑡, 0) is negative, the time Δt1 that is necessary to The gain of a player who parked at the lot, if cruising during a time return to a positive-reward state of 𝐾(𝑡, 𝑡1 ) > 0, increases. That interval [0, t] and then parked at the lot at the beginning of time is, the gain from “cruising a bit longer” for on-street parking step t + 1 is: decreases throughout the course of the game. “Myopic” and, thus, 𝐺𝑜𝑓𝑓 (𝑡) = 𝐵 − 𝐶𝑜𝑓𝑓 − 𝐿(𝑡 + 𝑤𝑜𝑓𝑓 ) (10) bounded-rational players, unlike their rational and “strategic” counterparts, may interpret this as the potential reward from a long For our experiment design, the walk time after parking off-street is and unsuccessful search that gradually diminishes regardless of woff = 45 sec = 4.5 time-steps in scenario A and woff = 135 sec = which course of action they choose. Eventually they become 13.5 time steps in scenarios B and C. The value of won evidently discouraged from very long cruising and head to the lot varies between drivers and in what follows employ the rough value prematurely. According to the results presented in section 3, this is what indeed happens in our game experiments. Namely, the of won = 2 min = 12 time steps in all three scenarios. players’ behavior is myopic and they cancel their search soon after the fine period starts (Figure 3). None of the players followed 4.1 Optimal strategy of a rational player optimal strategy and only in 2 out of 552 games players played until the very end of the game. A perfectly rational player is assumed to choose a strategy, depending on the game parameters, on the cruising duration of for finding on-street parking that results in a maximal possible gain M. 5 DISCUSSION Based on (8) – (10), the gain M(t) from unsuccessful cruising As we have demonstrated, PARKGAME players’ behavior can be during [0, t], and parking at the lot at t + 1 is: considered risk-averse. They do not follow the optimal strategy that is to search until the end of the game. Instead, when the fine 𝑀(𝑡) = (∑𝜏= 𝑡 𝜏= 1 𝑝 × (1 − 𝑝) 𝜏−1 × 𝐺𝑜𝑛 (𝜏)) + (1 − 𝑝)𝑡 × 𝐺𝑜𝑓𝑓 (𝑡 + 1) (11) for being late starts to grow the probability to quit on-street search In all three scenarios lot parking price exceeds on-street parking and park off-street grows as well. Shortly after that, the hazard price. This is the major reason why 𝑑𝑀(𝑡)/𝑑𝑡 is always positive, function peaks and then starts to decline (figure 3). That is, despite and thus M(t) monotonously increases in all three scenarios. This general risk aversion tendency, some players in certain games may behave in a risk seeking (and optimal) manner and, despite holds true even if we assume the highest observed won of 200 sec. accumulating losses, decide to search up to the very end of the The optimal strategy of a rational player in all scenarios is game. No player behaved in this optimal risk seeking way over therefore to cruise until the very end of the game. The optimal several games. Thus further experiments are needed to investigate strategy is especially rewarding considering each player the decline of the hazard function. It should be noted that this participated in a series of 8 or 16 games. For the exploited values decline may well be considered a game artifact: players were aware of parameters, the average gain (11) of an optimally behaving that the total loss is limited and, thus, additional loss from player will be between 9 – 10 ILS over 8 games, depending on the searching to the last minute or two of a game was not substantially scenario. high. However, recognition of this effect demands a different organization of the experiment. Players that did not follow the optimal strategy presented above The choice of when to quit cruising on-street and head to a may be considered as “myopic” that is, sensitive to the events parking lot is well approximated by the accelerated-failure time during the game and deciding anew, depending on the course of a model with the log-logistic hazard function. The parameter γ of the game, whether to continue cruising or quit and park at the lot. In log-logistic function is essentially larger than 1 reflecting the the latter case, their decisions are based on the accumulated search hazard function with a maximum soon after the time at which a late time t and the experience gained during previous games. fee for lot-parking starts to accumulate, while parameter λ of the accelerated-failure time model increases as the meeting time To understand these players’ choices, we consider a player who approaches and decreases if the distance between the destination searched for on-street parking unsuccessfully during the time Figure 5. Average gain K(t, Δt), when cruising between t and t + Δt and then parking at the lot for scenarios A (a [4] S. Lehner and S. Peer, ‘The price elasticity of parking: A meta- and parking lot increases. That is, in a very intuitive manner, the analysis’, Transportation Research Part A: Policy and Practice, 121: shorter the time to the meeting and larger the distance between the 177-191, (2019). destination and the off-street lot, the higher the probability [5] S. Carrese, B. B. Bellés, and E. Negrenti, ‘Simulation of the parking becomes to quit cruising and park at the lot (figure 4). phase for urban traffic emission models’, In TRISTAN V – Triennial The revealed rules of drivers’ parking decisions can be Symposium on Transportation Analysis, Guadeloupe, (2004). incorporated into an agent-based parking simulation model. An [6] D.G. Kleinbaum and M. Klein, Survival analysis, Springer, New advantage of the Log-logistic hazard (1) – (2) equations is in the York, 2010. estimated coefficients that can serve for the model’s initial [7] H. Akaike, ‘A new look at the statistical model identification’, In Selected Papers of Hirotugu Akaike, 215-222, Springer, (1974). parameters. Then, the modeler can investigate the consequences of stronger or weaker reactions of drivers to the time- and distance related factors by varying the parameters of these analytical rules. This approach of game-based modeling can benefit the reliability of policies and services established using the model. It is especially relevant in the context of parking search, where empirical studies are scarce and little is known about the dynamics of the process. The choice of whether and when to quit cruising and head to the expensive parking lot or continue searching for cheaper on-street parking is one of two major component of driver’s parking behavior. The second major decision that of the search path. We leave it for an additional paper. ACKNOWLEDGEMENTS We express our gratitude to Dr. Nadav Levy for coming up with the idea of a game-based parking search model. REFERENCES [1] A. Mllard-Ball, ‘The autonomous vehicle parking problem’, Transport Policy, 75: 99-108, (2019). [2] E. Inci, J.V. Ommeren, and M. Kobus, ‘The external cruising costs of parking’, Journal of Economic Geography, 17(6): 1301-1323, (2017). [3] I. Benenson and P. Torrens, Geosimulation: Automata-based modeling of urban phenomena, John Wiley & Sons, Hoboken, 2004.