Improving the Nomad microscopic walker model Mario Campanella*. Serge Hoogendoorn* Winnie Daamen*

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1 th IFAC Symosium on Transortation Systems Redondo Beach, CA, USA, Setember -4, 9 Imroving the Nomad microscoic walker model Mario Camanella*. Serge Hoogendoorn* Winnie Daamen* *Transort & Planning Deartment, Delft University of Technology, Delft, the Netherlands, (Tel: ; m.c.camanella@ tudelft.nl) Abstract: This aer resents the results of two calibration efforts and imrovements of the Nomad microscoic walker model. Each calibration consisted in comaring the outcome of 9 sets of model arameters with results from laboratory exeriments. Three erent flows were used in the calibrations: bidirectional, unidirectional and a narrow bottleneck. For the first two tyes of flow the macroscoic seed-density relation is used for comarison. For the narrow-bottleneck the caacity for the bottleneck is assessed. Additionally, quantitative measures of self-organizing lane formation for the bidirectional flow are included in the calibration. In the first calibration effort only 4 arameter sets did not resent gridlocks in the bidirectional flow and their results are resented. These four sets over estimated the caacity of the bottleneck and the efficiency of the unidirectional flows. These results are discussed and it is shown that a modification in the model is necessary. A modified model is resented and submitted to a new round of calibration. One arameter set showed significant imrovement for the seed-density relations and the caacity of the bottleneck. The exerience gained in this calibration effort indicates that edestrian microscoic models can be calibrated over several tyes of flows simultaneously. However, this research shows that care must be taken when using only macroscoic flow roerties for calibration. They may not guarantee the generality of the model due to the comlexity and variety of ossible flows. Keywords: Pedestrian microscoic model, calibration, Nomad edestrian model, social force models.. INTRODUCTION Microscoic traffic models are modelled over high dimension saces and usually resent a large set of arameters. Calibrating a microscoic model is a icult task and one of the goals is to achieve a general rediction caability Brockfeld et al., 4. For edestrian models this roblem is exacerbated by the fact that there is an uncountable diversity of ossible flows and oulation comosition. The usual method of calibrating microscoic edestrian models is by comaring relations between density, seed and flow (so-called fundamental diagrams) to those obtained emirically (Seyfried and Schadschneider, 8; Buchmueller and Weidmann, 6; Klüfel, 5). Most reorts on calibration of microscoic edestrian models focus in few aggregated asects of the flows (Asano et al., 7; Berrou et al., 5) and generally do not show results for erent tyes of flows. A erent aroach of arameter estimation was roosed by (Hoogendoorn et al., 5) using trajectory data of real life exeriments. They estimated model arameters for individual edestrians and used the samle to discuss inter-edestrian erences and derive arameter correlations in the oulation on multile flows.. Self-organisation Self organizing henomena occur in many traffic systems. In articularly in edestrian flows several kinds are observed, such as lane formation in bidirectional flows, formation of diagonal stries in crossing flows and zier-effects in bottlenecks. What these henomena have in common is the aearance of satial atterns characterized by a secific distribution of individuals over the walking area (Hoogendoorn and Daamen, 5; Helbing et al., 5). In bidirectional flows edestrians tend to walk in the same direction in dynamically formed lanes. In crossing flows, clusters of edestrians walking in the same direction dislay atterns resembling diagonal stries. Since edestrian behaviour is characterised by selforganisation henomena, the calibration of microscoic edestrian simulation models has to consider the reroduction of these henomena among other things. The majority of the microscoic simulation models claim to reroduce the most imortant self organizing henomena (Teknomo, 6; Pelechano et al., 7). However, there is not much evidence indicating that microscoic simulation models have been calibrated on self-organisation henomena quantitatively.. Paer outline This aer resents a calibration rocess for the Nomad edestrian microscoic simulation model combining the fit of seed-density fundamental diagrams, caacity of narrow corridors and a quantitative measure of self-organizing lane formation. First, the basic Nomad walker model is resented in section. In section 3, the emirical results obtained in

2 laboratory exeriments are resented in the form of seeddensity diagrams for two tyes of edestrian flows: unidirectional and bidirectional. The exerimental data of the bidirectional flow is also used to extract a distribution of the number of lanes. A narrow bottleneck is used to calculate averaged caacity. An equivalent simulation set-u has been created and twenty six arameter sets for the Nomad edestrian model have been investigated (section 4). The investigation comares seed-density relations for the bidirectional, unidirectional flows, caacity for the narrowbottleneck and lane distribution for a set of arameters. The results for the basic model are discussed (section 5). A modification of the Nomad model is resented (section 6) and calibrated again (section 7). The section 7 ends with a discussion about the new results and the quality of the redictions of the modified model. In the conclusion we outline some conclusions about this calibration effort.. NOMAD WALKER MODEL Nomad is a microscoic edestrian simulation tool develoed by the deartment of Transort & Planning of the Delft University of Technology. The tool is imlemented using a model roosed by (Hoogendoorn and Bovy, 3). The model describes all actions of the edestrians as activities and is based on the micro-economic notion of subjective utility maximization. The walker model describes the walking behaviour of edestrians. Pedestrians are described as comressible (circular) articles. Let x, v ( t ) and a ( t ) resectively denote the location, the velocity and the acceleration of edestrians. The walker model is described as follows: dx = v () dt dv = a () dt The acceleration is assumed to be a linear addition of erent factors affecting edestrian walking behaviour, namely the desire to stay as close as ossible to a desired trajectory leading as direct as ossible to the edestrian s destination s, the avoidance of other edestrians r, the avoidance of obstacles o ( t ), the contact forces that arise when edestrians are colliding and a stochastic noise ε ( t ) accounting for the oulation heterogeneity and unreresented factors. The acceleration model for the basic Nomad model is described in (3): a = s + r + o + + ε Where: (3) v ( t ) v s = Τ v ( t ) Desired velocity of edestrian T Relaxation time of edestrian The desired seed v is a vector tangent to the desired trajectory with length equal to the free seed of edestrian. The model assumes free seeds to be normally distributed with variance s. * d q R r = A e (5) q P A Interaction factor between edestrian and edestrians q P Set of edestrians q erceived by edestrian d * q ( t ) Perceived distance of edestrian q by edestrian / R Satial discount of edestrian * for < o < d d o ( t ) = A - d - d / d for d < d < d ( ) w * * o o o O * for d o > d d * ( t ) Perceived distance of obstacle o from edestrian o d o w A (4) (6) Threshold distance between edestrian and obstacles Interaction factor between edestrian and obstacles Obstacles are only taken into account when these are located within a secific distance to the edestrian. Obstacles nearby have maximum influence, while obstacles far away do not have influence. In between these distance thresholds, the reulsive force increases gradually when distance is decreasing. The hysical force is the force that arises when edestrians are in contact with each other. In other terms: when the distance between their centres is equal or smaller then the sum of their radius (edestrians are assumed to be slightly comressible). These forces are only resent in high densities when collisions occur. The calibration erformed in this investigation never reached such large densities and therefore its arameters were not included in the calibration. Consequently the formulations of these comonents are not elaborated further. A edestrian is only affected by edestrians and obstacles within a limited region of the walking area (influence area). Thus P in (5) only accounts for edestrians within this influence area. Different forms of influence areas are ossible and the anisotroic shae used in the Nomad model derives from observations on edestrian behaviour (Goffman, 97). Pedestrians react stronger to events occurring in front of them 3

3 and additionally react stronger to events closer to their axis of movement. Pedestrians are also aware of events occurring close to their back. To model this behaviour the influence area in the Nomad model consists of two elongated regions: an area in the front (larger) and an area in the back (Fig..). θ c i b Influence area c + i f Fig. The Nomad influence area with the reelling force reresented by the thick arrow (second term of (3)) Four arameters describing the shae of the influence area are imortant in the calibration resented here, namely c +, i f, c and i b. The constants c controls how much the areas are elongated, if < c <, the edestrian is more sensitive to hindrances closer to the walking axis. The maximum distance at which another edestrian or obstacle can be erceived in front for a c + smaller than one is c + i f.the i b and c are the equivalent for hindrances that are felt in the back. 3. LABORATORY EXPERIMENTS The calibrations erformed in this aer used data from controlled laboratory exeriments conducted in the facilities of the Delft University of Technology. Various exeriments have been erformed to cover a wide range of edestrian behaviours in unidirectional flows, bidirectional flows, crossing flows and in bottlenecks. The exeriments have been filmed and the trajectories have been extracted via automated extraction software. A comlete overview and further analyses can be found in Daamen and Hoogendoorn, 3. unidirectional flows. These are the most basic edestrian flows and need to be correctly reroduced by any model. To imrove the calibration of the bidirectional flow the distribution self organized lanes was included. The caacity of entrances is another very imortant asect in edestrian alications esecially for evacuation simulations. Therefore, the caacity for a narrow bottleneck with one meter width has been used as the fourth macroscoic measure. 3. Fundamental diagrams from the exeriments The seed-density relations resented in Fig. 3 were derived at each time in intervals of. seconds from the derived trajectories. The seed is obtained by averaging the seed (v) of all edestrians in the walking area and lotted against the density (k) at that time. The density is calculated dividing the amount of edestrians by the walking area. seed (m/s).5.5 v = -.3*k density (ed/m) seed (m/s).5.5 v = -.33*k density (eds/m) a. bidirectional flow b. unidirectional flow Fig 3. The seed-density relations for the three flows In Fig.3 are resented the linear regression equations for both exeriments. Higher order olynomials did not imrove the coefficient of determination. The variation of seeds around the regression line in the exeriments (Fig.3) is due to the heterogeneity of the oulation. The effect of free flow seed heterogeneity is very imortant in edestrian flows Camanella et al., 9. It can be observed in the seeddensity grahs from the exeriments that at low densities the seed variation is larger. At low densities the seed averages are closer to single edestrians free flow seeds thus the larger variation. 3. Lane distribution The lane distribution for the bidirectional flow exeriment (Fig. 4) was obtained from the trajectories with an algorithm develoed by Hoogendoorn et al., 8. Fig. The narrow bottleneck exeriment from Daamen and Hoogendoorn, 3 Relative frequency.6.4. To increase the efficiency of the calibration effort four macroscoic measures have been used. The first two choices went to the seed-density relations of the bidirectional and 3 4 Number of lanes formed Fig 4. The frequency of lanes for the bidirectional flow 4

4 Fig 4 shows the relative frequency (count of times that a certain amount of lanes was formed / total count of times) of lanes formed. The values for the frequencies are resectively: f =.3, f =.43, f 3 =.3 and f 4 = Bottleneck caacity The caacity for the narrow bottleneck exeriment was estimated for the eriod of saturated flow. The value was obtained counting the amount of edestrians that crossed the last section of the corridor during the eriod of time in which the bottleneck was saturated. These average count divided by the saturation eriod time in seconds resulted in.53 edestrians/second. 4. CALIBRATION PROCEDURE The calibration erformed in this aer consists of comaring the relative erence of the values (V) of the macroscoic measures of the simulations according to (7): sim em V V erence = * (7) em V The four measures generated nine values to be comared: The two coefficients of the seed-density regression (seed decay d and v ) for the bidirectional and unidirectional flows (Fig.3 for the exeriments), the frequencies (f,f,f 3,f 4 ) of the four lane amounts (Fig.4 for the exeriments) and the bottleneck caacity (c). Both the exerimental and simulated fundamental diagrams showed a large scatter causing the R values of the linear regression to be around.. As mentioned in the section 3. this mainly reflects the heterogeneity behaviour of real edestrians. Evidently the simulations should show similar outcomes and deviations of the exerimental scatter will indicate roblems in the combination arameters/model. The regression coefficients are used for quantitative comarison between the simulated and exerimental data. Differences between the scatter are discussed qualitatively in the following sessions. Eight arameters from the model were chosen to be the variable criteria (4), (5) and (Table ). These arameters are the most imortant affecting the interactions between edestrians in the simulated flows. To minimise the search sace 9 erent sets of arameters have been generated modifying only one criteria arameter from a base arameter set (Table ). The underlined values in the Table refer to the base arameter set. For each arameter set simulations have been run. All seed-density airs obtained for each of the twenty runs were used to create the fundamental diagrams resented in the (Figs. 5, 6 and 7). For further details refer to Camanella et al., 8. Table. Parameters varied in the calibration arameter Values s,.6,.35 T.,.5,.5,.5 A,, 7, 3 R.,.6,.3 i f, 3, 6 i b.65,, 3 c +.8,.85,.9 c.9,.95,.5 5. RESULTS FOR THE BASIC NOMAD MODEL The erformance of the arameters sets varied significantly. One asect was decisive for the quality of the calibration: the robability of gridlock. Gridlock is the total standstill of edestrians obstructing each other. The robabilities varied along the sets. Six sets resented % of gridlocks and only four arameter sets never resented gridlocks: the base set (a.) with all underlined arameters, the set with s = (b.), the set with T=.5(c.) and the set with A = 7 (d.). Since the densities reached by the bidirectional flow were only moderate (around ed/m ) all flows with gridlock are not further included in this aer. The Tables, 3 and 4 shows the results for the four arameters sets that did not resent gridlocks in the simulated densities. Table. Results for the seed-density regression sets d bid v bid Diff d uni v uni a b c d Table 3. Results for the lane distribution sets f f Diff f 3 f 4 a b c d Table 4. Results for the caacity sets c a..8 8 b..8 6 c..7 7 d

5 The results for the seed density regressions have been quite erent for the bidirectional and the unidirectional flows. The former resented good fits for sets c. and d. and reasonable fits for the remaining sets. However, the four sets showed very bad fits for the unidirectional flow. All of them had a too efficient flow with an underestimated seed decay value (Table ). The lane distribution of all sets did not show good fits. All the flows resented too many one lanes and too little four lanes (Table 3). The caacity for all sets was over estimated with the excetion of set c (Table 4). It can be observed in the Fig. 5 that for all the sets there is a much bigger variation of seeds bellow the regression line when comared with the exeriments. The sets a., c. and d. had the same value for s and dislay larger variation of seeds. However, the set b. with s = also showed a large variation bellow the regression line. An insection of the simulated data showed that these too low seeds occurred due to head-on collisions of edestrians. These collisions reduced the seed of some edestrians to almost stand still, regardless of the surrounding densities. A head-on collision occurs when two edestrians are walking towards each other along a similar ath. When this occurs the angle between the current seed and the reelling acceleration (angle θ in Fig. ) is very small. Therefore the tendency to change the seed direction is very small, since the lever of the force is very small. The edestrians thus continue walking towards each other until the reelling accelerations almost sto the edestrians. At this moment any small direction erence multilied by the very large accelerations due to the roximity finally make the edestrians ass each other. seed (m/s) seed (m/s).5.5 v = -.*k density (ed/m) seed (m/s).5.5 v= -.5*k density (ed/m) a. base set b. s = m/s v = -.3*k density (ed/m) seed (m/s).5.5 v = -.9*k density (ed/m) c. T =.5 s d. A = 7m/s Fig 5. Seed-density relations for simulated bidirectional flows with the basic Nomad model All sets but b. (Fig 5b.) show a large variation of seeds above the regression line. The set b. on the contrary shows a much lower variation. The increase of seeds well above the free flow seeds in the low densities is also exlained by insecting the trajectories. When two edestrians are walking in the same direction and a faster follower edestrian does not deviate early enough he gets very close behind the slower edestrian. At this moment the leader feels an extra acceleration from the back due to the back side of the influence area. This acceleration occurs due to the nature of the reulsion term of (3) and the shae of the influence area (Fig.) and not due to contact between the edestrians. Deending on the roximity this extra acceleration ushes the edestrian above his desired seed for some instances. This also exlains why the arameter set b. does not show this uward variation since all edestrians have the same desired seed and seldom edestrians will walk very close behind another edestrian. It has to be mentioned that arameter sets with very low influence from the back art of the influence area resented the highest robability to gridlock. This shows that this ush from behind is being used to comensate other deficiencies in the model. seed (m/s) seed (m/s).5.5 v = -.69*k+.4.5 density (ed/m).5.5 seed (m/s).5.5 v = -.4*k density (ed/m) a. base set b. s = m/s v = -.69*k density (ed/m) seed (m/s).5.5 v = -.89*k density (ed/m) c. T =.5 s d. A = 7m/s Fig 6. Seed-density relations for the simulated unidirectional flows with the basic Nomad model The results for the unidirectional seed-density relations are shown in Fig.6. All sets resent very low decay for the regression indicating that the flows are too efficient. The cause can also be attributed to the ush from behind roblem. This is confirmed by the results for the arameter set s= (Fig.6b) were the value of the decay is twice as large as for the other sets since there is very little ush from behind. Additionally sets with large c and small i b resented larger decays. 6

6 lateral acceleration ushing the trajectories away from each other. The value of the anticiation time used is.5s. 6. MODIFICATION OF THE NOMAD MODEL To imrove the manoeuvrability of edestrians in oosite flows, the edestrian reulsion term r (t ) (5) is modified by 7. RESULTS OF THE MODIFIED NOMAD MODEL adding the extra reulsion defined by (8). a front (t ) = A The modifications resented in the revious section have been imlemented and new simulations for the 9 sets have been run. The manoeuvrability of edestrians is imroved and is indicated by the reduction of the robability of grid locking for most sets. The arameter set ib =.65 (e) with smaller back art of the influence area delivered the best results. y* d *q ( t )*d q (t ) e R (8) q Pfront Where: Pfront Set of edestrians erceived by edestrian walking Table 5. Results for the seed-density regression in the front art of the influence area and in oosing direction A Interaction factor for oosing edestrians y* (t ) d q Perceived lateral distance from edestrian towards sets dbid e. -.8 / R vbid.4 duni vuni.4 5 Table 6. Results for the lane distribution edestrian q -7 sets f e..34 Satial discount of edestrian for oosing 63 f.38 - f3.8 - f4. -9 edestrians This extra term accentuates the reulsion acceleration arisen y* (t ) from edestrians walking in the by lateral distances d q Table 7. Results for the caacity sets e. oosite directions. The lateral distance is the distance the edestrian q is from the walking axis of edestrian (Fig. 7). c.6 4 The seed-density regression values for the unidirectional flow resented much better fit (Table 5). The seed variation along the densities for the bidirectional flow diminished. Additionally, the caacity of the bottleneck showed good fit. However, the seed variability in the lower densities for both bidirectional and unidirectional flows (Figs.8a and 8b) is still too high. y* (t ) d q Fig 7. Perceived lateral dislacement of edestrian q.5.5 y' = y + vy a a.5 density (ed/m) a. bidirectional flow The other modification is a limited form of anticiation (9) that dislaces the erceived osition (x, y) of edestrians in the direction of their seed (vx, vy). x ' = x + vx a v = -.8*k +.4 seed (m/s) seed (m/s) q v = -.5*k density (ed/m) b. unidirectional flow Fig 8. Seed-density relations for the modified Nomad model The overall lane distribution (Table 6.) did not resent a good result with the same over-estimation of one lane frequency and under-estimation of four lanes. These discreancies were exacerbated in the new model. Insecting the trajectories revealed that the imroved caacity of avoiding head-on collisions had the side effect of increasing the robability of a edestrian joining an existing lane instead of creating new ones. Pedestrians with a larger ush from behind (so as in the basic model) are able to create more stable lanes by having their acceleration more aligned to the corridor direction. (9) Anticiation time The dislaced osition (x, y ) is alied only on oosing edestrians and edestrian itself. This anticiation decreases the erceived distances roortionally to the seeds of oosing edestrians. Smaller lateral distances increase the 7

7 These observations may have an imortant imlication for the quality of the model. 8. CONCLUSIONS This investigation resented a detailed data analysis of edestrian simulation flows. Two roblems with the basic Nomad model were identified: an excessive ush from behind and head-on collisions. A solution for both was imlemented and showed to imrove the quality of the redictions. The Nomad model was effectively calibrated for four imortant measures of edestrian flows: seed-density relations for bidirectional and unidirectional flows and the caacity of narrow bottlenecks. These results show that a microscoic model can be generalised redicting correctly erent tyes of flows. However, the roblems with the distribution of lanes described in the Section 7 indicate that the modified model may still not be roerly calibrated for all tyes of flows. The second calibration effort after the basic Nomad model has been modified delivered better results when comared with the basic model. This indicates that the trajectory analysis erformed in the Section 5 was effective in revealing the causes of bad fits. The necessity of recurring to trajectories to understand the shortcomings of calibrations suggests that a microscoic aroach to calibration may be more effective in delivering generalized microscoic models. Future research will incororate flows with higher densities in the calibration rocess. The flows investigated in this aer resented only low and moderate densities. The narrow bottleneck exeriment resented moderate to high densities but only the caacity was used for the calibration. Furthermore, crossing flows should also be investigated to increase the alicability of the model. REFERENCES Asano, M., Kuwahara, M. and Tanaka, S. (7). Multidirectional edestrian flow model based on emirical data. th World Conference on Transortation Research. ed. Berkely, USA. Berrou, J. L., Beecham, J., Quaglia, P., Kagarlis, M. A. and Gerodimos, A. (5). Calibration and validation of the Legion simulation model using emirical data. Pedestrian and Evacuation Dynamics. Sringer-Verlag, Brockfeld, E., Kühne, R. D. and Wagner, P. (4). Calibration and Validation of Microscoic Traffic Flow Models. Transortation Research Record, 876, 6-7. Buchmueller, S. and Weidmann, U. (6). Parameters of edestrians, edestrian traffic and walking facilities. Ivt Reort no.3. Zürich, ETH Camanella, M., Hoogendoorn, S. and Daamen, W. (8). Calibration of edestrian models with resect to selforganisation. TRAIL congress 8. Delft, TRAIL Research School. Camanella, M., Hoogendoorn, S. and Daamen, W. (9). Effects of Heterogeneity in Self-Organized Pedestrian Flows. to aear in Transortation Research Record (TRR). Daamen, W. and Hoogendoorn, S. (3). Controlled exeriments to derive walking behaviour. Euroean Journal of Transort and Infrastructure Research 3, Goffman, E. (97). The Individual as a Unit. Relations in Public: Microstudies of the Public Order. Allen Lane The Penguin Press, London. Helbing, D., Buzna, L., Johansson, A. and Werner, T. (5). Self-Organized Pedestrian Crowd Dynamics: Exeriments, Simulations, and Design Solutions. Transortation Science, 39, -4. Hoogendoorn, S. and Bovy, P. H. L. (3). Simulation of edestrian flows by otimal control and erential games. Otim. Control Al. Meth., 4, Hoogendoorn, S. and Daamen, W. (5). Self-Organization in Pedestrian Flow. Traffic and Granular Flow Hoogendoorn, S., Daamen, W. and Camanella, M. (8). Self-organization and Chaos in Pedestrian Flow: Exeriments and modelling. Proceedings of the Chaotic Modeling and Simulation International Conference. Chania, Crete. Hoogendoorn, S., Daamen, W. and Landman, R. L. (5). Microscoic calibration and validation of edestrian models: cross-comarison of models using exerimental data. IN WALDAU, N., et al. (Eds.) Pedestrian and Evacuation Dynamics. Sringer-Verlag, Klüfel, H. (5). The simulation of crowd dynamics at very large events Calibration, emirical data, and validation. IN WALDAU, N., et al. (Eds.) Pedestrian and Evacuation Dynamics. Sringer-Verlag, Pelechano, N., Allbeck, J. M. and Badle, N. I. (7). Controlling Individual Agents in High-Density Crowd Simuation. ACM SIGGRAPH / Eurograhics Symosium on Comuter Animation (SCA'7) San Diego (USA). Seyfried, A. and Schadschneider, A. (8). Fundamental Diagram and Validation of Crowd Models. Proceedings of the 8th international conference on Cellular Automata for Reseach and Industry. Yokohama, Jaan, Sringer- Verlag. Teknomo, K. (6). Alication of microscoic edestrian simulation model. Transortation Research Part F: Psychology and Behaviour, 9,