Atlantis Press Journal style Received 17 June 2015 Accepted 28 August 2015 Dealing with Emergencies: The Case of a Heavy Disruption of the Mexico City Metro System Diego Padilla-Pérez, Jaime Santos-Reyes SARACS Research Group, Systems Engineering Department, SEPI-ESIME ZAC, IPN, U.P. "Adolfo Lopez Mateos", Edif. 5, 2do. Piso, Mexico City, C.P. 07738, Mexico E-mail: jrsantosr@hotmail.com Samuel Olmos-Peña Centro Universitario UAEM Valle Chalco, Hermenegildo Galeana No. 3, Col. Ma. Isabel Chalco Edo. de México, C.P. 56616, Mexico E-mail: samuelop@gmail.com Abstract The paper presents the results of a forecasting model associated with the affluence of users of the metro line-B of Mexico City's metro system. It also presents in a way a retrospective analysis of the metro incident that occurred on September, 2011, in the same metro line; the incident affected seven metro stations and about 17 thousand commuters. The approach has been the use of Artificial Neural Networks (ANN). The main conclusions may be summarized as follows: (i) the metro incident has illustrated the fact that different modes of urban transport are highly interdependent; (ii) the proposed ANN model has the potentiality to be used to forecasting the affluence of users for any metro line for the case of Mexico City's metro system; (iii) the above (ii) can be used as input to the decision process in order to implement the required number of coaches to assist the affected commuters; (iv) Both (ii) and (iii) should be part of an emergency response plan to mitigate the impact of cascading failures due to interdependencies amongst the different modes of urban transport. Keywords: ANN, Emergency response, Metro system, Megacity. 1. Introduction Megacities have become a global phenomena that has dispersed around the planet (a megacity has been defined as an urban area with more than 10 million residents) (Kotkin, et al., 2014). In the early 80s there were only three megacities; i.e., Tokyo, New York and Mexico City. It is believed that there are about 29 such cities as in 2014 and account for roughly 13% of the world’s urban population (Kotkin, et al., 2014). However, one of the biggest challenges facing megacities lies in lagging infrastructure; i.e., these cities continue to add population, without the infrastructure that paralleled the growth (Kotkin, et al., 2014). An example of a lack of infrastructure is related to transportation (Kotkin, et al., 2014). Moreover, in the ultra dense environment of developing country megacities, traffic congestion is also worsening and effectively affecting the urban mobility (Heinrichs, et al., 2012; Kotkin, et al., 2014). For example, nearly half of Mumbai (India) commuters spend at least one or two hours to get to work, far more than workers in smaller rivals such as Chennai, or Hyderabad (India). On the other hand, about 50% of formal sector workers in Mumbai expressed the desire to move elsewhere, in part to escape train or car commute; only a third of workers in other cities expressed this sentiment (Kotkin, et al., 2014). In the literature review, on the other hand, it has been found that infrastructures are highly Journal of Risk Analysis and Crisis Response, Vol. 5, No. 3 (October 2015), 142-151 Published by Atlantis Press Copyright: the authors 142 interdependent and present a great challenge to society today concerning how they are to be managed so as to produce an acceptable risk is a question which has come to the fore in dramatic ways in recent years (Gómez, 2011; Gutierrez, 2014; Kroger, 2008; Zhang, et al., 2012; Lee, et al., 2003; Alam, 2012; AP, 2014; Hayward, 211; Santos-Reyes, et al., 2015). A vast amount of research has been published on the subject (Balakrishnan, et al., 1998; Haimes, et al, 1998; Rinaldi, 2001; Amin, 2001; Lee, et al., 2003; Cagno, et al., 2009; Rosato, et al., 2008; Panzieri & Setola 2008; Baiardi & Telemon 2008). Overall, it may be argued that metro underground systems are highly efficient and reliable; e.g., the Mexico City metro carries more than 1,600 million users per year, equivalent to 5.1 million users on weekdays (STCM, 2014). In addition, its efficient operation contributes to the economic and social benefits, and to the reduction of environmental pollution. On the other hand, it has been found that given the nature of interdependencies amongst these systems, when a failure occurs, usually cause cascading failures affecting, inter alia, other systems; e.g. other modes of transportation. The following two examples illustrate this: (i) on September 11, 2011, there was an electrical fault in the metro line-B of Mexico City's metro underground system; it affected seven metro stations and about 17 thousand commuters. It is believed that the users had to leave the underground metro and find alternative modes of transportation to reach their final destinations (Gómez, 2011). (ii) on November 14, 2014, nearly 300 thousand commuters were affected by the collapse of the metro system in the capital City of Santiago, Chile (Gutierrez, 2014). A power failure occurred in three of the five metro lines. The accident did not allow the commuters to reach to their destinations and caused a huge traffic chaos on the streets of the capital City. Thousands of commuters took their vehicles to work, which led to a collapse in most of the capital's arteries, while pedestrians were unable to use the public transport and most waited between one and two hours without getting a bus; taxis could not cope with the amount of commuters either (AP, 2014; Gutierrez, 2014). The paper attempts to answer the following questions: Why did the 2011 metro disruption cause such a chaos in the City? Were there enough other modes of transport (e.g. coaches) to cope with the disruption? Given this, it is clear that a better understanding of the metro transport system under different scenarios may become a necessary step forward towards an efficient and reliable urban transport system. In the literature search, however, there is very little attention given to this. The paper addresses this very issue by analyzing an scenario regarding a disruption of the metro line-B of Mexico City's metro underground system. The approach has been the application of an artificial neural network (ANN). The paper gives an account of the key findings of the ongoing research project. 2. Emergency response system in place in case of a disruption of the metro system 2.1. The Mexico City's metro and the affected metro line-B The Mexico city metro underground system carried an estimated 1.6 billion passengers in 2012 (STCM, 2014). The metro system is being regarded as the second largest metro system in North America after the New York City metro. Fig. 1 shows the metro network and the affected metro line-B on September 13, 2011. The affected stations (i.e., Stn-B7 to Stn-B13) were the ones shown in red colour in the figure (Gómez, 2011). Fig. 2 shows the number of trains versus the users demand for this particular metro line-B (i.e. 05 hrs - 24 hrs). It can be seen that at peak hours (i.e. 07:00 - 09:00 hrs and from 18:00 - 21:00 hrs) the highest number of trains required (about 38) for coping with the demand of users (STCM, 2014). The data from Figs 1&2 have been used to the analysis being reported in section 3. 2.2. The emergency response in case of a disruption in the metro system In Mexico City, one of the existing emergency plans, is the use of the coach 'passenger transportation network'(known as 'RTP'). That is, these transport systems are implemented, either when the metro underground system undergoes maintenance, or when accidents occurring in the system (RTP, 2015). Table 1 Published by Atlantis Press Copyright: the authors 143 shows the fleet available in the City for the case of an emergency. Fig.3, on the other hand, shows the map where the eight parking stations of the coaches are located (these are shown as 'stars' like symbols and in red colour). Table 1. Types of coaches available during an emergency (RTP, 2015). Type of Coach Capacity (Number of people) Fleet Type-I 100 934 Type-II 90 210 Type-III 70 146 Type-IV 240 51 Type-V 160 12 Type-VI 53 105 Total 1458 3. Materials & Methods An artificial neural network (ANN) is a mathematical model that can be implemented as a software simulation that tries to simulate two essential properties of the human brain in relation with its high capabilities of parallel information processing (Safi & Bouroumi, 2013). Technically speaking, the conception of a neural solution to a practical problem requires three main steps (Safi & Bouroumi, 2013). The first step is the choice of a suitable architecture for the ANN; i.e., the number of neurons to use and a suitable way for connecting them in order to form the whole network. The second step is the choice of a suitable algorithm for training the network, i.e., a method for determining the best possible value for each synaptic weight modeling the physical connection between two neurons. The third step is the Fig. 1. The affected metro line-B of the Mexico City's metro network. (Adapted from STCM, (2014)). Fig. 2. Number of required trains in relation to the demand of users (STCM, 2014). Published by Atlantis Press Copyright: the authors 144 choice or the collection of a good set X of sample examples, i.e., the learning database which will serve as input data for the learning algorithm or training algorithm (Safi & Bouroumi, 2013). Fig. 4 shows, on the other hand, that each signal is weighted by a weight, they add up when the activation function is applied in order to obtain the corresponding output. Fig. 4. A neuron (Paz, 2008). An ANN is a model consisting of a vector p representing inputs, a weight vector W, representing the weight of the connections that amplifies or attenuates the input p, an activation function f and a scalar a, which represents the output, and is given by the following expression (Paz, 2008): (1) where, (2) The subscripts of the weight matrix W, represents the terms involved in the connection, the first subscript represents the destination neuron and the second, is the source of the signal fed to the neuron. For example, W1R subscripts indicate that this weight is the connection from the R-th input to the first neuron. Fig. 5 shows an Elman architecture network; this architecture network is commonly associated with a two-layer network with a feedback from the output of the first layer at the entrance of the first layer. This connection allows the Elman network to detect and generate patterns that vary over time. From the above figure, it can be seen R inputs, S 1 neurons in the first layer, S 2 neurons in the second layer; the output of layer-one is the input of layer-two and feeds back to the layer-one, so that layer-two can be seen as a network of layer R=S 1 inputs, S=S 2 neurons Fig. 3. Location of the eight coach stations in the capital City (RTP, 2015). Published by Atlantis Press Copyright: the authors 145 and a weight matrix W 2 with dimensions S 2 x S 1 ; the entry of the second layer is a 1 and the output is a 2 . The activation function f takes the total input Sk. The activation is given by, (3) The hyperbolic tangent function ('tansig') in the range -1 to 1 for the hidden layers is given by: (4) The identity function ('purelin') to the output layer is being defined as: y = x (5) Therefore, the output of each layer is given by the following: Hidden layer, a1(k) = tansig ((IW1,1p + LW1,1ªkk-1) + b1) Output layer, a2(k) = purelin ((LW2,1a1(k) + b2) The ANN model proposed in this study has been the retro-propagation Elman architecture and it shown in Fig. 6. Overall, the proposed ANN model contains an input neuron, three hidden layers and one output neuron. Each of the hidden layer contains 18 neurons, as a hyperbolic tangent sigmoid transfer function. The output layer has one neuron and an identity function as transfer function. The number of users in the metro line-B has been considered as the input neuron; the output neuron, on the other hand, has been considered as the total number of trains needed to transport the users (Fig. 2). Fig. 6. Elman architecture retro-propagation network for the present case. Fig. 5. Elman architecture network (Paz, 2008). Published by Atlantis Press Copyright: the authors 146 4. Results & Discussion 4.1. Forecasting of the affluence of users in the metro line-B Table 2 shows the results of the forecasting of the affluence of commuters in the metro line-B and for August 2012. It can been that the forecasting of the number of users is given per day of the month being considered in the analysis. Once the forecasting has been done, the next question considered was the following: How many coaches may be required to transport commuters in case of a failure of the metro line-B? Table 2. Forecasting of the affluence of commuters in the metro line-B for August 2012. Day No. Users Day No. Users 1 923592 17 986990 2 883815 18 892790 3 966931 19 715361 4 726103 20 1011153 5 710545 21 906211 6 1016453 22 741689 7 950034 23 759497 8 920144 24 961916 9 868086 25 726986 10 985053 26 724792 11 842271 27 1018134 12 714392 28 984340 13 1026027 29 1001494 14 1010184 30 1023320 15 974482 31 982659 16 912878 Total 27868323 In order to be able to answer the above question, it was necessary to determine the number of users per hour and for each of the metro stations of the line-B (Fig. 1). In order to achieve this, two sets of data were used: first, the affluence of users in the metro line from April to June 2012 (STCM, 2014); second, the data associated with the number of trains running every hour; i.e., from 05:00 hrs to 24:00 hrs (Fig. 2). (This data has been provided by the Metro system organization (STCM, 2014)). Table 3 shows the results for each hour and for each station of the metro line under study. From Table 3, it can be seen, for example, that between 07:00 to 10:00 hrs, the affluence of users has been estimated as 8,056; i.e., the amount of users per hour at Station 1 (Fig. 1). Regarding the number of coaches needed in case of a failure in the metro line-B; this was obtained straightforward by dividing the data shown in Table 4 with those shown in Table 1. Based on this consideration, the calculated number of coaches needed when a failure occurs and at a rush hour (i.e., 08:00 hrs), are shown in Table 4. The calculated number of coaches needed in case of an emergency shown in Table 4 considers only three types of coaches; i.e., types I, II, and III (Table 1). This is because they are the ones that are explicitly used in case of an emergency of the metro system (STCM, 2014). 4.2. Number of coaches needed during the 2011 metro disruption The model and the results presented in the previous sections helped to assess the number of coaches needed during the emergency situation on 13 September 2011 (the incident occurred at a peak hour; i.e., 08:00 hrs). An electrical fault affected stations 7 to 13, as shown in Fig. 1. As motioned in the introduction section, thousands of commuters were affected by the incident. According to the analysis, the required number and type of coaches (Table 1) are the following:  160 coaches Type-I;  178 coaches Type-II; and  229 coaches Type-III. Finally, the following question has been addressed: how long does it take the coaches to get to the Stations- 7-13? Table 5 shows the results of the analysis. (It should be emphasised that the analysis has been conducted by using the information shown in Fig. 3). 4.3. Discussion 4.3.1. The proposed ANN model Inspired by biological neural networks, ANNs are massively parallel computing systems consisting of an extremely large number of simple processors with many interconnections. ANN models attempt to use some “organizational” principles believed to be used in the human (Jain, et al., 1996). ANN have been applied to a variety of problems ranging from pattern classification, clustering/categorization, function approximation, Published by Atlantis Press Copyright: the authors 147 Table 4. Number of Coaches required at peak hour (08:00) in each of the stations of the metro line-B (Table 1). No. Station Type I Type II Type III 1 81 90 115 2 12 14 17 3 25 28 36 4 17 19 24 5 9 10 12 6 12 13 17 7 25 28 35 8 19 21 27 9 21 24 30 10 23 25 33 11 16 18 23 12 24 26 34 13 32 36 46 14 16 18 23 15 18 21 26 16 20 22 28 17 17 19 25 18 19 21 27 19 15 16 21 20 15 16 21 21 16 18 23 22 17 19 25 23 23 25 33 24 73 81 104 prediction/forecasting, optimization, control (Jain, et al., 1996). In the present case, an ANN model has been put forward to forecast the number of users of a particular metro line of the metro underground system of Mexico City. The model has been based on Elman's architecture retro-propagation network (Figs. 5&6). The proposed model contains an input neuron, three hidden layers and one output neuron (Fig. 6). Each of the hidden layer contains 18 neurons and an hyperbolic tangent sigmoid transfer function has been considered. The output layer, on the other hand, contains one neuron and an identity function as a transfer function. The number of users in the metro line-B has been considered as the input neuron; the output neuron has been considered as the total number of trains needed to transport the users demand (Fig. 2). The software Matlab (R2009a version) has been used to train the ANN model; e.g., 'Trainscg', the step conjugate gradient with a value of 1x10 -18 and with 33000 iterations has been considered to train the model. Moreover, the users data from 2000 to 2011 has been used to train the proposed model. Finally, the forecasting of the affluence of users for the metro line-B has been done for August 2012. Table 3. Affluence of commuters in the metro Line-B from 05:00 - 24:00 hrs. Station No. 05:00 hrs 06:00 hrs 07:00 - 10:00 hrs 11:00 - 17:00 hrs 18:00 - 21:00 hrs 22:00 hrs 23:00 hrs 24:00 hrs 1 424 5300 8056 7632 8056 4028 2756 1696 2 64 801 1218 1153 1218 609 416 257 3 131 1637 2448 2357 2448 1244 852 524 4 88 1101 1672 1585 1672 837 572 352 5 46 575 874 827 874 437 299 184 6 63 781 1187 1124 1187 594 406 250 7 131 1628 2476 2346 2476 1238 847 521 8 100 1251 1901 1801 1901 951 651 401 9 112 1400 2128 2016 2128 1064 728 448 10 120 1510 2294 2174 2294 1148 785 483 11 86 1069 1626 1540 1626 812 557 342 12 125 1560 2372 2247 2372 1186 811 500 13 170 2120 3222 3052 3222 1612 1103 679 14 83 1036 1575 1493 1575 788 539 331 15 97 1216 1849 1751 1849 924 632 389 16 105 1307 1987 1882 1987 1530 680 418 17 92 1150 1749 1657 1749 875 599 368 18 98 1225 1862 1764 1862 931 637 392 19 77 971 1476 1399 1476 738 505 311 20 77 973 1479 1402 1479 740 506 312 21 85 1066 1621 1536 1621 810 555 341 22 92 1140 1732 1642 1732 867 593 365 23 120 1501 2281 2161 2281 1140 781 480 24 382 4779 7264 6881 7264 3585 2485 1529 Published by Atlantis Press Copyright: the authors 148 One way to validate the forecast of the affluence of users of the metro line-B, is by applying the 'goodness of fit'. This indicates, for example, the discrepancy between the actual number of users of the metro line and the forecasting with the ANN model. Table 6 summarizes the results of the validation process of the proposed model. Table 6. Summary of the validation of the proposed model. Mean Error (ME) -20170.22 Mean absolute error (MAE) 85262.0828 Sum of squared error (SSE) 3.8128x10 11 Mean Square Error (MSE) 1.23x10 10 Standard deviation error (SDE) 112736.7418 Bias Error Estimation (U M ) 0.0107837 Model Variability (U S ) 0.0302528 Error Remnant (U C ) 0.0509638 U of Theil 0.00363271 Overall, it can be argued that the proposed model may be considered good enough to forecast the affluence of users such as the present case study. For example, the Model Variability (U S ) shows the ability to replicate the degree of variability of the forecasting with respect to the number of users of the metro line being considered. The degree of variability found is 0.0302528 and it is in the range between -1 to 0 and 0 to 1, being zero the maximum variability. 4.3.2. The emergency response system One of the biggest challenges that megacities face is the problem associated with transport and traffic congestion (Kotkin, et al., 2014; Heinrichs, et al., 2012). One the one hand, urban mobility has been the subject of importance in recent years (CEC, 2007; Heinrichs, et al., 2012). That is, major cities worldwide have implemented policies aiming at enhancing mobility while at the same time reducing, among other things, congestion, accidents and pollution (CEC, 2007). On the other hand, there has been very little done on how to prevent, for example, the disruption of urban mobility (Santos-Reyes, et al., 2014, 2015). Traffic congestion may be regarded as a condition on road networks that is characterized by slower speeds, longer travel times, and increased vehicular queuing. Congestion in the EU is often located in and around urban areas and costs nearly 100 billion Euro, or 1% of the EU's GDP, annually (CEC, 2007). There are a number of specific circumstances which cause or aggravate congestion; e.g. traffic accidents. Traffic research still cannot fully predict under which conditions a traffic congestion may suddenly occur. It has been found that accidents may cause (and have caused) cascading failures which then spread out and create a sustained traffic jam; for example, the failure of the metro line-B that occurred on September 11, 2011 in Mexico City (Gomez, 2011). The above example illustrates the effects of cascading failure. Studies such as the present case, may help to gain a better understanding of cascading failure. For example, the proposed model may help to better prepared for an emergency in case of a disruption of the Table 5. Distance and the time from the parking stations to the metro stations 7 and 13 (Figs 1&3). Parking Station No. Fleet Station-7 Distance (Km) Station-7 Time Station-13 Distance (Km) Station-13 Time 1 170 43.5 1 hr 5 min - 2 hrs 50 min 38.2 55 min - 1hr 30 min 2 168 28.1 45 min - 2hrs 20 min 20.3 35 min - 55 min 3 168 21.6 28 min - 1 hr 40 min 15 28 min - 1hr 4 153 17.4 18 - 55 min 21.8 40 min - 1hr. 5 183 14.6 22 min - 1 hr 20 min 11.3 30 min - 1hr 6 233 9.8 18 - 40 min 11.8 18 - 35 min 7 221 7.6 20 - 35 min 12.9 30 - 50 min 8 162 14 22 - 40min 15.1 35 min - 1hr 10 min Published by Atlantis Press Copyright: the authors 149 operation of any metro line (Tables 2-4). By forecasting the affluence of users at any given time may help to take better decision, for example, on the number of coaches to take the affected users to their destinations (Tables 4,5). Moreover, it can be argued that by conducting studies such as this, it may help to eliminate or mitigate the impact of the following: a) wasting time of motorists and passengers; b) delays, which may result in late arrival for employment, meetings, and education, resulting in lost business, disciplinary action or other personal losses; c) wasted fuel increasing air pollution and CO2 emissions owing to increased idling, acceleration and braking; d). the probability of collisions due to tight spacing and constant stopping- and-going. 4.3.3. Considerations and limitations Last but not least, it is important to mention the limitations of the application of the proposed ANN model. That is, the data used in the analysis has been obtained from the organization running the metro system (STCM, 2014). In other words, it is unknown whether the quality of data has been assured. Another limitation of the model is that it does not consider the road traffic. Effectively, this can (and should) be considered explicitly by the model; this may contribute to further enhance its applicability. 5. Conclusions The paper has presented the results of a forecasting model associated with the affluence of users of the metro line-B of the Mexico City's metro. It also has presented in a way a retrospective analysis of the metro incident that occurred on September, 2011, in the same metro line. The approach has been the use of artificial neural networks (ANN). The main conclusions may be summarized as follows: (i) the two examples of the disruption of the metro systems mentioned in the introduction section have shown the effects of cascading failure due to the interdependencies amongst the modes of urban transport. Moreover, the consequence of this (i.e., traffic congestion) shows that lack of a coherent and effective emergency response plan to cope with cascading failure. (ii) the proposed ANN model has the potentiality to be used to forecasting the affluence of users for any metro line for the case of the Mexico City's metro system. (iii) the above (i) can be used as input to the decision process in order to implement the required number of coaches to assist the affected commuters. (iv) both (ii) and (iii) should be part of an emergency response plan to mitigate the impact of cascading failure due to interdependencies amongst the different modes of urban transport. More research is needed to explore other scenarios for analysis. Moreover, data associated with Mexico City's road traffic is badly needed to enhance the applicability of the proposed model. Acknowledgements This project was funded under the following grant: SIP- IPN: No. 20151117. References Alam, A., Crisis transmission: global financial crisis. Journal of Risk Analysis and Crisis Response, 2(3) (2012) 157-165. 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