MICRO-SIMULATION OF A NIGHT TAXI-BUS SERVICE FOR THE HISTORICAL CENTRE OF ROME

MICRO-SIMULATION OF A NIGHT TAXI-BUS SERVICE FOR THE HISTORICAL CENTRE OF ROME Francesco Filippi 1), Marco Lemessi 2) and Thomas Schulze 3) Abstract: The Municipality of Rome plans to introduce a taxi-bus service to connect the historical centre of Rome to the areas within the outer road ring. Such service has been analysed through micro-simulation and post-processing animation using SLX and Proof Animation. The approach is object-oriented, based on three active classes: taxi-buses, customers and the control centre. The control centre is the link between customers and taxi-buses and governs the system from a strategic point of view. The centre collects all the calls, groups customers having common origins and destinations, finds the best route to pick up and deliver all customers, chooses the taxi-bus to assign to each group, and finally sends information to taxis. The most significant module from a strategic point of view is the Travelling-Salesman-Problem module. Given a set of points where to collect or deliver customers, the TSP module (activated by the control centre) explores all possible routes through the points and finds the best route. The one analysed is an open, asymmetric TSP problem. Distances and times to cover them are calculated from a road network developed using TransCAD. The flexibility of the model allows it to be applied to simulate similar services in different cities or even different services, as bus lines, standard taxis or freight distribution services. 1 Introduction To the aim of reducing private traffic flows and the negative externalities connected to it (pollution, noise accidents, etc.), the Municipality of Rome plans to introduce a night taxi-bus service to connect the historical centre of Rome (ZTL-Italian acronym for Limited Traffic Zone) to the urban area within the outer road ring (in Italian GRA). Such a service will run daily from 8.00 p.m. to 2.00 a.m. The area covered by the service will be partitioned into a number of corridors leading from the GRA to the ZTL. Each corridor can be seen as the catchment area for one of the main radial roads (via Tiburtina, via Ardeatina, via Nomentana, etc.) connecting the ZTL to outer areas. Each corridor will be given its own fleet of taxibuses. The capacity of each taxi-bus is fixed and equal to 8 passengers plus the driver. Users will call a control centre and reserve a ride for a specific hour. Taxi-buses will pick them up directly at home (or wherever users ask to be picked up) and will bring them to one of 23 fixed destination inside the ZTL. The same service can be reserved for the backward trip. Trip routes are not fixed and change according to location of origins (for the onward trips) or destinations (for the backward trips) of customers. The best route for each trip is identified by solving a Travelling Salesman Problem. 1 Department Hydraulics Transport and Roads (DITS), University of Rome La Sapienza, Via Eudossiana, 18 00184 Rome, Italy. Tel.: +39-0644585147, E-mail: francesco.filippi@uniroma1.it 2 Department Hydraulics Transport and Roads (DITS), University of Rome La Sapienza, Via Eudossiana, 18 00184 Rome, Italy. Tel.: +39-0644585148, E-mail: marco.lemessi@uniroma1.it 3 Institut für Technische und Betriebliche Informationssysteme, Otto-von-Guericke Universität Magdeburg, Universitaetsplatz 2-39106 Magdeburg, Germany. Tel.: +49-3916712825, E-mail: tom@isg.cs.uni-magdeburg.de. 1

Trip fares vary according to distance of customers from the ZTL. The annulus between the GRA and the ZTL has been subdivided into two concentric fare zones. The first zone, internal and close to the ZTL, has a lower fare, while the second one has a fare 50% higher. A micro-simulation model has been developed to test the feasibility of the taxi-bus service. The model is part of a larger feasibility study, involving a survey to know travellers choices and intentions, the development of a modal split model to quantify potential customers, and the use of a transportation software to calculate distances and travel times between sources and destinations. The micro-simulation model has been written in SLX, Simulation Language with extensibility [1, 2], and animated with Proof Animation [3, 4]. Through micro-simulation it has been possible to model the random process of calls generation, and analyse the behaviour of each customer and taxi-bus, under different service hypotheses. In particular, for each corridor, the micro-simulation model provides information on: Fleet to be assigned to the corridor, Frequency of trips, Delay on departure for each trip, Best route for each taxi-bus, i.e. the one that minimises travel times, Duration of each trip (onwards and backwards), Length of each trip (onwards and backwards), Time needed to run a complete cycle to ZTL and back, Number of hourly trips run by each taxi-bus, Total number of customers served by the fleet as a whole, Percentage of customers served compared to all calls received, Number of customers on each taxi-bus, Time spent running by each taxi-bus in the fleet, Fare to adopt for a single trip, Hourly revenues for each taxi-bus and for the fleet as a whole. The micro-simulation model has been tested on two sample corridors, corresponding to the catchment areas of two main radial roads in Rome, via Tiburtina and via Ardeatina. These two corridors have similar area but very different population (about 85,000 people live in the Ardeatina s catchment, about 178,000 in the Tiburtina s one 4 ) see Figure 1. 4 Data refer to 1997 (source: General Registry Archive of the Municipality of Rome ). 2

Figure 1. Population density in the two sample corridors Different population means different demand and, as a consequence, the need for a different supply (number of vehicles, frequency of trips, etc.). In this way, the model allows to dynamically test the behaviour of the service under two border-line conditions, i.e. very low and very high demand, and to quantify the corresponding revenues for the operator. Each corridor has been given a terminal (starting point for trips to ZTL) located near the GRA, and a number of gates to enter (in-gates) or leave (out-gates) the ZTL. The model allows to give any number of terminals and gates to each corridor. The same gate can be given to two different corridors. 2 Input data 2.1 Analysis of demand In order to quantify potential customers for the taxi-bus service, travellers behaviour in a standard day has been analysed. The analysis based on a telephone survey on a sample of 20,000 people living in the Municipality of Rome. The survey took into account all trips made by the sample in a standard day (from 0:00 to 24:00), for any purposes and using any transport means. The survey shows that about 1.37% of the sample made trips to the ZTL from 8:00 p.m. to 2:00 a.m. the day before the survey. Such a percentage has been applied to people over 14 years living inside the GRA and outside the ZTL (1,844,415 people). The process led to a total of 25,311 people moving to the ZTL (and back) between 3

8:00 p.m. and 2:00 a.m. in a standard day: 1907 of them live in the Tiburtina s catchment, 916 in the Ardeatina s one. The survey proved that people travelling towards the ZTL are many more between 8:00 and 12:00 p.m. Vice versa, the highest number of travellers from ZTL is between 10.00 p.m. and 2:00 a.m.. Assuming that travellers are uniformly distributed over the 4 rush hours and that demand=0 in the other 2 hours, demand distribution over the 6 studied hours is presented in Figure 2. 7000 6000 Hourly demand 5000 4000 3000 2000 1000 To ZTL From ZTL 0 8:00 p.m. - 10:00 p.m. 10:00 p.m. - 12:00 p.m. 12:00 p.m. - 2:00 a.m. Time interval Figure 2. Hypothesis of demand distribution during the 6 hours when the taxi-bus service is operating That being stated, the behaviour of the taxi-bus service has been simulated in one of the two peak hours (from 11:00 p.m. to 12:00 p.m.). The percentage of taxi-bus users, out of the total number of people (25,311) moving towards the ZTL between 8:00 p.m. and 2:00 a.m. using any transport means, has been quantified using a modal split model [5]. Such percentage varies depending on travel time, trip fare and trip frequency (for more details, see section 5). Assuming that the average number of calls generated and attracted in each of the 339 zones between GRA and ZTL is directly proportional to population living in the same zone, data collected through the survey and the modal split model made it possible to quantify the number of potential taxi-bus users in each zone. As for the ZTL, three hypotheses have been made: 1. each of the 23 stops generates the same number of calls, 4

2. each of the 23 stops attracts the same number of calls, 3. the total number of customers departing from the ZTL in the rush hours is equal to the number of customers arriving there (see Figure 2). 2.2 Travel times and distances The TransCAD s [6] procedure to calculate minimum paths between points on a road network has been used to quantify travel times and distances between any couple of points served by the taxi-buses. The network considered is the road network of the Municipality of Rome. Being a night service, distances and times have been quantified referring to the hypothesis of empty network. Travel times calculated using TransCAD are an input to the micro-simulation model. The model then estimates travel times in a stochastic way, on the basis of a normal distribution, whose mean is the deterministic value calculated using TransCAD. Since the deterministic value refer to an empty network, only higher travel times are acceptable (right side of the distribution curve). 3 Model characteristics The model simulates the behaviour of three active classes: The customers The control centre, The taxi-buses. As for customers, three processes are simulated. First, the registration time (i.e. the time when the customer calls the control centre to reserve a ride) is randomly chosen based on a uniform time distribution. Second, the customer is randomly located in one of the possible sources on the basis of the frequency classes assigned to each source point. Finally, the destination point is randomly chosen out of a set of possible points, according to the probability assigned to each point to be chosen. Customers are temporarily in the model: they call the control centre, wait for a taxi-bus and are carried to destination. The control centre is the most important object from a strategic point of view. It collects all calls from customers, storing their registration time, origin and destination; creates groups of customers having common origins and destinations; calculates the best route to pick up and deliver customers, solving a TSP problem for each trip; assign a taxi-bus to each trip; and finally send the information to taxibuses. Taxi-buses are permanently in the model. Their actions are cyclic: they wait for orders from the control centre; receive from the centre the list of passengers to serve 5

and the route to follow; pick the customers up in the source points and deliver them in the destination points; stop and wait for new orders from the centre. Two passive object classes are required additionally. Objects of these classes operate as data storage. They contain information about catchment areas like generation and attraction frequencies and distances and times between points. A number of statistic indicators have been chosen to evaluate the behaviour of the taxi-bus service. They are both quality-of-service indicators and use-of-fleet indicators. The micro-simulation model computes all the indicators in the peak hour. Quality-of-service indicators Travel time for each customer served, Time expired between registration and taxi arrival, for each customer, Time between two taxi-buses in any of the corridors, Number of customers waiting at the end of the simulation period (i.e. customers not served). Use-of-fleet indicators Number of customers served, Number of one-way trips made, Duration of each trip, to and from the ZTL, Average km covered per trip, Number of customers on each taxi-bus moving to the ZTL, Number of customers on each taxi-bus departing from the ZTL, Time spent for a complete cycle (to the ZTL and back), Total revenues. Table 1. Statistic indicators evaluated through micro-simulation Random Variable #Obs Mean Std Dev Minimum Maximum kmpertrip[1] 48 30.77 2.60 24.61 36.34 kmpertrip[2] 21 29.17 3.39 24.95 37.37 kmpertrip_tot 69 30.28 2.93 24.61 37.37 tround[1] 21 5216.55 315.17 4357.41 6009.24 tround[2] 9 5125.21 307.14 4814.86 5615.53 tround_tot 30 5189.15 310.39 4357.41 6009.24 Table 1 shows the values of two indicators: the length of a single trip kmpertrip, and the time spent for a complete cycle tround (in seconds). For each indicator the model reports its name (Random_Variable), the number of times it has been 6

observed (#Obs), its average value (Mean), its standard deviation (Std Dev), and its minimum (Minimum) and maximum (Maximum) values. Such values are computed separately for each single corridor 5, and also for all corridors as a whole. 4 The Travelling Salesman Problem Given a set of points to be visited, the control centre has to identify the best route for each trip, i.e. the route minimising the total travel time. The one faced is an asymmetric (travel time from A to B is generally different from travel time from B to A) and open (the first and last point visited by each taxi-bus are not the same) Travelling Salesman Problem [7]. The route is not fixed and the number of points to be visited in each trip (to the ZTL or backwards) varies according to the random process of demand generation. Figure 3 schematically shows a trip to the ZTL. The taxi-bus departs from a depot located near the GRA, picks customers up in n s source points, enter the ZTL through one of n gi possible in-gates, and delivers customers in n d destination points. Depot Sources Gates Destinations Number of points 1 n s n gi n d Figure 3. Typology of points for the Travelling Salesman Problem The best route needs to be identified out of (n s! * n gi * n d!) possible routes for an onward trip (to the ZTL), and out of (n d! * n gu * n s!) possible routes for a backward trip (from the ZTL), where n gu are the possible out-gates. Referring to the Tiburtina s and Ardeatina s corridors (3 in-gates each), being 8 the capacity of each taxi-bus, it is possible to have (8 passengers having 8 different sources and 8 different destinations) n s =8, n d =8 and n gi =3, i.e. 8!*3*8! (about 5 billion) possible routes. The same for a backward trip. In order to simplify the optimisation problem to face, each route has been split into two sub-routes: boarding (the taxi-bus picks the customers up and reaches the nearest gate) and delivering (from the gate to the destination points). In such a way, 5 The index [1] refer to the Tiburtina s corridor, the index [2] to the Ardeatina s one. 7

the original optimisation problem has been split into two easier-to-solve subproblems. As a consequence, the number of possible routes for an onward trip is reduced to (n s! * n gi ) for the boarding problem and to n d! for the delivering one. Referring to the example above (n s =8, n d =8 and n gi =3), it is necessary to find out the two best routes out of two sets of 120,960 and 40,320 possible routes respectively, instead of finding out one best route out of a set of about 5 billion possible routes. For a backward trip the situation is specular: (n d! * n gu ) possible routes for the boarding problem, n s! for the delivering one. In both cases the optimisation problem is significantly simplified. For each sub-problem the best route is identified out of all possible routes. However, such procedure does not assure that the sum of the two best sub-routes is the best route for the original problem. Figure 4 shows a particular case where the best route (the sequence 1-2-3-4) is not the sum of the two best sub-routes (1-2-5 and 5-4 respectively). 4 3 ZTL 1 5 2 Figure 4. The best route is not the sum of the two optimal sub-routes The procedure of problem splitting is advantageous for two main reasons: 1. If the travel time between gates is small (e.g. a couple of minutes), the difference between the best route and the sum of the two best sub-routes is basically negligible. 2. By splitting the original optimisation problem, the number of possible routes to be explored is significantly reduced and the model runs much faster. The algorithm adopted to find out the best route for each sub-problem is the Branchand-Bound. Given a reference route whose travel time is t 0, the algorithm cuts the other possible routes as soon as their travel time is higher than t 0. If a route is found whose travel time is t 1 <t 0, such route is taken as the new reference route and the exploration continues. The algorithm excludes entire sets of routes without the necessity to evaluate the total travel time for each of them. An heuristic method has been developed to establish a proper reference route for each sub-problem. By such method, the reference trip is the one having all points to 8

visit ordered according to the ascending travel time from the starting point. A good reference route makes the exploration of all possible routes much faster, since only a limited number of complete routes need to be calculated. 5 Model application As formerly written, the micro-simulation model has been tested on two sample corridors in Rome. The capacity of each taxi-bus is fixed and equal to 8 passengers plus the driver. Departures are scheduled and frequency of trips is fixed, both towards and from the ZTL. Consequently, when the scheduled time for departure comes, the taxi-bus leaves, even if the number of customers is, in that moment, lower than the capacity of the vehicle. The taxi-bus service has been dimensioned taking into account three constraints, as follows: 1. The taxi-buses have to be able to serve, on average, 80% or more of all calls received in the peak hour, on both corridors. This constraint has been introduced to avoid taxi-buses to run nearly empty during the non-peak hours, where the demand is much lower. The 20% of customers not served at the end of the peak hour will be given the possibility to be served in the following hour or to shift to other transport means (bus, car, standard taxi, etc.). 2. The average delay to the departure time has to be 10 seconds or less. When frequency of trips is high (15 minutes or less), an average delay inferior to 10 seconds assures high regularity of services. The micro-simulation model proved than average delays of 60 70 seconds lead to maximum delays of about 15 minutes, i.e. to the cancellation of one trip (the delay is basically equal to the frequency). Delays inferior to 10 seconds, on the contrary, maintain the maximum delay generally under 4 minutes, thus leading to a high level of service to the users. 3. The average number of passengers served by each trip needs to be 7.8 or more. This constraint mirrors the point of view of the service operator. Since the trip fare is lower and the trip duration is longer than those on a standard taxi, taxibuses should carry as many passengers as possible to be economically profitable for the operator. Since the frequency of trips is fixed while calls are random, in some cases it is not possible to have 8 passengers for each trip. The microsimulation model proved that when trip frequency is high (5 minutes or less), the objective of full taxi-buses requires an excess of calls over the number of customers served that is often in conflict with the first constraint. The constraint of 7.8 passengers or more considers acceptable the possibility to have one seat vacant every 5 trips, thus conciliating the objective of maximising operator s revenues with the condition of fixed departures. The micro-simulation model has been used together with a modal split model [5]. The modal split model has been applied to four categories of travellers (car users, 9

standard taxi users, Metro users and bus users) and quantified their shift towards the new taxi-bus service. The modal split model is a binomial Logit model, based on Stated Preference data. Each interviewee has been asked to choose between his/her current choice and the new taxi-bus service under different hypothetical situations ( scenarios ). Each scenario presented different values ( levels ) of three variables: Travel time (defined as percentage increase compared to a trip on a normal taxi), Trip frequency, Trip fare (distinguishing two fare zones based on distance from the ZTL). The logic process at the basis of the joint use of the two models is outlined in Figure 5. Quantify and compare travel time on taxi-buses and normal taxis Trip frequency (reference value) Trip fare Quantify potential users of the taxi-bus service Reduce frequency and fleet Increase fleet Quantify trip delay, calls served and passengers served by each trip Increase frequency and fleet NO Is the average delay on departure < 10 s? LEGEND Micro-simulation model Modal split model Input data Conditions to be respected Changes to be made Is the 80% of calls served, on average? END Yes Yes Is the average # of passengers per trip >7.8? Yes NO NO Figure 5. Logic process for joint use of the micro-simulation and the modal split models As a first and preliminary step the micro-simulation model has been used to quantify and compare the average travel time on a taxi-bus (capacity=8) and on a normal 10

taxi 6. The micro-simulation model proved that the average travel time on a taxi-bus is about 120% higher than the average travel time on a normal taxi. The value obtained for the average travel time is basically the same on both sample corridors and independent from trip frequency and fare, demand and fleet. As a consequence, such value has been used in all further applications of the modal split model as an input datum. Once the average travel time on taxi-buses and normal taxis is known, the modal split model has been applied to quantify potential users of the taxi-bus service in relation to fixed values of trip frequency and fare (input data). Two couples of trip fares have been analysed: the first couple is 8000 Lit for the inner fare zone and 12,000 Lit for the outer one; the second couple is 10,000 Lit and 15,000 Lit. As for trip frequency, the input value is 600 s on both corridors. Trip frequency has been subsequently changed, in order to satisfy the above mentioned constraints. Once potential users are quantified through the modal split model, the input data about calls generated and attracted by each zone have been updated accordingly. Subsequently, these data have been used as input for the micro-simulation model. 50 simulation runs have been carried out, each of them simulating the behaviour of the service in the peak hour. Through micro-simulation the delay of trips, the number of passengers served by each trip and the percentage of calls served on both corridors in the peak hour have been estimated. The subsequent step consisted in verifying whether the three above mentioned constraints were satisfied on both corridors. If the first constraint is not satisfied (average delay on departure > 10 s), it is necessary to increase the number of vehicles. Variations in the number of vehicles, without any changes to frequency of trips, do not cause changes in the demand; therefore, it is not necessary to apply again the modal split model in order to quantify potential users. It is enough to apply the micro-simulation model taking into account the increased number of vehicles. If the second constraint is not satisfied (% of calls served < 80%, on average), the frequency of trips (and, consequently, the number of vehicles) need to be increased. An increase of frequency causes and increase in the demand; it is therefore necessary 6 50 simulation runs have been carried out under the following hypotheses: The warm-up interval is three hours and the simulation interval is one hour; The trip fare is 8000 Lit for the inner zone and 12,000 Lit for the outer zone; The frequency of trips is 10 minutes on both corridors; Taxi-buses run always with a number of customers equal to the capacity; There are 8 taxi-buses on each corridor; Ascent and descent times for customers are 30 s. 11

to apply the modal split model to quantify the new value of potential users. Once potential users are known, the micro-simulation model can be applied accordingly. If the third constraint is not satisfied (average customers served by each trip < 7.8), the service is over-dimensioned and taxi-buses run with few passengers. The frequency of trips (and, consequently, the number of vehicles) needs to be reduced. This causes a reduction of the demand. It is therefore necessary to apply again the modal split model prior to run the simulation again. The two models have been iteratively applied till all three constraints were satisfied on both sample corridors, thus identifying the optimal frequency of trips and number of vehicles to be assigned to each corridor. 6 Animation The taxi-bus service on Ardeatina s and Tiburtina s corridors has been animated using Proof Animation, as shown in Figure 6. Figure 6. Animation of the taxi-bus service The left side of Figure 6 schematically shows the two corridors and the ZTL. Different colours are used for call points and gate points. Similarly, taxi-buses moving towards the ZTL and taxi-buses departing from it have different colours. 12

The right side of Figure 6 dynamically shows the values of a number of statistic indicators that have been selected to analyse the taxi-bus service. The values of three input data (capacity of vehicles, activation/deactivation of the best routing algorithm, and number of vehicles in the fleet) and three output data (trips made, customers served, and km covered by the fleet) are dynamically reported. Two dynamic bars show the values of two more indicators (driving customers and running taxis). Finally, a dynamic plot draws the variation of revenues (in million Lit) of the taxi-bus fleet running on the Tiburtina s corridor. The whole daily duration of the service is animated (from 8:00 p.m. to 2:00 a.m.). 7 Results achieved As for the Tiburtina s corridor (see Table 2), the first fare solution (8000 Lit for the inner zone, 12,000 Lit for the outer one) requires 22 vehicles along the corridor, with a trip frequency of 4 minutes. Average hourly revenues in the peak hour will be 2,603,280 Lit. Considering the whole duration of the service (6 hours) the operator will get 1,735,520 Lit/hour 7, i.e. about 78,900 Lit/hour per taxi. Service characteristics Table 2. Tiburtina s corridor: results achieved Trip fare 8000/12,000 Lit 10,000/15,000 Lit Fleet 22 taxi-buses 15 taxi-buses Frequency A trip every 4 minutes A trip every 7 minutes Average delay on departure 7.6 seconds 4.0 seconds % of customers served in peak hour (average) Customers served in peak hour (average) Customers served by each trip in peak hour (average) Average hourly revenues for the entire fleet Average hourly revenues per taxi-bus 92.1% 92.6% 232.5 136.1 7.9 8.0 1,735,520 Lit 1,257,270 Lit 78,900 Lit 83,800 Lit 7 It has been assumed that customers in a peak hour are twice as many as in a non-peak hour. For more details see section 2.1 and Figure 2 in particular. 13

The second fare solution (10,000 Lit for the inner zone, 15,000 Lit for the outer one), on the other hand, requires 15 vehicles, with a trip frequency of 7 minutes. Average hourly revenues in the peak hour will be 1,885,900 Lit. Considering the whole duration of the service the operator will get 1,257,270 Lit/hour, i.e. about 83,800 Lit/hour per taxi (about 5000 Lit higher than the hourly revenues per taxi corresponding to the first fare solution). Consequently, it can be said that in a high-population-density area, as the Tiburtina s corridor, the second fare solution is surely more profitable for the service operator. However, the shift from the first fare solution to the second one causes a severe reduction in the absolute number of customers served in the peak hour (232.5 on average in the first case, 136.1 in the second one, with a loss of about 41.5% users). If the aim of the taxi-bus service is to reduce private traffic flows to and from the ZTL, the first fare solution is significantly better. As for the Ardeatina s corridor (see Table 3), the first fare solution requires 10 vehicles along the corridor, with a trip frequency of 10 minutes. Average hourly revenues in the peak hour will be 992,880 Lit. Considering the whole duration of the service (6 hours) the operator will get 661,920 Lit/hour, i.e. 66,190 Lit/hour per taxi. Service characteristics Table 3. Ardeatina s corridor: results achieved Trip fare 8000/12,000 Lit 10,000/15,000 Lit Fleet 10 taxi-buses 7 taxi-buses Frequency A trip every 10 minutes A trip every 15 minutes Average delay on departure 3.4 seconds 4.4 seconds % of customers served in peak hour (average) Customers served in peak hour (average) Customers served by each trip in peak hour (average) Average hourly revenues for the entire fleet Average hourly revenues per taxi-bus 89.7% 92.5% 95.2 62.9 8.0 8.0 661,920 Lit 550,900 Lit 66,190 Lit 78,700 Lit The second fare solution, on the other hand, requires 7 vehicles, with a trip frequency of 15 minutes. Average hourly revenues in the peak hour will be 826,400 Lit. Considering the whole duration of the service the operator will get 550,900 Lit/hour, i.e. about 78,700 Lit/hour per taxi (about 12,500 Lit higher than the hourly revenues per taxi corresponding to the first fare solution). 14

Consequently, also in a low-population-density area, as the Ardeatina s corridor, the second fare solution is more profitable for the service operator. However, as noted for the Tiburtina s corridor, the shift from the first fare solution to the second one causes a severe reduction in the absolute number of customers served in the peak hour (92.5 on average in the first case, 62.9 in the second one, with a loss of about 32.0% users). Again, if the aim of the taxi-bus service is to reduce private traffic flows to and from the ZTL, the first fare solution is significantly better. 8 Conclusions and further research The most significant feature of the micro-simulation model is its flexibility. The user has the possibility to: Decide any number of corridors where to test the model, without any constraints in their shape and dimension; Decide the capacity of vehicles; Assign to each area (corridors and ZTL) any number of source/destination points, having any co-ordinates (x,y); Assign to each corridor any number of in- and out-gates, having any co-ordinates (x,y); in-gates and out-gates may coincide, even those belonging to different corridors; Assign to each corridor any number of depots, having any co-ordinates (x,y); Fix any number of frequency classes, both for the generation and the attraction processes, assigning any frequency to each of them; Attach to each source/destination point any generation class and attraction class; generation and attraction classes can be different; Estimate travel times and distances, in order to take into account different roadnetwork loading in different time periods; Fix any number of fare zones, without any constraints in their shape and dimension, each of them having any fare; Assign to each corridor any frequency of trips; Assign to each corridor any number of taxi-buses. By properly modifying the input data, the model may be applied to other corridors in Rome or even to other cities. Possible applications of the micro-simulation model are not restricted to multi-user taxis, but extends to several other systems, even outside the transport sector. The model can be, e.g., adapted to simulate a standard taxi service, by reducing the capacity of vehicles to one 8 and changing the procedure of 8 Capacity=1 means that, if there is more than one customer served by a single trip, they all have the same origin and the same destination. 15

destination choice (the destination area is no more necessarily the ZTL). By fixing routes and stops and increasing vehicle capacity, the model can be adapted to simulate one or more bus lines. In this case, being the routes fixed, the best routing algorithm is no more necessary and the time to run the simulation is significantly reduced (despite a large increase in vehicle capacity). A freight collection and distribution service can be represented as well just changing the idea of capacity (for example capacity=1 may correspond to 100 kg of goods). As previously stated, the aim of the micro-simulation model was to test the feasibility to introduce a new taxi-bus service in Rome. The problem has been faced mainly from the point of view of the operator, thus aiming at maximising the revenues of the service. However, the introduction of such a service can generate positive externalities at the social level, by reducing the use of private cars. The authors are fully aware of the positive consequences of a reduced car use in terms of pollution, noise, etc. It is therefore necessary to formalise an optimisation problem able to take into account the operator s objective as well as the social objectives in terms of positive consequences to the community. The formalisation of such a problem will be the next step the authors will move. References [1] Henriksen, J. O.: An Introduction to SLX, Proceedings of the 1996 Winter Simulation Conference, ed. J. M. Charnes, D. J. Morrice, D. T. Brunner, J. J. Swain, 1996. [2] Henriksen, J.O. and T. Schulze: Simulation needs SLX, Otto-von-Guericke Universität Magdeburg, 1998 (in German). [3] Henriksen, J. O.: The Power and Performance of Proof Animation, Proceedings of the 1996 Winter Simulation Conference, ed. J. M. Charnes, D. J. Morrice, D. T. Brunner, J. J. Swain, 1996. [4] Wolverine Software Corporation Ed.: Using Proof Animation Second Edition, 1995. [5] Filippi, F., M. Lemessi and F. Marinucci: Study of an innovative multi-user taxi service for the city of Rome, Final Report, July 2000 (in Italian). [6] Caliper Corporation ed.: TransCAD User s Guide Version 3.0, U.S.A., 1996. [7] Laporte, G.: The traveling salesman problem: an overview of exact and approximate algorithms. European Journal of Operational Research 59, p. 231 247, 1992. 16