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Flexible services for people transportation: a simulation model in a discrete events environment
Available online at www.sciencedirect.com
Procedia Social and Behavioral Sciences 20 (2011) 846–855
14th EWGT & 26th MEC & 1st RH
Flexible services for people transportation: a simulation model in a discrete events environment Pasquale Carotenutoa,*, Artem Serebrianyb, Giovanni Storchic a
Consiglio Nazionale delle Ricerche – Istituto per le Applicazioni del Calcolo “M. Picone”, Via dei Taurini 19 – Roma 00185, Italy b ATM SpA “Azienda Trasporti Milanesi”, Via Monte Rosa, 89 – Milano 20149, Italy c University of Rome “La Sapienza” – Dpt. of Statistics Science, Piazzale Aldo Moro 5 – Roma 00185, Italy
Abstract The realization of innovative transport services requires greater flexibility and inexpensive service. In many cases the solution is to realize demand responsive transportation system. A Demand Responsive Transport System (DRTS) requires the planning of travel paths (routing) and customer pick-up and drop-off times (scheduling) according to received requests. In particular, the problem has to deal with multiple vehicles, limited capacity of the fleet vehicles and temporal constraints (time windows). A DRTS may operate according to static or dynamic mode. In the static setting, all the customer requests are known beforehand and the DRTS solves a Dial-a-Ride Problem (DaRP) instance, to produce the tour of each bus, respecting the pick up and delivery time windows while minimising the solution cost. In the dynamic mode, the customer requests arrive over time to a control station and, consequently, the solution may also change over time. In this work, we address a Demand Responsive Transport System capable of managing incoming transport demand using a two-stage algorithm by solving a DaRP instance. The solutions provided by the heuristics are simulated in a discrete events environment in which it is possible to reproduce the movement of the buses, the passengers' arrival to the stops, the delays due to the traffic congestion and possible anomalies in the behaviour of the passengers. Finally, a set of performance indicators evaluate the solution planned by the heuristics. © 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the Organizing Committee. Keywords: Discrete event simulation, Dial-a-Ride Problem, Demand Responsive Transport Sistem, Heuristics
1. Introduction The realization of innovative transport services require greater flexibility and inexpensive service. In many cases the solution is to realize demand responsive transportation system. A Demand Responsive Transport System (DRTS) requires the planning of travel paths (routing) and customer pick-up and drop-off times (scheduling) according to the received requests. In particular, it has to tackle the problem of multiple vehicles, the limited capacity of fleet vehicles and temporal constraints (time windows). The problem of working out optimal service paths and times is called a Dial-a-Ride Problem (DaRP), which derives from the well-
* Corresponding author. Tel.: +39-064-927-0926; fax: +39-064-404-306. E-mail address: [email protected]. 1877–0428 © 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the Organizing Committee doi:10.1016/j.sbspro.2011.08.093
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known Vehicle Routing Problem (VRP) (Toth and Vigo, 2002), with the addition of precedence constraints between pick-up and drop-off locations (Cordeau and Laporte, 2003b) The most common example arises in door-to-door transportation services for elderly or disabled people (see, e.g., Madsen et al. 1995; Toth and Vigo 1996, 1997; Borndörfer et al. 1997; Colorni and Righini 2001; Diana and Dessouky 2004; Rekiek et al. 2006; Melachrinoudis et al. 2007). From a modelling point of view, the DaRP generalizes a number of vehicle routing problems such as the Pickup and Delivery Vehicle Routing Problem (PDVRP) and the Vehicle routing Problem with Time Windows (VRPTW), see Cordeau et al. (2007a, 2007b, 2007c). Although an exact three-index formulation for the DaRP has been presented by Cordeau (2006) and a more compact two-index formulation has been proposed by Ropke et al. (2007), the computational complexity makes VRP, PDVRP, VRPTW and DaRP NP-hard problems, so that attempts to develop optimal solutions are steel limited to simple and small-size problems. It can be argued that heuristic procedures are more suitable for realistic networks and demand, because they allow good solutions to be attained in a limited amount of time. In the DaRP, customers formulate requests for transportation from a given origin-destination pair (i.e., from a pick-up point to a delivery point). Transportation is carried out by vehicles that provide a shared service. Hence, several customers may be in the same vehicle at the same time. Since the DaRP is a special Vehicle Routing Problem with Pickup and Delivery (VRPPD) (Savelsbergh and Sol, 1995; Cis, 2004) including restrictions on the time at which each point may be visited by a vehicle, the problem of finding a feasible pick up and delivery plan is NP-hard. Clearly, the DaRP has to take into account specific constraints as we are considering people instead of goods. As a consequence, each customer specifies a possible pickup and delivery time, as well as an upper bound on the riding time (Coslovich, et al., 2006). Furthermore, in this context, customers often formulate two requests per day, specifying an outbound request from the pick-up point to a destination and an inbound request for the return trip. Classical DaRP instances consider the vehicle capacity constraints as tight. A DRTS may operate according to static or dynamic mode. In the static setting, all the customer requests are known beforehand and the DRTS solve DaRP instance, to produce the tour of each bus, respecting the pick up and delivery time windows while minimising the solution cost using single vehicle (Psaraftis, 1980; Sexton, 1979; Sexton and Bodin, 1985a and 1985b; Desrosiers et al.1986) or multiple vehicle (Jaw et al., 1986; Toth and Vigo, 1997; Borndörfer et al., 1997; Uchimura et al., 1999; Cordeau and Laporte, 2003a; Aldaihani and Dessouky, 2003, Diana and Dessouky, 2004; Bergvinsdottir et al., 2004; Rekiek et al., 2006; Xiang et al., 2006; Wong and Bell, 2006; Wolfer Calvo and Colorni, 2006; Melachrinoudis et al. 2007; Jørgensen et al., 2007). In the dynamic mode, the customer requests arrive over time to a control station and, consequently, the solution may also change over time. Also in this case single vehicle (Psaraftis, 1980; Gendreau et al., 2001) or multiple vehicles can be used (Madsen et al., 1995; Jih and Hsu, 1999; Teodorovic and Radivojevic, 2000; Colorni and Righini, 2001; Coslovich et al., 2006; Carotenuto et al. 2006). 2. Technological initiatives and European Projects to support the DRTS In the last years, in many European Countries research program and pilot projects have been funded. DRTS have been realized to integrate, to extend and also to improve the transport public service for the disadvantaged consumers and in the districts with low level of demand. In these applications, the Intelligent Transport Systems (ITS) have played a key role as interface toward the potential services users as a tool of both optimization and management of travel requests. Some of the main technological initiatives to support the DRT services are: x PowerDriverDTSS® (RoutingPlanner) has been developed by Powersoft. It is constituted by an hardware and software architecture based on proprietary algorithms. Such solution furnishes a transport service comparable to a taxi service, it is able to accept the reservations while the vehicles are running, optimize the route and it is able to create door to door services; x MobiRouter was realized in Finland. It could considerably increase the use of DRTS since it can be easily integrated with the public transport system. MobiRouter reacts to new requests immediately and can modify a route with only a few minutes notice if necessary. Its functionality can be both service line-style transportation and freely routed, taxi-style transportation;
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x Optitod, realized in France, is a software package very similar to that previously described and manages detailed reports on the remarkable information of the service; x NOVUS has been realized in Canada. It is an easy-to-use solution designed to help the transport operators to manage the unique needs of their demand response transportation service. It ensures accurate scheduling solutions with flexible mapping and accurate report in a variety of formats; x RING has been realized in Belgium and it is a system for the management of the DRT services in the Region of the Flanders and around the region of Bruxelles; x InterConnect has been implemented in England in the suburban zone of the Lincolnshire. The system picks up the travel requests both through telephone and through Internet up to 30 minutes before the collecting. The key strategy of InterConnect is to use some hubs of interchange to facilitate and to optimize the connection among the different routs of the vehicle. x PersonalBus, realized in Italy by Softeco Sismat for the management of the Public Demand Responsive Transport Service, is a tool that offers a service characterized by "dynamic run-vehicle" without predefined time-schedule, with available vehicle to the stops only when necessary, without constraints on the run to follow and with the possibility of using web-pages for the bookings; x Telebus, realized in Italy by PluService, allows the collection of the transport requests by telephone or by internet. The system processes the requests and gives an optimized vehicle path solution displaying it on cartographic base. The satellite tracking and connectivity to the vehicles allow real time interaction and the a service call with already running vehicles. 3. Flexible Transport system Demand responsive transport systems are a form of flexible transportation that can provide service in rural or suburban areas where a regular bus service may not be as viable or adequate. Depending on the requested system flexibility we have several modes of operation: x it will be restricted to a defined operating zone, within which journeys must start and finish on the base of flexible schedules; x door to door transport service which provides the maximum flexibility; x reconfigurable route service with designated bus stops. The latter operation mode is the approach that we are going to describe in this paper. This operation mode offer a trade-off between a regular fixed transit route service (low cost but not flexible transportation) and a taxi service (very flexible but with high cost for passengers). Demand Responsive Transport System can be distinguished in service in which the customer has to make a booking to a central dispatcher, for example one day before the travel, or in real-time service that quickly answers passenger requests. In both cases the customers contact the service centre by telephone, or Sms or Internet and they book their journey. The requests are processed by the service centre in their arrival order. Passengers are picked up and dropped off in accordance with their needs (location and time); so customers are not tied to a conventional public transport system. Automated vehicle location systems are used to provide information about status and location of the fleet in order to assign passengers to vehicles in real time and to plan previous booked journeys. The presented modelling approaches and applications always refer to deterministic situations in which noise due to congestion or failure of agreed arrival of the user to stop is not considered. Our approach instead aims at estimating how much degrades the a priori solution found with a deterministic algorithm in the presence of noise. To do this, we used a discrete event simulation environment to simulate the commercial road network in which the system operates and the user behaviour, but integrating in it the algorithm that operates in the real context. In this paper, we present the simulation model and validation tests before its integration in the route planning algorithm. 4. The algorithmic framework In figure 1 we can see the algorithmic framework (Carotenuto et al. 2006) used to produce the operational plan used in our simulations. The route planning algorithm is composed of two procedures: a multi-vehicle insertion heuristic and an hybrid genetic algorithm. In the operational phase the route planning algorithm starts from an initial operational plan (empty for examples). When a new request arrives the multi-vehicle insertion heuristic tries to
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insert the request in the route of a vehicle of the fleet. If it finds an admissible solution, the request is accepted, otherwise it is rejected. The outcome is quickly communicated. Hence an hybrid genetic algorithm is recalled to improve the operational plan up to a new event occurs. These events can be the arrival of a new requests, but also a user picked up or dropped off by a vehicle. To build the simulation model of our DRTS we have implemented the following steps: the booking requests have been generated in a random way using excel and visual basic routines; these requests are been processed by the heuristic to produce an executive plan that is finally stored in the database; the network has been arranged using AVM data and GIS tools to get times and distances of the passengers pick-up or delivery points; the communication between the database an the simulation software has been faced by integrating three different programming languages (Visual Basic, Siman and SQL language); the control of the entities during the simulation (vehicles and users) has been realized by means of automated procedures and functions of the Siman object library. Finally about 170 database instances have been prepared to do meaningful simulation tests. In this context we have developed several models to gradually increase the fitness and the flexibility of the simulation model. New user takes the bus
User leaves the bus
Requests
Boarded users
Hybrid Genetic Algorithm
New Request
Operative Starting Program
Multi-vehicle Insertion Heuristics
•Improves solution •Runs until new event happens •Update operative program
Operative Program
•Acceptance •Rejection •Fast response
Figure 1. Algorithmic framework
5. The discrete event simulation model The discrete event simulation model has been implemented with the Arena software. This simulation software allows to build a graphic representation of real processes using behavioural module. In this way an entities that advance in the model reproduce the behaviour of the entities in the real system. During the realization phase of the model we have replaced the simple modules used in the first configuration with more complicated modules to achieve more flexibility and programmability. To this aim, the use of the VBA modules has been fundamental. The final model realized can be defined as: a model feeded in automatic way capable to modelling services with high flexibility.
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Phase 1 - Preparation and allocation of transport requests
Phase 2 - management of user arrivals to the stops
Figure 2a. The implemented simulation model: Phase 1 and 2.
The model consist of three main phases (see figure 2a and 2b): preparation and allocation of transport requests; management of user arrivals to the stops; transport of users to destination. In these three phases the algorithmic framework play a fundamental role: it manages and optimizes the transportation requests giving an operational plan on which works the simulation model. In the first phase the simulation generates the transportation request. The generated entity crossing the module in the model acquires some information from the algorithmic framework stored in the database: for example, the assigned time and the location for pick-up and delivery. Based on the acquired information, the entities are prepared and sorted by the last module in their respective waiting queue ready for the second phase of the model. The most important module in this first preparation phase is the VBA module that manage inside the assignment operations and the communication with the database. When an entity crosses the VBA block its control is passed to a Visual basic assignment sub-procedure, that embeds a SQL statement to allow the entity to communicate with the database and acquire the necessary information that has been elaborated by the algorithmic framework. At the end of this operation, a Siman procedure is employed for the control of the entity. This procedure makes visible all the assignments to the logical flow level in the model as attributes of the entity. The second phase of the model manages the arrivals of users to the stops: they will be picked up by the vehicle of the transportation system based on their “origin” attribute. This happens in three phases: transfer of the user entity to the stop; waiting by the user until his arrival time and placing of the entity in the queue of the stop. Crossing the blocks of the model, the “users” entity have a delay and it is released in time for its arrival to the stop. Finally, the
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entity is located in a queue that develops two functions: to hold the entities users up to the moment of their pick-up and to make the entity users visible to the “vehicles” entity in the model.
Phase 3 - Transport of users to destination.
Figure 2b. The implemented simulation model: Phase 3.
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The third phase of the model (see figure 2b) manages the physical transport of users and the procedures to automate the transport. It begins with the creation of the “drivers” entities. In this phase, the drivers entities, acquire the necessary data for users transportation. This phase ends when the simulation time ends or when all the scheduled transport request have been suited. During the simulation, the entities vehicles are controlled by the “ActiveEntity” Siman function. This function acts as a sort of “satellite localizer” connected with all the entities in the model. It allows the knowledge of the exact position of each entity at each time. In this way it is possible to change the technical and operational characteristics of entities at any time during the simulation, allowing a frequent update of some parameters to better control the transport phase. In particular, third stage of the model can be split into seven steps: x Acquisition of data related to the first reservation to be satisfied. This first step is to create a "driver" entity and to acquirie the data to go to the place of the first reservation. The data are acquired by the "driver" entity as attributes when the "driver" entity enters the VBA block and connects to the database (see figure 2b, topmost left). x Request and allocation of the vehicle and waiting for the first user to stop. This second step consists of a series of logical checks preceding the expected users in the "delay", module, the subsequent allocation of the vehicle and exit from the deposit (see figure 2b, topmost - right) x Movement of the vehicle from depot to the origin of the request. The third step concerns the movement of the vehicle towards the origin location of the request and the identification of users to pick up assigned to that specific vehicle (see figure 2b, middle – left). x Pick up of the users at bus stops. The fourth step corresponds to the effective pick up of identified users (pick-up module, see figure 2b, middle). The pick up phase is not constrained by the capacity. The optimization algorithm takes into account the capacity of the vehicles during the requests acceptance phase. x Acquisition of data about the next mission. The fifth step (VBA module, see figure 2b, middle - right) concerns the communication of the pick up outcome and the verification that there are no other users to picking up. In this last case the vehicle moves towards the next destination that is indicated by the optimizer. x Transport of users to their destinations based on information acquired from the database. The sixth step concerns the movement of the vehicle toward the destination of the request and the drop off of all users designed in that station (see figure 2b, bottommost – left). x Waiting for subsequent users or simulation end. The last step evaluates whether to continue the simulation or to finish the service. The end of service occurs for two reasons: lack of reservations or end of the working shift. 6. The Ostia-Acilia test case The proposed simulation model has been applied to a real case study: the suburban area of Ostia-Acilia. In this suburban area the public bus service is suppressed in high days and it is replaced by on demand bus services. The objective of the public transport agency was to rationalize the service reducing the number of vehicles/km and improving the service in terms of reliability and reduction of the waiting times. The Ostia-Acilia area is characterized by a demand level of 82 daily bookings, the fleet is composed of 1 vehicle with 9 seats. The service cover an area of about 12 km/sq with 23 stops. The users reserve the transport calling a toll-free number with at least 2 hours of warning. In the implementation phase the topology of the network has been re-arranged, the number and the location of the stops (23 points of pick-up and delivery) has been rationalized and in some cases several stops have been merged in only one. Moreover a GIS software, has been used for reconstructing the distances between among every pick-up or delivery point. Different typologies of random instances have been produced using the same level of demand and with the fleet dimension varying by 1 to3 and up to 5 vehicles and then successively varying the demand level in the range of {20, 80, 160, 240} requests. For each typology, 7 instances have been produced by randomly generating pickup and delivery points. 84 total simulation test have been performed. 2 indexes have been used to evaluating the performance of the service related to users expectations and service utilization. The indexes are: the total users average waiting time and the vehicles usage. The lower usage indexes corresponds to a demand level of 20 requests and 5 cars, while the average waiting time and usage indexes improve according to the increasing demand level. This behaviour is common to both the simulation model and the route planning algorithm.
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As the topmost graph of figure 3 shows, the average waiting time to the stops decrease by fixing the number of cars, increasing the number of requests and unchanging the coverage zone of the service. It is common to different situation and it is a sort of economy of scale. It seems that the system work better with lower total average waiting time by increasing both the demand level and the number of vehicles. The bottommost graph in figure 3 depicts the vehicle usage index for fixed fleet and varying the number of requests. The number of requests is not enough to saturate the usage of vehicles, but from a certain point on the vehicle usage index keeps the same course. Both the simulation model and the route planning algorithm provided the same results. Therefore the simulation model can be used to evaluate the behaviour of the system by introducing in it some annoyance elements.
Average waiting time (1 vehicles) Average waiting time (3 vehicles) Average waiting time (5 vehicles)
Requests
Averag vehicles usage index (1 vehicles) Averag vehicles usage index (3 vehicles) Averag vehicles usage index (5 vehicles)
Requests
Figure 3. Average waiting time to the stops with respect to the number of vehicles and the number of requests (top). Variation of the percentage of the average usage index with respect to the number of vehicles and the number of requests (bottom).
7. Conclusions The technological solutions presented in the second paragraph, have similar characteristics. Some solutions work in an integrated fashion with urban services (Mobirouter, Optitod), other solutions preferably work in peripheral areas of the city (Ring Interconnect), other solutions still provide accurate scheduling and solution reports in a variety of formats (NOVUS) or finally they acquire the transportation requests before the service starts or with already running vehicle (Power Driver DTSS, Telebus, Interconnect, Personal Bus). All the analysed models work using one stage to accept and optimize the transport plan. On the contrary, the proposed model works in two stage: when a new request arrives the multi-vehicle insertion heuristic tries to insert the request in the route of a vehicle of the fleet. If it finds an admissible solution, the request is accepted, otherwise it is rejected. The outcome is quickly communicated. Subsequently, an hybrid genetic algorithm is recalled to improve the operational plan. At this stage (behavioural validation phase) the proposed model is useful when more scenarios need to be evaluated in the planning phase, when we have to estimate the dimension of the fleet and the behaviour of the system, and also to simplify the managerial approach by graphically animating what the mathematical model has
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performed. The tests show that the behaviour of the model agree with the results of the heuristic, therefore the model can be considered validated. The final goal is to simulate external annoying factors that are not considered by the heuristic algorithm. To this aim, we have to integrate the two stage algorithm in the simulation model. In this way, it is possible to make a Dynamic re-assignment and evaluate the effect of the annoyance.
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Procedia Social and Behavioral Sciences 20 (2011) 846–855
14th EWGT & 26th MEC & 1st RH
Flexible services for people transportation: a simulation model in a discrete events environment Pasquale Carotenutoa,*, Artem Serebrianyb, Giovanni Storchic a
Consiglio Nazionale delle Ricerche – Istituto per le Applicazioni del Calcolo “M. Picone”, Via dei Taurini 19 – Roma 00185, Italy b ATM SpA “Azienda Trasporti Milanesi”, Via Monte Rosa, 89 – Milano 20149, Italy c University of Rome “La Sapienza” – Dpt. of Statistics Science, Piazzale Aldo Moro 5 – Roma 00185, Italy
Abstract The realization of innovative transport services requires greater flexibility and inexpensive service. In many cases the solution is to realize demand responsive transportation system. A Demand Responsive Transport System (DRTS) requires the planning of travel paths (routing) and customer pick-up and drop-off times (scheduling) according to received requests. In particular, the problem has to deal with multiple vehicles, limited capacity of the fleet vehicles and temporal constraints (time windows). A DRTS may operate according to static or dynamic mode. In the static setting, all the customer requests are known beforehand and the DRTS solves a Dial-a-Ride Problem (DaRP) instance, to produce the tour of each bus, respecting the pick up and delivery time windows while minimising the solution cost. In the dynamic mode, the customer requests arrive over time to a control station and, consequently, the solution may also change over time. In this work, we address a Demand Responsive Transport System capable of managing incoming transport demand using a two-stage algorithm by solving a DaRP instance. The solutions provided by the heuristics are simulated in a discrete events environment in which it is possible to reproduce the movement of the buses, the passengers' arrival to the stops, the delays due to the traffic congestion and possible anomalies in the behaviour of the passengers. Finally, a set of performance indicators evaluate the solution planned by the heuristics. © 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the Organizing Committee. Keywords: Discrete event simulation, Dial-a-Ride Problem, Demand Responsive Transport Sistem, Heuristics
1. Introduction The realization of innovative transport services require greater flexibility and inexpensive service. In many cases the solution is to realize demand responsive transportation system. A Demand Responsive Transport System (DRTS) requires the planning of travel paths (routing) and customer pick-up and drop-off times (scheduling) according to the received requests. In particular, it has to tackle the problem of multiple vehicles, the limited capacity of fleet vehicles and temporal constraints (time windows). The problem of working out optimal service paths and times is called a Dial-a-Ride Problem (DaRP), which derives from the well-
* Corresponding author. Tel.: +39-064-927-0926; fax: +39-064-404-306. E-mail address: [email protected]. 1877–0428 © 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the Organizing Committee doi:10.1016/j.sbspro.2011.08.093
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known Vehicle Routing Problem (VRP) (Toth and Vigo, 2002), with the addition of precedence constraints between pick-up and drop-off locations (Cordeau and Laporte, 2003b) The most common example arises in door-to-door transportation services for elderly or disabled people (see, e.g., Madsen et al. 1995; Toth and Vigo 1996, 1997; Borndörfer et al. 1997; Colorni and Righini 2001; Diana and Dessouky 2004; Rekiek et al. 2006; Melachrinoudis et al. 2007). From a modelling point of view, the DaRP generalizes a number of vehicle routing problems such as the Pickup and Delivery Vehicle Routing Problem (PDVRP) and the Vehicle routing Problem with Time Windows (VRPTW), see Cordeau et al. (2007a, 2007b, 2007c). Although an exact three-index formulation for the DaRP has been presented by Cordeau (2006) and a more compact two-index formulation has been proposed by Ropke et al. (2007), the computational complexity makes VRP, PDVRP, VRPTW and DaRP NP-hard problems, so that attempts to develop optimal solutions are steel limited to simple and small-size problems. It can be argued that heuristic procedures are more suitable for realistic networks and demand, because they allow good solutions to be attained in a limited amount of time. In the DaRP, customers formulate requests for transportation from a given origin-destination pair (i.e., from a pick-up point to a delivery point). Transportation is carried out by vehicles that provide a shared service. Hence, several customers may be in the same vehicle at the same time. Since the DaRP is a special Vehicle Routing Problem with Pickup and Delivery (VRPPD) (Savelsbergh and Sol, 1995; Cis, 2004) including restrictions on the time at which each point may be visited by a vehicle, the problem of finding a feasible pick up and delivery plan is NP-hard. Clearly, the DaRP has to take into account specific constraints as we are considering people instead of goods. As a consequence, each customer specifies a possible pickup and delivery time, as well as an upper bound on the riding time (Coslovich, et al., 2006). Furthermore, in this context, customers often formulate two requests per day, specifying an outbound request from the pick-up point to a destination and an inbound request for the return trip. Classical DaRP instances consider the vehicle capacity constraints as tight. A DRTS may operate according to static or dynamic mode. In the static setting, all the customer requests are known beforehand and the DRTS solve DaRP instance, to produce the tour of each bus, respecting the pick up and delivery time windows while minimising the solution cost using single vehicle (Psaraftis, 1980; Sexton, 1979; Sexton and Bodin, 1985a and 1985b; Desrosiers et al.1986) or multiple vehicle (Jaw et al., 1986; Toth and Vigo, 1997; Borndörfer et al., 1997; Uchimura et al., 1999; Cordeau and Laporte, 2003a; Aldaihani and Dessouky, 2003, Diana and Dessouky, 2004; Bergvinsdottir et al., 2004; Rekiek et al., 2006; Xiang et al., 2006; Wong and Bell, 2006; Wolfer Calvo and Colorni, 2006; Melachrinoudis et al. 2007; Jørgensen et al., 2007). In the dynamic mode, the customer requests arrive over time to a control station and, consequently, the solution may also change over time. Also in this case single vehicle (Psaraftis, 1980; Gendreau et al., 2001) or multiple vehicles can be used (Madsen et al., 1995; Jih and Hsu, 1999; Teodorovic and Radivojevic, 2000; Colorni and Righini, 2001; Coslovich et al., 2006; Carotenuto et al. 2006). 2. Technological initiatives and European Projects to support the DRTS In the last years, in many European Countries research program and pilot projects have been funded. DRTS have been realized to integrate, to extend and also to improve the transport public service for the disadvantaged consumers and in the districts with low level of demand. In these applications, the Intelligent Transport Systems (ITS) have played a key role as interface toward the potential services users as a tool of both optimization and management of travel requests. Some of the main technological initiatives to support the DRT services are: x PowerDriverDTSS® (RoutingPlanner) has been developed by Powersoft. It is constituted by an hardware and software architecture based on proprietary algorithms. Such solution furnishes a transport service comparable to a taxi service, it is able to accept the reservations while the vehicles are running, optimize the route and it is able to create door to door services; x MobiRouter was realized in Finland. It could considerably increase the use of DRTS since it can be easily integrated with the public transport system. MobiRouter reacts to new requests immediately and can modify a route with only a few minutes notice if necessary. Its functionality can be both service line-style transportation and freely routed, taxi-style transportation;
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x Optitod, realized in France, is a software package very similar to that previously described and manages detailed reports on the remarkable information of the service; x NOVUS has been realized in Canada. It is an easy-to-use solution designed to help the transport operators to manage the unique needs of their demand response transportation service. It ensures accurate scheduling solutions with flexible mapping and accurate report in a variety of formats; x RING has been realized in Belgium and it is a system for the management of the DRT services in the Region of the Flanders and around the region of Bruxelles; x InterConnect has been implemented in England in the suburban zone of the Lincolnshire. The system picks up the travel requests both through telephone and through Internet up to 30 minutes before the collecting. The key strategy of InterConnect is to use some hubs of interchange to facilitate and to optimize the connection among the different routs of the vehicle. x PersonalBus, realized in Italy by Softeco Sismat for the management of the Public Demand Responsive Transport Service, is a tool that offers a service characterized by "dynamic run-vehicle" without predefined time-schedule, with available vehicle to the stops only when necessary, without constraints on the run to follow and with the possibility of using web-pages for the bookings; x Telebus, realized in Italy by PluService, allows the collection of the transport requests by telephone or by internet. The system processes the requests and gives an optimized vehicle path solution displaying it on cartographic base. The satellite tracking and connectivity to the vehicles allow real time interaction and the a service call with already running vehicles. 3. Flexible Transport system Demand responsive transport systems are a form of flexible transportation that can provide service in rural or suburban areas where a regular bus service may not be as viable or adequate. Depending on the requested system flexibility we have several modes of operation: x it will be restricted to a defined operating zone, within which journeys must start and finish on the base of flexible schedules; x door to door transport service which provides the maximum flexibility; x reconfigurable route service with designated bus stops. The latter operation mode is the approach that we are going to describe in this paper. This operation mode offer a trade-off between a regular fixed transit route service (low cost but not flexible transportation) and a taxi service (very flexible but with high cost for passengers). Demand Responsive Transport System can be distinguished in service in which the customer has to make a booking to a central dispatcher, for example one day before the travel, or in real-time service that quickly answers passenger requests. In both cases the customers contact the service centre by telephone, or Sms or Internet and they book their journey. The requests are processed by the service centre in their arrival order. Passengers are picked up and dropped off in accordance with their needs (location and time); so customers are not tied to a conventional public transport system. Automated vehicle location systems are used to provide information about status and location of the fleet in order to assign passengers to vehicles in real time and to plan previous booked journeys. The presented modelling approaches and applications always refer to deterministic situations in which noise due to congestion or failure of agreed arrival of the user to stop is not considered. Our approach instead aims at estimating how much degrades the a priori solution found with a deterministic algorithm in the presence of noise. To do this, we used a discrete event simulation environment to simulate the commercial road network in which the system operates and the user behaviour, but integrating in it the algorithm that operates in the real context. In this paper, we present the simulation model and validation tests before its integration in the route planning algorithm. 4. The algorithmic framework In figure 1 we can see the algorithmic framework (Carotenuto et al. 2006) used to produce the operational plan used in our simulations. The route planning algorithm is composed of two procedures: a multi-vehicle insertion heuristic and an hybrid genetic algorithm. In the operational phase the route planning algorithm starts from an initial operational plan (empty for examples). When a new request arrives the multi-vehicle insertion heuristic tries to
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insert the request in the route of a vehicle of the fleet. If it finds an admissible solution, the request is accepted, otherwise it is rejected. The outcome is quickly communicated. Hence an hybrid genetic algorithm is recalled to improve the operational plan up to a new event occurs. These events can be the arrival of a new requests, but also a user picked up or dropped off by a vehicle. To build the simulation model of our DRTS we have implemented the following steps: the booking requests have been generated in a random way using excel and visual basic routines; these requests are been processed by the heuristic to produce an executive plan that is finally stored in the database; the network has been arranged using AVM data and GIS tools to get times and distances of the passengers pick-up or delivery points; the communication between the database an the simulation software has been faced by integrating three different programming languages (Visual Basic, Siman and SQL language); the control of the entities during the simulation (vehicles and users) has been realized by means of automated procedures and functions of the Siman object library. Finally about 170 database instances have been prepared to do meaningful simulation tests. In this context we have developed several models to gradually increase the fitness and the flexibility of the simulation model. New user takes the bus
User leaves the bus
Requests
Boarded users
Hybrid Genetic Algorithm
New Request
Operative Starting Program
Multi-vehicle Insertion Heuristics
•Improves solution •Runs until new event happens •Update operative program
Operative Program
•Acceptance •Rejection •Fast response
Figure 1. Algorithmic framework
5. The discrete event simulation model The discrete event simulation model has been implemented with the Arena software. This simulation software allows to build a graphic representation of real processes using behavioural module. In this way an entities that advance in the model reproduce the behaviour of the entities in the real system. During the realization phase of the model we have replaced the simple modules used in the first configuration with more complicated modules to achieve more flexibility and programmability. To this aim, the use of the VBA modules has been fundamental. The final model realized can be defined as: a model feeded in automatic way capable to modelling services with high flexibility.
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Phase 1 - Preparation and allocation of transport requests
Phase 2 - management of user arrivals to the stops
Figure 2a. The implemented simulation model: Phase 1 and 2.
The model consist of three main phases (see figure 2a and 2b): preparation and allocation of transport requests; management of user arrivals to the stops; transport of users to destination. In these three phases the algorithmic framework play a fundamental role: it manages and optimizes the transportation requests giving an operational plan on which works the simulation model. In the first phase the simulation generates the transportation request. The generated entity crossing the module in the model acquires some information from the algorithmic framework stored in the database: for example, the assigned time and the location for pick-up and delivery. Based on the acquired information, the entities are prepared and sorted by the last module in their respective waiting queue ready for the second phase of the model. The most important module in this first preparation phase is the VBA module that manage inside the assignment operations and the communication with the database. When an entity crosses the VBA block its control is passed to a Visual basic assignment sub-procedure, that embeds a SQL statement to allow the entity to communicate with the database and acquire the necessary information that has been elaborated by the algorithmic framework. At the end of this operation, a Siman procedure is employed for the control of the entity. This procedure makes visible all the assignments to the logical flow level in the model as attributes of the entity. The second phase of the model manages the arrivals of users to the stops: they will be picked up by the vehicle of the transportation system based on their “origin” attribute. This happens in three phases: transfer of the user entity to the stop; waiting by the user until his arrival time and placing of the entity in the queue of the stop. Crossing the blocks of the model, the “users” entity have a delay and it is released in time for its arrival to the stop. Finally, the
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entity is located in a queue that develops two functions: to hold the entities users up to the moment of their pick-up and to make the entity users visible to the “vehicles” entity in the model.
Phase 3 - Transport of users to destination.
Figure 2b. The implemented simulation model: Phase 3.
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The third phase of the model (see figure 2b) manages the physical transport of users and the procedures to automate the transport. It begins with the creation of the “drivers” entities. In this phase, the drivers entities, acquire the necessary data for users transportation. This phase ends when the simulation time ends or when all the scheduled transport request have been suited. During the simulation, the entities vehicles are controlled by the “ActiveEntity” Siman function. This function acts as a sort of “satellite localizer” connected with all the entities in the model. It allows the knowledge of the exact position of each entity at each time. In this way it is possible to change the technical and operational characteristics of entities at any time during the simulation, allowing a frequent update of some parameters to better control the transport phase. In particular, third stage of the model can be split into seven steps: x Acquisition of data related to the first reservation to be satisfied. This first step is to create a "driver" entity and to acquirie the data to go to the place of the first reservation. The data are acquired by the "driver" entity as attributes when the "driver" entity enters the VBA block and connects to the database (see figure 2b, topmost left). x Request and allocation of the vehicle and waiting for the first user to stop. This second step consists of a series of logical checks preceding the expected users in the "delay", module, the subsequent allocation of the vehicle and exit from the deposit (see figure 2b, topmost - right) x Movement of the vehicle from depot to the origin of the request. The third step concerns the movement of the vehicle towards the origin location of the request and the identification of users to pick up assigned to that specific vehicle (see figure 2b, middle – left). x Pick up of the users at bus stops. The fourth step corresponds to the effective pick up of identified users (pick-up module, see figure 2b, middle). The pick up phase is not constrained by the capacity. The optimization algorithm takes into account the capacity of the vehicles during the requests acceptance phase. x Acquisition of data about the next mission. The fifth step (VBA module, see figure 2b, middle - right) concerns the communication of the pick up outcome and the verification that there are no other users to picking up. In this last case the vehicle moves towards the next destination that is indicated by the optimizer. x Transport of users to their destinations based on information acquired from the database. The sixth step concerns the movement of the vehicle toward the destination of the request and the drop off of all users designed in that station (see figure 2b, bottommost – left). x Waiting for subsequent users or simulation end. The last step evaluates whether to continue the simulation or to finish the service. The end of service occurs for two reasons: lack of reservations or end of the working shift. 6. The Ostia-Acilia test case The proposed simulation model has been applied to a real case study: the suburban area of Ostia-Acilia. In this suburban area the public bus service is suppressed in high days and it is replaced by on demand bus services. The objective of the public transport agency was to rationalize the service reducing the number of vehicles/km and improving the service in terms of reliability and reduction of the waiting times. The Ostia-Acilia area is characterized by a demand level of 82 daily bookings, the fleet is composed of 1 vehicle with 9 seats. The service cover an area of about 12 km/sq with 23 stops. The users reserve the transport calling a toll-free number with at least 2 hours of warning. In the implementation phase the topology of the network has been re-arranged, the number and the location of the stops (23 points of pick-up and delivery) has been rationalized and in some cases several stops have been merged in only one. Moreover a GIS software, has been used for reconstructing the distances between among every pick-up or delivery point. Different typologies of random instances have been produced using the same level of demand and with the fleet dimension varying by 1 to3 and up to 5 vehicles and then successively varying the demand level in the range of {20, 80, 160, 240} requests. For each typology, 7 instances have been produced by randomly generating pickup and delivery points. 84 total simulation test have been performed. 2 indexes have been used to evaluating the performance of the service related to users expectations and service utilization. The indexes are: the total users average waiting time and the vehicles usage. The lower usage indexes corresponds to a demand level of 20 requests and 5 cars, while the average waiting time and usage indexes improve according to the increasing demand level. This behaviour is common to both the simulation model and the route planning algorithm.
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As the topmost graph of figure 3 shows, the average waiting time to the stops decrease by fixing the number of cars, increasing the number of requests and unchanging the coverage zone of the service. It is common to different situation and it is a sort of economy of scale. It seems that the system work better with lower total average waiting time by increasing both the demand level and the number of vehicles. The bottommost graph in figure 3 depicts the vehicle usage index for fixed fleet and varying the number of requests. The number of requests is not enough to saturate the usage of vehicles, but from a certain point on the vehicle usage index keeps the same course. Both the simulation model and the route planning algorithm provided the same results. Therefore the simulation model can be used to evaluate the behaviour of the system by introducing in it some annoyance elements.
Average waiting time (1 vehicles) Average waiting time (3 vehicles) Average waiting time (5 vehicles)
Requests
Averag vehicles usage index (1 vehicles) Averag vehicles usage index (3 vehicles) Averag vehicles usage index (5 vehicles)
Requests
Figure 3. Average waiting time to the stops with respect to the number of vehicles and the number of requests (top). Variation of the percentage of the average usage index with respect to the number of vehicles and the number of requests (bottom).
7. Conclusions The technological solutions presented in the second paragraph, have similar characteristics. Some solutions work in an integrated fashion with urban services (Mobirouter, Optitod), other solutions preferably work in peripheral areas of the city (Ring Interconnect), other solutions still provide accurate scheduling and solution reports in a variety of formats (NOVUS) or finally they acquire the transportation requests before the service starts or with already running vehicle (Power Driver DTSS, Telebus, Interconnect, Personal Bus). All the analysed models work using one stage to accept and optimize the transport plan. On the contrary, the proposed model works in two stage: when a new request arrives the multi-vehicle insertion heuristic tries to insert the request in the route of a vehicle of the fleet. If it finds an admissible solution, the request is accepted, otherwise it is rejected. The outcome is quickly communicated. Subsequently, an hybrid genetic algorithm is recalled to improve the operational plan. At this stage (behavioural validation phase) the proposed model is useful when more scenarios need to be evaluated in the planning phase, when we have to estimate the dimension of the fleet and the behaviour of the system, and also to simplify the managerial approach by graphically animating what the mathematical model has
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performed. The tests show that the behaviour of the model agree with the results of the heuristic, therefore the model can be considered validated. The final goal is to simulate external annoying factors that are not considered by the heuristic algorithm. To this aim, we have to integrate the two stage algorithm in the simulation model. In this way, it is possible to make a Dynamic re-assignment and evaluate the effect of the annoyance.
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