Proceedings of the IEEE ITSC 2006 2006 IEEE Intelligent Transportation Systems Conference Toronto, Canada, September 17-20, 2006
WA7.4
A Petri net modelling approach of intermodal terminals based on Metrocargoc system Angela Di Febbraro, Guido Porta , Nicola Sacco Abstract— To cope with the growing demand of moving freight, an innovative system for easily and quickly manage c containers moved by trains, named Metrocargo , has been designed. The leading idea of such a system is to speed up the operations of loading/unloading containers on/from trains, with the goal of assimilating goods to passengers in transportation, thus increasing the flexibility of the whole system and, possibly, optimising the space allocation inside each terminal. In this framework, whereas the performances of such a system appear to be promising, no models to evaluate them have been proposed yet. Then, to achieve this task, in the c paper a model of Metrocargo intermodal terminals based on timed Petri nets is presented, which allows to easily define a modular, performance-evaluation oriented representation of the considered system.
I. I NTRODUCTION In the last decade, the changes in the market have resulted in a growing need for moving freight. In general, transportation services are not only being required to deliver faster, but also to be more flexible and reliable. In this framework, intermodality appears as a mandatory strategy for a sustainable development of freight transport. As a consequence, a two-fold necessity is put significantly into evidence: on one hand, to better exploit the capacity of railway networks for freight transportation, and, on the other, to design and develop new technologies and management policies for intermodal freight terminals. An intermodal freight terminal, thought of as a node of a transportation network, can be viewed as a manufacturing plant where nothing is really “produced”, but its output consists in services, so an efficient material handling system is essential to an adequate functioning. In this sense, the system promptness in reacting to the time-varying demand requirements becomes a key feature to take into account when designing a model of an intermodal freight terminal, in order to prevent broken flows through the logistics chain as a whole [1]. The possibility yielded by railroads of moving cheaply large freight volumes is a major reason why intermodal terminals, seen as the sites where the switches between two different transport modes are operated, assume a key role in the whole freight transportation system. Then, making intermodal systems efficient means both to minimise delays, and to reduce costs and environmental impacts. Efficient DIMSET, University of Genova, Via Montallegro 1, 16145 Genova, Italy,
[email protected] ILOG srl, Genova, Italy
[email protected] DAUIN, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy,
[email protected]
1-4244-0094-5/06/$20.00 ©2006 IEEE
technologies of loading/unloading cargoes from a transport mode to another make it possible to eliminate, or at least to decrease the diseconomy, and to obtain a more effective intermodality. Intermodal terminals often are rarely located along the railway lines, so typically a link is required, which involves great delivery times and costs. In addition, nowadays containers are loaded vertically in a sequential and not in a parallel way, which means that trains have to be moved out of the rail line using diesel traction, loaded and formed, and then brought back to the electrical railroad. For such reasons, the actual average loading/unloading time is about 4 hours, with a remarkable employment of tracks and cranes, and critical aspects about the safety and the tracing of cargo units [2]. Moreover, freight transport by rail is almost totally effected through “block trains” moving from point to point (e.g., from a port to a cargo area), without intermediate stops. To be advantageous, such a system should be characterised by large volumes and steady flows, determining a remarkable rigidity of the service, that cannot compete with road transport in terms of flexibility and delivery times. On the other hand, intermodality [3] must employ efficient load transfer technologies to use rail for long distances, and trucking for collecting and delivering in limited areas. Moreover, an efficient intermodal service should be formed by a network of shuttle trains with a fixed composition, preset itineraries and schedules, and a number of interchange terminals where unitised freight is transferred from one train to another, as it happens for passengers in a normal net service. Such a characteristics should guarantee an overall economy and relevant benefits for the community in terms of pollution, traffic fluidity, and road accidents. c intermodal transport system The innovative Metrocargo was developed according to the above outlined philosophy and, starting from the restrictions of the traditional railway system, it is intended to yield technical and organisational solutions. In this paper, a model of an intermodal freight terminal c is defined, intended to evaluate the based on Metrocargo system performances and to define control and optimisation procedures. The proposed model makes use of Petri nets, and exploits their capabilities to suitably represent the synchronisation requirements in the concurrent use of shared resources [4]. In the following sections, after a brief description of the c (Sec. II), and the definition of main features of Metrocargo Timed Petri Nets (Sec. III), the proposed model is introduced (Sec. III-A). Some conclusions and indications about the relevant work in progress end the paper.
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Fig. 1.
c A detailed representation of an intermodal terminal based on Metrocargo .
c II. M ETROCARGO
In this section, a description of the main characteristics c of an intermodal terminal equipped with Metrocargo are introduced. The basic idea is that such a system will use scheduled trains on fixed itineraries, with fixed composition and stops, regularly placed at 100-200km intervals in industrial areas, and farther apart in areas that are not economically relevant. The stations (i.e., the intermodal terminals) are preferably located outside cities, in areas near major roads or motorways, or placed at the intersections of railroad lines as knot terminals. These features allow a high integration among the different modes. In the following sections, the main characteristics of the terminals architecture and the main operations are described.
•
A. The Architecture c From a general point of view, the core of the Metrocargo terminals consists of a technology based on a technique of horizontal translation, that allows to operate under the electric feeding line. Moreover, the railway is placed between two motorised rollers and chains, arranged in synchronised modules, that are used for displacing cargo units in the c to operate terminal. Such characteristics allows Metrocargo effectively near the already existing railroads. More precisely, as pointed out in Fig. 1, it is possible to identify the following elements: • containers, which represent the freight units managed by any terminal. They enter the terminal by means of trucks or trains, and have to be redirected towards their destinations by means of other trucks or trains; • roller ways, which are made up of independent sectors (10m long, 3m wide), longitudinally positioned to a distance of about 2m one from each other. Each sector is independently powered in such a sequence to move bidirectionally load units to the desired position. Due
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•
to their (standard) sizes, containers may interest either only a part sector, or a whole sector. Moreover, each sector has an independent electric motor, automatically activated by an integrated system of photocells just when a load unit approaches, and de-activated as soon as such a unity has passed. As depicted in Fig. 1, there are three roller ways which are used to pickup/delivery containers from a truck (roller way A), or to load (resp., unload) containers on a train (roller way B (resp., C)); load/unload devices, which have a combined system for the longitudinal and transversal movements; both movements are controlled by photocells that guarantee centring the load units with respect to the train wagons. Moreover, load units have twist-locks sticking out from the base plan, so special pallets are interposed to move the freight units on the roller ways. Therefore, there is a double flow of containers and empty pallets, although pallets are only used within the terminal and are not loaded on trains. In addition, it is worth underlining that, when the train is gone, load/unload devices make a “temporary bridge” which connects the two longitudinal B and C roller ways, thus allowing to move the unloaded units either to the stocking areas for further reshipment, or to the trucks loading area for local delivery; storage areas, which are used to store containers. In the general framework, as depicted in Fig. 1, there are three “buffers” which are used to collect containers to be loaded, just loaded, or waiting for in a stocking area; such buffers are based on the same technology of independent sections and, for this reason, are completely automated. In particular, as regards the storage area which gathers the containers to load, it is divided into n “destination sub-buffers”, as depicted in Fig. 2 for n = 4, each one including the containers to be loaded on a particular train. For the example considered in the
above mentioned figure, the storage area is subdivided for the four destinations {A, B, C, D}, and it is easy to note that three containers are waiting for the train A, five containers are waiting for the train B, and so on. In addition, a container is entering the buffer. trains: A
B
C
D
way before (possibly just in time) the corresponding train arrives; 2) collecting and redistributing the containers unloaded from the last arrived train. It is worth noting that the actions here described mainly consist in moving containers along the independent sectors of rollers and buffers, as described above. Due to these characteristics, the system here described can be suitably represented as a discrete event dynamic system [6], where the beginning/ending of each operation represents an event. For instance, train arrivals or departures are events just as, on the other hand, the container movement from a sector of a roller way to another is an event. Thus, the intermodal terminal architecture introduced in the previous section can be suitably represented via timed Petri nets, which are a graphic and mathematical modelling tool suitable to represent several systems, and, more specifically, all those systems presenting such particular characteristics as concurrency, distribution, parallelism, nondeterminism, and/or stochasticity.
Fig. 2. The stocking area for containers to load. In such a buffer, containers are positioned taking into account their destinations. •
trains and trucks, which move containers between terminals, or from (resp., towards) their origin (resp., destination) inside the terminal.
B. The Operations In this section, a description of the operations of the whole system is given. In such a framework, only the “macrooperations” are considered, whereas the “micro-operations” (i.e., the mechanics of each element) performed by the system in any single action are neglected. Anyway, the reader can refer, for example, to [5] for a detailed description of the system. Then, the main behaviour of the system consists of the following steps: 1) cargo units that reach the terminal, by track or by rail, are positioned by roller ways in the storage area according to their destinations; 2) when a train is going to arrive, the relevant units are pre-addressed and temporarily stocked on the roller way near the railway line; 3) when a train reaches the station, the units are directly unloaded from/loaded on it using a proprietary loading machine; 4) when the train has gone, the two longitudinal roller ways are connected by a temporary bridging made by the loading devices, to move the unloaded units to the storage bays for further reshipment, or to the trucks loading area for local delivery. In addition, other macro-operations of paramount importance consist of managing the automated stocking areas with the aim of preparing the buffers of containers to load or unload. They mainly consists in the following two actions: 1) gathering the containers with a common destination in a sub-buffer, and distributing them along the B roller
III. BASICS OF TIMED P ETRI NETS In this section, the basic characteristics and properties of Petri nets (PN) are introduced. For a detailed review about Petri nets, the reader can refer, for instance, to [7]. Definition 1: A timed marked Petri net TPN is a six-tuple TPN = {P, T, P re, P ost, M0 , Θ} where • P is a finite non-empty set of n = card(P ) places p1 , . . . , pn ; • T is a finite non-empty set of m = card(T ) transitions t1 , . . . , tm ; • P re is a [n × m] matrix (the pre-incidence matrix) whose element P rei,j is equal to w if an arc with a positive weight w joining pi and tj exists, and 0 otherwise; • P ost is a [n × m] matrix (the post-incidence matrix) whose element P osti,j is equal to w if an arc with a positive weight w joining tj and pi exists, and 0 otherwise; • M0 is the initial marking vector; • Θ is the firing time vector. The set {P, T, P re, P ost} defines the structure of the TPN, whereas the marking and the firing time vectors rule its time evolution. The marking vector Mk , which specifies the number of tokens present in each place of the TPN, represents the state of the net. In addition, to be able to fire, any transition must fulfill the following constraint: Definition 2: A transition tj is enabled, i.e., is allowed to fire, by a marking M if M(pi ) ≥ P rei,j ,
∀ pi ∈ P
i.e., if any place pi of the Petri net has a number of tokens equal or greater than P rei,j .
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Rule 1: Firing Rule When a transition tj , enabled by marking M, fires, the marking of the net changes according to the state equation M = M + P ost − P re · etj = M + C · etj where M and M are the markings before and after the firing, respectively. In addition, C is the incidence matrix, and etj ∈ Nn0 1 is the characteristic vector, whose elements correspond to the number of firings of each transition tl ∈ T which have led M to M . From a dynamical point of view, the firing of an enabled transition tj , removes P rei,j tokens from each input place pi of tj and adds P osti,j tokens to each output place pl of tj . In this work, PNs will be used to model systems, i.e., wagons, conveyer bets, etc., which intrinsically have a finite capacity. For this reason, it is of paramount importance to introduce the concept of finite capacity for PNs. Definition 3: The capacity of a PN is defined as the function C : P → N+ 0 which assigns to each place the maximum admissible value that its marking can assume. In a PN with finite capacity, the firing of a transition must follow the Rule 1 and the following Rule 2. Rule 2: Strict firing. Any transition tj ∈ T is enabled only if each output place pi ∈ t•j will not exceed C(pi ) after the firing. Hereafter, the considered TPNs will be assumed to have finite capacity and, for the sake of clearness, the values C(pi ) = 1 are not indicated in the model. In addition, as regards the timing of a PN, the firing times of transition tj are gathered in vector ϑj = [ϑj,1 ϑj,2 . . . ϑj,k . . .]T , being ϑj,k a positive number specifying the (deterministic or stochastic) duration of the kth firing of tj . If ϑj,k = 0, ∀ k, then tj is said to be an immediate transition, whereas, if ϑj,k > 0, tj is a timed transition. Note that times ϑj,k can be a-priori known, if they are deterministic, or can represent samples of an assigned probability function, if they are stochastic. To conclude, the vector Θ = [ϑ1 ϑ2 . . . ϑm ]T gathers the vectors of the firing times of all transitions tj . The TPN representation of a given system, and in particuc , can be obtained by applying a suitable lar of Metrocargo modular synthesis which directly descends from the PN definition. As regards the graphical representation of PNs, places are drawn as circles, immediate transitions are drawn as bars, and timed transitions are depicted as black boxes. Moreover, arcs are represented by arrows. c A. Timed Petri Net Model of Metrocargo
To this end, consider the simplified structure of a c terminal reported in Fig. 3. With respect to Metrocargo the more realistic representation of Fig. 1, in Fig. 3 only the main structures are represented, that is, the stocking area 1 of the unloaded containers (SA1), the stocking area 2 of the stocked containers waiting for a train (SA2), and the stocking area 3 of the containers to load (SA3), the railroad, the roller ways A, B, and C (hereafter indicated with RW), and the load/unload devices. Then, to simplify the graphical representation, the stocking area 2 is not included in the proposed PN model. In effects, the dynamics of such a part of the system is similar to the dynamics of the stocking areas 1 and 3. In addition, in the representation of Fig. 3, several kinds of containers are depicted, so as to underline their destinations. Their characterisation is reported in Fig. 4. container already on the train stocked container container to load on the next train container to load on the arrived train container to unload from the train Fig. 4.
Characterisation of containers in Fig. 3.
As regards the TPN of the structure represented in Fig. 3, consider the net depicted in Fig. 5. In such a net, for the sake of clearness, some arcs are not reported, and the notation > tj (resp., > pi ) indicates an arc which is originated by transition tj (resp., place > pi ). Analogously, the notation tj > (resp., pi >) indicates an arc which is directed towards transition tj (resp., the place > pi ). Moreover, all the places of the net can contain only one token (C = 1), apart from place pL (resp., pU ), which can contain nL (resp., nU ) tokens that represent the finite loading (resp., unloading) resources. For what concerns the detailed description of the structure of the PN of Fig. 5, the reader can refer to tables I and II, which gather the meanings of all places and transitions of the net. On the other hand, for what concerns the timings of a timed transition ti , the relevant elements of vectors Θ represent the execution times of the operations associated with such transitions. Finally, as regards the dynamical behaviour of the whole net, it is worth pointing out that any operation described in Sec. II-B consists of a sequence of events, which corresponds in the PN representation to a sequence of transition firings. For example, consider the arrival of a truck with a container to put in second sub-buffer of the SA 3. Thus, the sequence of 2,3 3,4 1,2 event/firing {tU tr , tA , tA , t2 , t2 } “move” the token, i.e., A the container, from place p2 to place p22 , i.e., from the truck unloading resource to its destination in the buffer.
In this section, the TPN model of a intermodal terminal c system is described. based on Metrocargo
IV. C ONCLUSIONS AND FUTURE WORK
1 Nn is the n-dimensional vectorial space of non-negative integer num0 bers.
In this paper, a modelling approach via timed Petri nets has been presented for an intermodal freight terminal employing
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roller way C load/unload devices
train
roller way B
1
buffer
3
2
roller way A unloading truck Fig. 3.
loading truck
c A simplified layout of an intermodal terminal based on Metrocargo technology.
TABLE I
TABLE II
P LACES OF THE PN IN F IG . 5.
T RANSITIONS OF THE PN IN F IG . 5.
Place p pn ptr pen pdis pU pL pgi , i = 1, . . . , 6, g = {A, B, C} pir , j = 1, 2, 3 pij , j = 1, 2, 3, i = 1, 2, 3 pV j , j = 1, . . . , 6
Meaning (if marked)
Transition
there is a train at the terminal there are no trains at the terminal there is a truck to load a container the removable buffer is enabled the removable buffer is disabled wagons are enabled to unload containers wagons are enabled to load containers a container is in position i of the RW g a container is in position i of the backward buffer a container is in position i of the buffer j there is a container on wagon i
a recently designed automated system for managing containc ers, named Metrocargo . The proposed model exploits the valuable feature of high modularity, proper to Petri nets. Work is in progress about using the devised structure both for performance evaluation, and for defining and testing control and optimisation policies by means of SPSA (Simultaneous Perturbation Stochastic Approximation) optimisation algorithm, which has been proven to be suitable to optimise discrete event systems and hybrid systems [8], [9]. R EFERENCES [1] C. Degano and A. Di Febbraro, “Modelling automated material handling in intermodal terminals,” Proc. 2001 IEEE Int. Conf. on Advances in Mechatronics AIM01, pp. 1318–1323, July 2001. [2] European Commission, “Relaunching the european railroads. toward an integrated european railway space, luxemburg,” 5th Framework Program of Research, 2002. [3] ——, “Recordit project (real cost reduction of door-to-door intermodal trasport),” 5th Framework Program of Research, 2002. [4] P. Kemper and M. Fischer, “Modeling and analysis of a freight terminal with stochastic petri nets,” Proc. 9th IFAC Symposium “Control in Transportation Systems”, vol. 2, pp. 295–300, 2000.
Meaning
tarr
a train arrives at the terminal
tdep
a train departs from the terminal
ten
enables the removable buffer
tdis
disables the removable buffer
trem
a container moves to the rem. buffer
ti,i+1 , i = 1, 2, j
a container moves from position i
j = 1, 2, 3 or j = r
to i + 1 in the buffer j
ti,i+1 , i = 1, . . . , 5, g
a container moves from position i
g = {A, B, C}
to i + 1 in the RW g
ti,i−1 , g
a container moves from position i
i = 2, . . . , 6,
g = {A, B, C}
to i − 1 in the RW g
tj , j = 1, 2, 3 or j = r
a container enters buffer j
tLW , i = 1, . . . , 6 i
a container is loaded on wagon i
tU i , i = 1, . . . , 6 tL i , i = 1, . . . , 3 tU r tarr tr tU tr tL tr
a container is unloaded from wagon i a container enters RW B from buffer i a container enters RW A from buffer r a truck arrives to load a container a truck unload a container in RW A a truck load a container from RW A
[5] “Feasibility study of a prototype of “innovative system of intermodal transport”,” Technological and Scientific Park of the Liguria Region, Genoa, Italy, 2005. [6] C. G. Cassandras and S. Lafortune, Introduction to Discrete Event Systems. Kluwer Academic Publishers, 1999. [7] T. Murata, “Petri Nets: Properties, Analysis and Applications,” Proceedings IEEE, vol. 77, no. 4, pp. 541–580, 1989. [8] M. C. Fu and S. D. Hill, “Optimization of discrete event systems via simultaneous perturbation stochastic approximation,” IIE Transactions, vol. 29, pp. 233–243, 1997. [9] F. Dabbene, P. Gay, N. Sacco, and C. Tortia, “Optimisation of freshfood supply chains in uncertain environments: an application to meat refrigeration processes,” Proc. 2005 IEEE 44th Int. Conf. on Control and Decision, pp. 2077–2082, December 2005.
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Fig. 5.
Timed Petri net representation.
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p dis
t arr
p
nL
t dep
pn
t en
t dis
pL
L i
t >
L i
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nU
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2,3
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p 11
L
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1,2
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tB
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4,3
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tC
2,3
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p 31
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t
t
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p>
p U>
>p
p C3
p 12
L
t2
4,3
tA
3,4
tA
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5,4
tC
t2
1,2
t2
p 22
2,3
t2
p 32
5,4
tB
4,5
tB
>pL
p V4
U 4
LW 4
t
t
p A4
p>
p B4
pL >
>p
p>
p U>
>p
p C4
5,4
L
t3
p B5
p>
p 13
4,5
tA
>pU
6,5
tC
t3
1,2
t3
p 23
2,3
t3
p 33
6,5
tB
5,6
tB
>pL
p V5
U 5
LW 5
t
t
p A5
p>
>p pL >
tA
p C5
>p p U>
4,5
tC
>p
6,5
tA
5,6
tA
p 14
L
t4
p>
pL >
>p
>pU
7,6
tC
t4
1,2
t4
p 24
2,3
t4
p 34
p B6 t 7,6 B
6,7
tB
>pL
p V6
U 6
LW 6
t
t
p C6
p A6
p>
p U>
5,6
tC
>p
>p
7,6
tA
6,7
tA
p 15
L
t4
p>
pL >
arr
t tr
p A7
t5
1,2
t5
p 25
8,7
8,7
tA
7,8
tA
8,7
tC
7,8
tC
ptr
7,8
tB
tB
2,3
t5
p 35
p B7
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t
t
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L
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p C8
