Voz del cliente

After running the simulation model, the following observations were drawn for the month that included the security incident:

u the number of chassis on terminal has increased by 4.2% because fewer trucks were able to use them;

u the number of full containers on terminal has increased by 19.6%;

u the number of empty containers on terminal has increased by 16.8%;

u the average queue for trucks at the police gates has increased by 188.6%; and

u an increase in the truck turnaround time by 4.4%.

Figures 6 and 7 show the difference in the moving average of the trucks’

turnaround time without and with the incident scenario, respectively. The moving average was calculated in increments of 2.5 hours and as can be seen

in Figure 4, there is a clear increase in turnaround time due to increased security at day 15 (hour 360 on the x axis). The turnaround time eventually goes back to normal port operations at hour 465. It should be noted, however, that even after the security went back to normal (after four days), the trucks’

turnaround time stayed relatively high and did not go back to normal until nine hours later.

From the results, one can conclude that due to tightened security trucks were having problems getting on terminal and, therefore, the number of chassis and containers increased as there were not enough trucks to pick them up. Not only does this impact container throughput, but may also have a serious terminal congestion problem due to container storage space limitations.

Another important impact caused by the scenario is the large increase in the police gate queue. Obviously such a queue will impact the highways and roads around the terminal, causing traffic congestion and backups.

Figure 6: Truck Turnaround Time under Normal Conditions

Figure 7: Truck Turnaround Time with a Security Incident

4 C O N C L U S I O N S

A discrete-event simulation model was developed for port operations in a US marine intermodal terminal. The main objective of the model is to evaluate

the impact of security scenarios on port recoverability, i.e. its ability to go back to normal operations. The model captures the movements of full and empty containers from sea to inland and vice versa. It also includes the movements of trucks, train and ships, which are modelled as dynamic entities. Terminal gates are modelled as recourses with specific capacities, while straddle car-riers, cranes and transtrainers are modelled as transporters. Model inputs and stochastic processes are based on historical data that was fitted to statistical distributions to reflect the variability in the real system. The model was then validated by comparing its output to historical data whenever possible, and by presenting the output to subject-matter experts whenever data was unavail-able. To demonstrate the proposed approach for risk evaluation, a hypothetical scenario was implemented and tested to show its impact on port recovery in terms of throughput, delays and queue times. The simulation results for the hypothetical scenario showed that the number of containers and chassis on terminal, as well as the truck turnaround time would increase significantly, while the police gate queue time might be unacceptable. An estimate of how long it will take for the terminal to go back to normal can also be obtained by comparing the simulation runs with and without the scenario.

The simulation model can be further utilized by the port authority to evaluate additional security and business scenarios. In the future, this model can be extended beyond the terminal’s gates to evaluate the impact on the transportation network (e.g. traffic congestion) and supply-chain security.

R E F E R E N C E S

Kelton, W.D., Sadowski, R.P. and Sturrock, D.T. (2004) Simulation with Arena, 3rd edn, McGraw Hill.

Koh, P-H., Goh, J., Ng, H-S. and Ng, H-C. (1994) ‘‘Using Simulation to Preview Plans of Container Port Operations’’, Proceedings of the 1994 Winter Simulation Conference, eds J.D. Tew, S. Manivannan, D.A. Sadowski and A.F. Seila.

Law, A.M. and Kelton, W.D. Simulation Modeling and Analysis, 3rd edn, McGraw Hill, (2000).

Leathrum J.F., Mielke, R.R., Mazumdar, S., Mathew, R., Manepalli, Y., Pillai, Y., Malladi, R.N. and Joines, J. (2004) ‘‘A simulation architecture to support intratheater sealift operations’’, Mathematical and Computer Model-ling, 39(6–8), pp. 817–838.

Legato, P. and Mazza, R.M. (2001) ‘‘Berth planning and resources optimisa-tion at a container terminal via discrete event simulaoptimisa-tion’’, European Journal of Operational Research, 133(3), 537–547.

Nagle, K. (2005) ‘‘Nation’s Ports Concerned About Security, Harbor Dredg-ing FundDredg-ing Shortfalls in Fy’06 Budget’’, The Propeller Club Quarterly, Spring, 13–14.

Parola, F. and Sciomachen, A. (2005) ‘‘Intermodal container flows in a port system network: Analysis of possible growths via simulation models’’, Inter-national Journal of Production Economics, 97, 75–88.

Shabayek, A.A. and Yeung W.W. (2002) ‘‘A simulation model for the Kwai Chung container terminals in Hong Kong’’, European Journal of Operational Research, 140(1), 1–11.

Talley, W.K. (2006) ‘‘An Economic Theory of the Port’’, Port Economics:

Research in Transportation Economics, eds, K. Cullinane and W. Talley, Vol.

16, 43–66. Amsterdam, Elsevier.

S E C U R I T Y A N D R E L I A B I L I T Y O F T H E L I N E R C O N TA I N E R - S H I P P I N G

N E T WO R K : A N A LY S I S O F R O B U S T N E S S U S I N G A C O M P L E X N E T WO R K

F R A M E WO R K

Panagiotis Angeloudis, Khalid Bichou and Michael G.H. Bell Port Operations Research and Technology Centre (PORTeC), Centre for

Transport Studies, Imperial College London, UK

Abstract

Since the events of 9/11, more focus has been given to the role of sea ports as critical nodes in the functioning and security of international shipping and logistics, with particular emphasis being placed on container ports and terminals. However, little or no work has addressed the robustness and the reliability of the container port network, be it at the level of terminal operating systems or at the level of international trade and logistics patterns.

In this chapter, ports and scheduled liner containership services between Western Europe and North America are modelled as the nodes and links of a global network. Following recent work in urban transportation, the properties of the network are examined in the context of complex network theory, with particular reference to error and attack robust-ness. Generic frameworks and a hypothetical case study are presented to identify points in the network where failure would lead to a wider collapse.

1 I N T R O D U C T I O N

The theory of complex networks is a fast growing field of applied mathematics.

Having its roots in the random graph model by Erd ¨os and Ranyi (1959), interest in the field has been sparked by the recent development of the small-world and scale-free models by Watts and Strogatz (1998). Studies on the subject have shown interesting results in fields as diverse as ecology and social science, possibly the most famous being the discovery that on average only six degrees of separation exist between any two people selected at random.

Networks such as the air travel grid, road and subway systems have been analysed this way (Angeloudis and Fisk, 2006; Albert et al., 2002; Dunne et al., 2002), but the technique has yet to find application in other major transportation networks. There has been parallel interest in the application of complex networks theory to supply-chain topologies, regarding such aspects as robustness, resilience and agility (Swaminathan et al., 1998; Thadakamalla

95

et al., 2004). Nevertheless, there has been little or no use of the theory in the context of sea port and maritime transport networks.

Traditionally, international shipping networks have followed a trade-led pattern where new routes are opened and operated to link two or multiple markets, ideally on the basis of a balanced traffic. In liner shipping, much of the world’s containership capacity is deployed to serve within one or a combination of the three major trade lanes: the trans-Pacific; the trans-Atlantic; and the Europe–Asia routes. However, both traffic and operational constraints regard-ing traffic type and volume, route distance and seasonal variations, container-ship’s size and capacity, etc., have forced shipping lines to develop new operational patterns in an effort to optimize ship utilization and efficiency. The key point is that the pattern of routes is not master planned but has evolved from many micro decisions. Evolving complex networks such as hub-and-spoke and transhipment routes are a common feature of today’s liner routes, although neither model (in its current format) has succeeded in achieving optimal solutions with regard to the combination of economic, capacity, safety and scalability constraints.

In the post-9/11 era, the robustness and survivability of the maritime network against node failures is a high priority. Research to date has looked at different but fragmented areas of network robustness including such aspects as system vulnerability, risk avoidance, mitigation strategies and supply-chain resilience. In ports and shipping available models of risk assessment and attack avoidance, be it regulatory-based (e.g. the ISPS port facility security plan) or industry-led (e.g. the Lloyd’s Register See-threat programme), only identify risk elements based on logical mapping of internal processes, but there has been no applied research on the robustness of the shipping network link (route) and node (port/terminal) topology, quite apart from the perspective of the complex network theory (Bichou, 2005).

Current maritime transport networks have been designed to respond to an extensive set of market and operational requirements, but their robustness and reliability vis- `a-vis random or targeted failures have long been taken for granted.

We emphasize that system or node failure could be trigged by a variety of precursors and not just malicious or unexpected actions such as terrorist attacks.

Examples of node failure causes include industrial strikes, ship collision or safety incidents, government or regulatory measures such as port closure in extreme weather conditions, and any other operational incidents in ports (damage to ship’s structure while being operated at quay, system failure for automated terminals, etc.) or at intermodal interfaces (e.g. road network congestion).

This study proposes to investigate the robustness properties of the current liner-shipping routes using complex networks theory. We build a shipping network linking European and North American sea ports based on current liner routes, and use a simulation model specifically developed for the purpose of this study to test and analyse the robustness of the network. The subject of this paper is part of a larger project aiming to model the global liner network

and link it to selected port and intermodal networks in order to investigate its survivability and scalability with respect to a variety of objectives, including operational efficiency, system resilience and flexibility, as well as the design of optimal connectivity solutions. This chapter only reports on selected aspects of network robustness and node failure.

The remainder of the chapter is structured as follows. Section 2 briefly describes trade versus operational patterns in liner shipping, while section 3 reviews the literature on the complex network theory and its applications to date. Section 4 describes the dataset and the network architecture before reporting the results of the simulation model. Section 5 concludes with sum-maries and suggestions for future research.

2 R E V I E W O F O P E R AT I O N A L PAT T E R N S I N L I N E R S H I P P I N G

The international shipping industry may be divided into two different cate-gories: tramp shipping and liner shipping. Industrial shipping may be a third category, but this is generally treated as a closed and separate market. Unlike tramp ships that operate in the spot market and thus can go everywhere at any time, liner shipping consists of pre-scheduled and regular maritime routes linking fixed ports and terminals. Containerships operate on different markets and routes according to a number of criteria. The routes are normally those between two trade markets (supply and demand) with a range of ports being visited between and at either side of the route. Trade routes or lanes ideally link two or multiple markets based on an equitable traffic pattern and any other relevant requirements. Route optimization in this approach follows from the formulation of origin–destination (O/D) models, and much of the literature on shipping network planning and design falls into this category (see for instance Iakovou et al., 1999; Beuthe et al., 2001).

Too often though, traffic is unbalanced between regions in either or both direction and could be stable on some routes while variable on others. This can result from structural or seasonal variations but is sometimes due to the nature of the route, for instance, in terms of distance, traffic type and cargo volume. Similarly, the growth in containership size makes it less profitable for carriers to call at every port on their journey. For such reasons and others, the problem of liner network routing has been reduced to a ship’s scheduling problem (Bendall and Stent, 2001, Christiansen, et al., 2004; Fagerholt, 2004) and different operational patterns have evolved through the years. This means that within one or a combination of trade lanes, a different logistics pattern is undertaken to ensure optimum ship utilization and efficiency. Major operational patterns in liner shipping include the end-to-end, pendulum, triangular, hub-and-spoke, double-dipping and round-the-world services.

Finally, it is worth underlining that many aspects of maritime network design under supply-chain constraints and uncertainty remain largely unexplored in

the maritime and ports literature, contrary to the great amount of scholarly work on the subject for inland-based distribution networks.

Figure 1: Description of Selected Operational Patterns in Liner Shipping

3 O V E RV I E W O F C O M P L E X N E T W O R K T H E O RY

Random graphs are one of the earliest and most extensively studied network models. They are defined as networks with N nodes and n links which are assigned at random. On the opposite side of the network model spectrum, one encounters regular networks, where link creation adheres to strict rules.

Watts and Strogatz (1998) propose a network model that interpolates between regular and random networks by applying a random rewiring proce-dure on a regular ring lattice, as shown in Figure 2. In a variant to this model, Newman and Watts (1999) propose the ‘‘small world’’ model where the edges are added randomly between vertices without removing others in the ring lattice. Networks produced by this process have a smaller average shortest path length compared to a similar random graph network. The name of the model originates from its roots in social systems and more specifically from a well-known experiment by social psychologist Stanley Milgram who discov-ered that there are on average six degrees of separation between any two residents in the United States. Another property of small worlds is an increased clustering coefficient, which is used to quantify the tendency of

E n d -to -E n d Services

nodes in various parts of the network to form interconnected groups with many links within them, but only few between them. For a node i with kilinks, the local clustering coefficient Ci is obtained through the following relationship:

Ci = 2Ei

ki (ki − 1)

where Eiis the number of edges between the ki nodes. The overall clustering coefficient of the network is the average of all the local values.

Scale-free networks were introduced by Barabasi and Albert (1999) in order to explain the behaviour of many real world systems (like the WWW) that could not be adequately modelled as random networks. According to the model, the number of links k originating from a given node adheres to a power law P(k) ~ k^−y, which for large networks is free of a characteristic scale. This effectively means that some nodes will have an exceptionally large number of links when compared to the vast majority of nodes in the network. Scale-free network are thought to be created by a process of preferential attachment (‘‘the rich get richer’’), whereby new nodes will be more likely to be linked to existing nodes with a higher degree (number of links) in order to benefit from their increased connectivity to other parts of the network.

Figure 2: Illustration of the Small-world Rewiring Procedure (from Watts and Strogatz, 1998)

When studying scale-free networks, more emphasis is given to their robust-ness against errors and robustrobust-ness against attacks, which effectively represent two different strategies of node removal. In the investigation of error robust-ness, the underlying assumption is that nodes to be removed are selected at random in order to simulate the likely impact of evenly distributed operational errors on the network’s robustness. Regarding attack robustness, the modeller must hold sufficient prior information about the system, which is then targeted strategically with a view to maximizing the impact. Scale-free networks exhibit an exceptional degree of robustness against random node failures due to the dominance of few hubs over their topology. The situation is reversed in the case of intentional attacks, since major hubs are relatively easy to identify.

Soon after the initial publication of the two network types in the late 1990s, a movement began among researchers to model real world networks. Systems that have been modelled using such approaches include food webs, power grids,

rail and subway networks and supply-chain configurations (see, for instance, Albert et al., 2002; Angeloudis et al., 2006; Dunne et al., 2002). Nonetheless, we are not aware of any application of complex networks theory to shipping and ports, particularly in the contexts of security and system reliability.

Figure 3: Node Failure Scenarios in Scale-Free Networks. (from Albert et al., 2003)

4 M O D E L L I N G L I N E R S H I P P I N G R O U T E S