Simulation modeling of Houston Ship Channel vessel traffic for optimal closure scheduling

Simulation Modelling Practice and Theory 80 (2018) 89–103

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Simulation modeling of Houston Ship Channel vessel traffic for optimal closure scheduling Behnam Rahimikelarijani, Arash Abedi, Maryam Hamidi∗, Jaeyoung Cho Department of Industrial Engineering Lamar University, Beaumont, TX 77710, USA

a r t i c l e

i n f o

Article history: Received 27 June 2017 Revised 19 October 2017 Accepted 27 October 2017

Keywords: Ship channel operations Discrete event simulation Optimal closure schedule

a b s t r a c t This paper focuses on simulation and analysis of the Houston Ship Channel vessel traffic and operation, through a discrete event model in Arena. The model is applied to mitigate the consequences of the channel closure for constructing a new bridge over the waterway. To evaluate different closure scenarios, real world data is analyzed, and a single factor ANOVA is used to find significant vessel waiting time differences. In addition, Fisher pairwise comparison method is applied to specify the best closure alternative. The results reveal that the best closure scenario will decrease waiting time up to 70%. The model can be used for assessing the performance of the system under different decision making frameworks. © 2017 Elsevier B.V. All rights reserved.

1. Introduction The Port of Houston, ranked second in US in terms of overall tonnage, has a significant role in the country’s economic growth. In 2014, 210.7 million tons of cargo were imported and exported through the port of Houston, equal to 16.1% of Texas state GDP. Public and private terminals along the Houston Ship Channel (HSC) created 1,666,216 direct, indirect, induced and related jobs, $75.4 billion income, $405.6 billion economic output and $21.2 billion state and local taxes in 2014 [1]. The channel is frequently subject to scheduled and unscheduled closures due to maintenance, deepening, dredging, construction projects, oil spills, fog and thunder storms. Temporarily closures cause delays, customer dissatisfaction, rerouting to alternative ports, increased operational costs for ports and carriers. As a result of increased fuel consumption, closures have environmental impact, including increased CO2 emissions, as well [2]. Historical data shows that HSC was subjected to 17 and 20 days of closure in 2015 and 2016, respectively. The major focus of this paper is on the best closure schedule for Sam Houston bridge construction over the channel. Since demurrage cost is calculated based on extra waiting time, in this study the effect of channel closure is determined based on waiting time imposed to vessels. The contribution of this paper is three fold; first a model is developed which simulates the logic of vessel operations throughout the waterway, second the real world data of vessel operations such as arrival rate and operation time at docks are analyzed and the results are presented, and finally the model is applied to determine the best closure schedule with

Abbreviations: ANOVA, Analysis of variance; CON, Container ship; GEN, General cargo; LPG, Liquefied petroleum gas; RORO, Roll-on/Roll-off; T&B, Tug and Barge; TCO, Chemical/Oil tanker; TNK, Tanker; TPD, Product Tanker. ∗ Corresponding author. E-mail addresses: [email protected] (B. Rahimikelarijani), [email protected] (A. Abedi), [email protected] (M. Hamidi), [email protected] (J. Cho). https://doi.org/10.1016/j.simpat.2017.10.004 1569-190X/© 2017 Elsevier B.V. All rights reserved.

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minimum vessel waiting time. The developed model can be used to evaluate the performance of the system under different decision making frameworks. The paper is developed as follows; in Section 2 a thorough review of literature is presented, in Section 3 the problem is defined, in Section 4 the input data is analyzed and the simulation model is presented in Section 5. The warm up period and number of replications are determined in Section 6 and the developed model is validated, in Section 7 the results are discussed and finally Section 8 concludes the paper. 2. Literature review The simulation approach is used widely in transportation problems to predict the system behavior [3]. The operational vulnerability of London Heathrow airport due to severe weather closures is studied at Pejovic et al. [2]. The paper focuses on costs associated with delays, flight rerouting to alternate airports, flight cancellations, and CO2 emissions. Modeling emission and main factors that influence traveler behavior decision making in route choice is done through simulation in [4]. They model can be used for to optimize ferry service and reduce emissions. Kamrani et al. [5] used Arena to predict the effect of signalizing junctions to reduce traffic congestion. Their results show signalizing can reduce vehicle waiting time by 53% and number in queue by 60%. Motraghi and Marinov [6] developed an Arena simulation model to analyze existing metro rail in Newcastle. The results showed that rail is competitive to other type of transportation in urban freight delivery and it could save money for freight providers in long term and also has positive effects on environment. Maritime industry is a dominant research area in transportation with topics such as port management, shipping market and economic impact, competitiveness, efficiency and waterway traffic and container terminals [7]. Wang et al. [8] used a simulation model for container inspection in port of Dalian. Gori and Petrelli [9] simulated Port of Civitavecchia operations using real world data. The model considered vessels arrival time, explicit representation of the berth capacity and correlated berth allocation problem. Bielli et al. [10] developed a simulation model in Java programming language as a tool in port decision support system to assess different storage policies in yard. Kulak et al. [11] developed a container terminal model in Arena to analyze terminal operation in order to identify bottlenecks of the system to highlight future potential developments. Planimate is used in [12,13] to model maritime terminal operations to assess and develop sea-side operation through simulation models. Solari et al. [14] developed an integrated model for harbor management to verify operational and performance of system using failure and waiting measures. Petering et al. [15] built up a discrete event simulation model for query crane terminals. They mentioned yard crane dispatching algorithms which avoid deadlocks are preferable to look ahead yard crane dispatching schemes. Petering [16] assessed the effect of dual yard truck on container based terminals. A combination of simulation and optimization techniques for container based terminals can be seen in [17]. The study improved simulation optimization model for loading operation in container terminals, where the key factors for improving container terminals are fully discussed in [18]. Another area of Simulation application in maritime study is risk assessment. Sormunen et al. [19] assess the risk of collision leads to chemical spill in gulf of Finland through simulation. Merrick et al. [20] study the impact of ferry service expansions in San Francisco Bay to demonstrate the use of Bayesian simulation techniques to propagate uncertainty throughout the analysis. The impact of human descriptive error in a maritime system is studied in [21]. Simulation is also used to model channels and waterways. Almaz and Altiok [22] investigated the effect of deepening Delaware river on navigational efficiency and analyzed the risk of three different scenarios: increasing vessel arrival, deepening the river and shifting to large vessels. In a similar research Franzese et al. [23] developed a model for Panama canal using Arena and used their model as a strategic planning tool to simulate Panama canal. Liu et al. [24] modeled a dynamic ship domain, taking into consideration navigable waterway conditions, ship behaviors, ship types and sizes, and operators’ skills in a holistic manner. They considered safety and capacity restriction of waterway in their Arena simulation model. Qu and Meng [25] used cellular automata model for Singapore strait traffic by considering different navigational scenarios to predict the effect of global maritime trade increase on the strait. Qi et al. [26] used cellular automata to model ship traffic follow by considering dynamic ship domain, bottleneck of waterway and spatial-logical mapping rule. Xu et al. [27] developed simulation model for waterway with multiple channel using C++ programming language. While simulation models are widely used in the literature, none has evaluated the vessel delays (waiting time) associated with waterway closures. In this paper, we have determined the optimal closure schedule through a simulation model to minimize vessel waiting time. We have assessed the effects of temporary channel closures on docks and traffic congestion to support Houston Pilots to select the best closure alternative for constructing a bridge. 3. Problem definition and assumptions In order to expand the Sam Houston tollway, Harris County Toll Road Authority (HCTRA) plans on constructing a new cable-stayed suspension bridge over the Houston Ship Channel. This project requires coordination between different agencies and stockholders, including HCTRA, US coast guard and Houston Pilots, which is highly affected by this construction. In order to propose a closure schedule that reduces the impacts of construction, in this section we go through the details of the method of construction (erection method), daily construction schedule, hourly operation during closure, hourly closure scenarios, closure location and daylight restriction imposed on LPG tankers.

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Fig. 1. The 12-days bridge construction cycle.

Fig. 2. Two major scenarios for a closure day.

Table 1 Closure alternatives for each scenario. 3 − 2 − 3 Scenario Alternative

Closure (3 h)

Opening (2 h)

Closure (3 h)

1 2 3 4 5

06 − 09 07 − 10 08 − 11 09 − 12 10 − 13

09 − 11 10 − 12 11 − 13 12 − 14 13 − 15

11 − 14 12 − 15 13 − 16 14 − 17 15 − 18

3 − 5 − 3 Scenario

6 7

Closure (3 h)

Opening (5 h)

Closure (3 h)

06 − 09 07 − 10

09 − 14 10 − 15

14 − 17 15 − 18

Bridge erection method: Due to safety considerations and HSC site access conditions, the contractor will construct precast cable-stayed bridge segments and deliver them to the site via barges. Segments are then lifted vertically from the barge into final position, using beam and winch method. This is the safest method since segments are only handled once and by only one equipment, while on site. Generally, most operations will be conducted with no channel closure and from on top of the existing portions of superstructure, including: installation and stressing of the PT tendons, installation and stressing of PT bars, grouting of PT, installation and stressing of stay cables, casting closure joins, advancing of lifting equipment and jacking apart cantilever tips. The construction operation requiring channel closures will be lifting of the precast segments located within 250 feet of either side of navigation channel centerline, and channel closure is not a concern when working on existing bridge piers to channel banks. Daily construction cycle: Fig. 1 illustrates the 12-day construction cycle proposed by the contractor, where the cycle pattern continues for total of 14 cycles (24 weeks or 168 total days). The 12-day cycle starts with a channel closure day, three open days, another closure day, followed by a 7 open days. During the project period, the channel will experience total 28 closure days. Hourly closure operations: During a closure day, the channel will experience 2 closure intervals, where each closure is 3 h long with at least a two hour reopen gap in between, for preparation. During each 3-h closure, the contractor will install one precast segment of the bridge, where each segment installation consists of 4 tasks. First is lowering beam and winch cables, moving one precast segment from the shore to the position with a barge, and lifting the attached cables (takes 1 h). Second task is hoisting up the segment to deck and the barge moving out of channel (takes 1 h). Third task is coupling PT bars and applying epoxy to segment joints (takes 30 min), and finally the forth task is stressing PT bars and releasing segment from beam and winches (takes 30 min). The process repeats for each of the three-hour closures. During the total closure intervals, the contractor will install total of 55 precast segments at the closure window, where in each 12-day cycle 4 segment will be installed (approximately the entire project takes 14 cycles). Hourly closure scenarios: There are two possible scenarios for a closure day, proposed by the contractor, that need to be discussed: 3 − 2 − 3 scenario and 3 − 5 − 3 scenario, which are illustrated in Fig. 2. The 3 − 2 − 3 scenario is a 3 h closure, 2 h reopening and then another 3 h closure to install the segments, while the 3 − 5 − 3 scenario is 3 h closure, 5 h reopening and then 3 h closure. For safety considerations, the closures are only allowed from 06 to 18 (06 pm). Based on this constraint, all possible closure alternatives for each scenario are presented in Table 1. The major focus of this paper is to determine the optimal closure alternative per closure day to minimize the total waiting time of the vessels, which will best mitigate the traffic congestion.

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Fig. 3. Location of the zones, where bridge to zone 6 will be closed during closure hours.

Location of zones and channel closure: The Houston pilot authority divides HSC to 7 separate zones, where zone zero is the sea buoy and the rest of the zones along the channel can be seen in Fig. 3. This zoning strategy is based on the location and tariff of docks in the channel. The portion of the channel located below the bridge (from zone 1 to bridge) will be fully open during the whole construction period, while the portion located above the bridge (bridge to zone 6) will be closed to marine traffic during closure intervals. Throughout this paper, we use the term “Channel Closure” for just the part of channel located above the bridge, between bridge to zone 6. Daylight restriction: While HSC operates over a 24-h period, there are daylight restrictions imposed to Liquefied Petroleum Gas (LPG) tankers, which can only pass through the channel from 6:00 to 14:30. These tankers are not allowed to transport through the channel after 14:30 pm and will be freezed at any point of operation they are, until the next day 6:00. We will later study the effects of such restriction on total waiting time of vessels. Channel operation: Fig. 4 illustrates the vessel operation at the channel, where the operation starts with vessels arriving at sea buoy and determining the destination zone and dock. Most of the carriers have already signed a contract with their corresponding dock at a specific zone and need to get service at that specific dock. The corresponding dock availability will be scanned till it is satisfied, while the vessels stay at a queue in sea buoy. Once the dock is available, a pilot is assigned to the vessel and is directed to the corresponding dock to get loading/unloading service. It should be noted that there are three main vessel groups throughout the channel: 1. Vessels traveling back to the sea buoy after getting service at zone 1, 2 or 3 2. Vessels resuming their trip to either zone 4, 5 or 6 after getting service at zone 1, 2 or 3 and finally traveling back to the sea buoy. 3. Vessels traveling back to the sea buoy after getting service at zone 4, 5 or 6. It should be noted that most of the travels are from sea buoy to docks (groups 1 and 3), and travels from dock to dock (group 2) are minor. Totally, general cargo vessels and tanker vessels are the main types of vessels that travel dock to dock in HSC. The vessels in group 2, after getting service in zones 1 to 3, might be affected by the channel closure, so two constraints should be checked, the availability of next destination dock and the channel closure constraint. If these two conditions are not true, in order to avoid traffic in the dock and the channel, vessels are directed back to the sea buoy to wait in a queue. Once the conditions become true, a pilot is assigned to the vessel and it is routed to the destination dock. After getting service at the dock, the vessel need to travel back to the sea buoy, but if the channel is closed it will remain at the dock and keep the dock busy. The same logic is applied to vessels in group 3. It should be noted that LPG tankers are restricted by one additional constraints, which is daylight restrictions.

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Fig. 4. Vessel operation flowchart at HSC. Table 2 Summary of data in vessel traffic database. Travel Time(h)

Process Time (h)

Zone

Min

Average

Max

Min

Average

Max

1 2 3 4 5 6

2.83 2.58 1.23 2.83 2.62 4.42

3.79 4.25 5.15 5.61 6.33 6.36

5 6.67 10.3 7.95 9 8.75

16.75 12.00 15.25 6.75 6.00 15.83

31.71 62.78 50.97 59.09 55.35 43.40

55.02 232.33 246.83 422.50 145.00 112.95

4. Input data analysis In this section, we will analyze HSC’s 2015 vessel traffic database, which includes vessels arrival time, process time and number and type of docks in each zone. Vessels travel time and process time statistics are summarized in Table 2. The results of this section will be used as an input for the modeling at Section 5. Vessels’ arrival rate: It is known that Non-homogeneous Poisson Process (NHPP) is a natural model for the arrival process in a queuing model and maritime performance analysis [19]. Accordingly, here we assume the vessel arrival at sea buoy occur according to a NHPP, where the hourly relative frequency, λ(t), during each sub-interval is calculated based on data and illustrated in Fig. 5. The expected number of vessels arriving at the sea buoy over any period L is given by

E[N (L )] = (L ) =



L 0

λ(t )dt

(1)

and the probability of number arrival equal to n is

P [N ( L ) = n] =

e−(L ) [(L )]n n!

(2)

It should be noted that, the bridge construction will take about six months, and there is not an exact starting point, so in hourly arrival rate calculations we ignored seasonal trend. Process time distribution: Another random factor affecting system performance and waiting time is vessels process time for loading/unloading at each zone. The service time in each zone is estimated based on data by calculating difference between vessel arrival time and departure time at an specific dock, and the fitted distribution is reported in detail in Table 3.

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Fig. 5. Vessels arrival rate to sea buoy.

Table 3 Loading/unloading process time distribution in each zone.

∗

Zone

Distribution

Square error

Kolmogorov–Smirnov Test Test Statistic

Corresponding p-value

1 2 3 4 5 6

16 + ERLA(7.97, 2) 12 + EXPO(49.4) 12 + LOGN(41.8, 93.6) 6 + LOGN(53.8, 86.2) TRIA(6, 23.4, 145) 15 + LOGN(33.8, 67.7)

0.038886 0.016688 0.005502 0.011241 0.032033 0.019549

0.141 0.111 0.113 0.16 0.199 0.112

> > > > > >

.15 .15 .15 .15 .15 .15

Erlang (ERLA), Exponential (EXPO), Log-normal (LOGN), Triangular (TRIA)

Table 4 Dock type and quantity considered as resources in each zone. Zone

Type

#

Zone

Type

#

Zone

Type

#

Zone

Type

#

1

General Container LPG Tanker Tanker CTK Bulk liquid General Tanker T&B LPG

4 18 3 17 10 5 23 11 9 11 10

3

Bulk liquid CTK Container General Tanker TPD T&B LPG TCO

5 5 4 8 24 5 6 6 3

5

Bulk liquid CTK General Tanker TPD LPG T&B

7 3 6 9 3 3 3

6

Bulk liquid CTK General Tanker LPG TCO RORO PCC

11 3 19 11 2 2 2 5

2 4

As can be seen, all fitted distributions have p-value greater than .15, which means that the null hypotheses are not rejected at significance level 0.05. Dock resources: Table 4 represents different dock quantity and type including general (GEN), container (CON), rollon/roll-off (RORO), liquefied petroleum gas (LPG), tug and barge (T&B), product tanker (TPD), chemical/oil tanker (TCO) and tanker (TNK) at each zone based on HSC data set, also PCC and CTK are companies who have contract to specific docks. Travel time: Throughout the model we need to estimate the time vessels traverse different routes between seabouy, bridge location and different zones. Given that vessels travel with same speed through out the channel due to the safety issues, travel time just depends on travel distance. In other words, the vessels travel time to each zone are functionally linked to the distance of each zone from seabouy. Accordingly, Table 5 demonstrates the fitted travel time distributions, derived by the Arena input analyzer. It can be seen that no null hypotheses is rejected at significance level of 0.05.

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Table 5 Estimated travel time distribution. Travel Time sea to zone 1 Distribution: NORM(3.79, 0.369) Square Error:0.008784 Kolmogorov–Smirnov Test Test Statistic = 0.0377 Corresponding p-value = .0511 Travel Time sea to zone 2 Distribution:2 + LOGN(2.25, 0.796) Square Error:0.008784 Kolmogorov–Smirnov Test Test Statistic = 0.03453 Corresponding p-value = .105 Travel Time sea to zone 3 Distribution: 4 + GAMM(0.334, 3.56) Square Error:0.003826 Kolmogorov–Smirnov Test Test Statistic = 0.0248 Corresponding p-value= .0809 Travel Time sea to zone 4 Distribution: 2.31 + ERLA(0.132, 25) Square Error:0.002226 Kolmogorov–Smirnov Test Test Statistic = 0.0378 Corresponding p-value > .15 Travel Time sea to zone 5 Distribution: NORM(6.33, 0.664) Square Error: 0.001897 Kolmogorov–Smirnov Test Test Statistic = 0.0333 Corresponding p-value > .15 Travel Time sea to zone 6 Distribution:NORM(6.36, 0.646) Square Error: 0.003575 Kolmogorov–Smirnov Test Test Statistic = 0.0364 Corresponding p-value = .0952 ∗

Normal (NORM), Log-normal (LOGN), Gamma (GAMM), Erlang (ERLA)

5. Simulation model development Houston Ship Channel vessel traffic is simulated in Arena software, where the logic of operation is presented in Fig. 4. The operations at different zones can be applied to determine the performance of the system under different decision making frameworks. Without loss of generality, we have applied the model to determine the vessels waiting time under different channel closure scenarios. The model is built based on the following assumptions: • Vessels’ arrival rate to sea buoy is not affected by closure, meaning that no vessel is rerouted to an alternate port and no vessel cancelled departure to HSC. • Vessels do not leave the system due to waiting time. • Other than bridge construction, no disruption, collision, or oil spill causing channel closure is assumed. • There is no restriction on the number of available pilots. • Travel times are calculated based on vessels’ travel time to the zones, and vessels speed and time are not considered. The layout of the model, consisting of 6 sub-models, corresponding to the operations in 6 zones, is presented in Fig. 6. As can be seen, a CREATE module (named Ship Arrival) is used to generate a stream of vessel arriving at sea buoy, where the hourly arrival rate of the vessels at the sea buoy is presented in Fig. 5. Next, a DECIDE module (named Which zone) distributes vessels to zones 1 to 6 based on corresponding destination zone. According to the collected data, 17.72%, 7.41%, 36.61%, 11.46%, 8.76% and 18.04% of the vessels travel to zones 1 to 6, respectively. The details of the operations at zones 1 to 6 are discussed later. The second DECIDE module (named second zone) is used to model the group of vessels who resume their travel to zones 4 to 6, after getting service in zones 1 to 3. The DECIDE module directs 4% of TNK vessels from zone 1 to 6, 2% of TNK vessels from zone 2 to 6, 15% of GEN from zone 3 to 6, 15% of TNK from zone 3 to 4, and 3.6% of GEN vessels from zone 1 to 5, based on the collected data.

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Fig. 6. High level Arena simulation model.

Fig. 7. Zone 1 sub-model.

After getting service at zones 4 to 6, three ROUTE modules (named Z4, Z5, Z6 to sea) route entities to the sea buoy STATION (names SEA NODE), and a DISPOSE module makes them leave the system.

5.1. Zones 1, 2 and 3 sub-models Fig. 7 presents the Zone 1 sub-model corresponding to operations of vessels whose destinations are zone 1. An ASSIGN module (named Assign zone 1) is created to assign process time and travel time to each vessel, based on Tables 3 and 5, respectively. Next, a DECIDE module is created to determine the four different types of vessel traveling to zone 1, where based on the data 5% of vessels are GEN, 17.78% are TNK, 5.29% are LPG and the rest are CON. Next, four ASSIGN modules are used to assign vessels type as an attribute to entities (Fig. 8). Vessels must be directed to the dock associated with their type, where the docks are considered as resources. As an example, a GEN type vessel needs to stay at a queue until a GEN type dock is available. To model this, four “scan for

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Fig. 8. Zone 4 sub-model.

Table 6 HOLD (queue) conditions to check availability of docks in zone 1. Name Hold Hold Hold Hold

1 1 1 1

Condition GEN TNK LPG CON

NR(Resource NR(Resource NR(Resource NR(Resource

Description 1 1 1 1

GEN) < MR(Resource 1 GEN) TNK) < MR(Resource 1 TNK) LPG) < MR(Resource 1 LPG) CON) < MR(Resource 1 CON)

checks checks checks checks

zone zone zone zone

1 1 1 1

GEN dock availability TNK dock availability LPG dock availability CON dock availability

Table 7 DECIDE modules to check dock availability and channel status. Name

Expressions

Description

Z5GENa

((T.T Z1 GEN < 6||T.T Z1 GEN > 9)&& (T.T Z1 GEN < 11||T.T Z1 GEN > 14) && (T.T Z1 GEN < 102|| T.T Z1 GEN > 105)&& (T.T Z1 GEN < 107||T.T Z1 GEN > 110)) && MR(GEN Z5) > NR(GEN Z5)

Z6 TNK

((T.T Z1 TNK < 6||T.T Z1 TNK > 9)&& (T.T Z1 TNK < 11||T.T Z1 TNK > 14) && (T.T Z1 TNK < 102|| T.T Z1 TNK > 105)&& (T.T Z1 TNK < 107||T.T Z1 TNK > 110)) && MR(TNK Z6) > NR(TNK Z6)

Checks zone 5 GEN dock availability and channel status Checks zone 6 TNK dock availability and channel status

a

General vessels travel time from sea buoy to zone 1 + current simulation time (TNOW)=T.T Z1 GEN

condition” type HOLD modules (queues) are used to scan the predefined conditions of dock availability, where the conditions for each HOLD module is specified in Table 6. Next, in order to model the pilot assignment to the vessels, which takes about 15 min, a PROCESS module with one shared resource is used. Once the HOLD module condition becomes true and a pilot is assigned, vessels are directed to the destination dock by a ROUTE module and a dock STATION. The process operations of vessels at docks are modeled with SEIZE, DELAY and RELEASE modules. The quantity and type of docks in zone 1, which are presented in Table 4, are defined in the four SEIZE modules. After a vessel seizes a resource (dock) for as long as its process time, it releases the related dock. At this point, two DECIDE modules are created to direct 3.6% of GEN vessels to zone 5 and 4% of TNK vessels to zone 6, and the rest of the vessels will travel back to the sea buoy by the ROUTE modules. For those vessels traveling above the bridge, after assigning new travel time, two constraints of availability of next destination dock and channel closure are checked by the DECIDE modules, as explained in Table 7.

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Table 8 HOLD (queue) conditions for vessels traveling to zone 4 from sea buoy. Name

Expressions

Description

Z4 BLK Enter

((T.T Z4.TNOW < 6||T.T Z4.TNOW > 9) && (T.T Z4.TNOW < 11|| T.T Z4.TNOW > 14)) && MR(Resource Z4 BLK) > NR(Resource Z4 BLK) ((T.T Z4.TNOW < 102|| T.T Z4.TNOW > 105) && (T.T Z4.TNOW < 107|| T.T Z4.TNOW > 110)) && MR(Resource Z4 BLK) > NR(Resource Z4 BLK) ((T.T Z4.TNOW < 6||T.T Z4.TNOW > 9) && (T.T Z4.TNOW < 11|| T.T Z4.TNOW > 14)) && MR(Resource GEN Z4) > NR(Resource GEN Z4) ((T.T Z4.TNOW < 102|| T.T Z4.TNOW > 105) && (T.T Z4.TNOW < 107|| T.T Z4.TNOW > 110)) && MR(Resource GEN Z4) > NR(Resource GEN Z4) ((T.T Z4.TNOW < 6||T.T Z4.TNOW > 9) && (T.T Z4.TNOW < 11|| T.T Z4.TNOW > 14)) && MR(Resource TNK Z4) > NR(Resource TNK Z4) ((T.T Z4.TNOW < 102|| T.T Z4.TNOW > 105) && (T.T Z4.TNOW < 107|| T.T Z4.TNOW > 110)) && MR(Resource TNK Z4) > NR(Resource TNK Z4) ((T.T Z4.TNOW < 6||T.T Z4.TNOW > 9) && (T.T Z4.TNOW < 11|| T.T Z4.TNOW > 14)) && MR(Resource T&B Z4) > NR(Resource T&B Z4) ((T.T Z4.TNOW < 102|| T.T Z4.TNOW > 105) && (T.T Z4.TNOW < 107|| T.T Z4.TNOW > 110)) && MR(Resource T&B Z4 > NR(Resource T&B Z4) ((T.T Z4.TNOW < 6||T.T Z4.TNOW > 9) && (T.T Z4.TNOW < 11|| T.T Z4.TNOW > 14)) && MR(Resource LPG Z4) > NR(Resource LPG Z4) ((T.T Z4.TNOW < 102|| T.T Z4.TNOW > 105) && (T.T Z4.TNOW < 107|| T.T Z4.TNOW > 110)) &&MR(Resource LPG Z4) > NR(Resource LPG Z4)

Check BLK dock availability and channel status Check BLK dock availability and channel status part 2 Check GEN dock availability and channel status Check GEN dock availability and channel status part 2 Check TNK dock availability and channel status Check TNK dock availability and channel status part 2 Check T&B dock availability and channel status Check T&B dock availability and channel status part 2 Check LPG dock availability and channel status Check LPG dock availability and channel status part 2

Z4 BLK Enter 1 Z4 GEN Enter Z4 GEN Enter 1 Z4 TNK Enter Z4 TNK Enter 1 Z4 T&B Enter Z4 T&B Enter 1 Z4 LPG Enter Z4 LPG Enter 1

Table 9 HOLD modules checking day light restriction for vessels traveling to zone 4. Name

Expressions

Description

Z4 LPG Entrance Z4LPGExita

CalHour(TRAVEL TIME Z4 TNOW) < 14&& CalHour(TRAVEL TIME Z4 TNOW) > 6.30 CalHour(TRAVEL TIME EXIT 4) < 14 && CalHour(TRAVEL TIME EXIT 4) > 6.30

Checking daylight restriction Checking daylight restriction

a

Vessels travel time from zone 4 to sea buoy + current simulation time(TNOW)=TRAVEL TIME EXIT 4

Table 10 HOLD module checking channel closure condition. Name

Expressions

Description

Z4 BLK EXIT

(T.T EXIT 4 < 6||T.T EXIT 4 > 9) && (T.T EXIT 4 < 11|| T.T EXIT 4 > 14) || (T.T EXIT 4 < 102|| T.T EXIT 4 > 105) && (T.T EXIT 4 < 107|| T.T EXIT 4 > 110)

Check channel status

If these two conditions are not true, vessels are directed to the sea buoy to wait in a queue. It should be noted that the constraints are developed for the first alternative of 3 − 2 − 3 scenario (see Table 1) throughout this section. Zones 2 and 3 sub-models are similar to Zone 1 sub-model in terms of simulation logic with some minor differences, which are the dock types and quantity, travel time and process time (see Tables 3–5).

5.2. Zones 4, 5 and 6 sub-models Here, sub-model of zone 4 will be elaborated as an example of zones 4 to 6 sub-models. In sub-model 4, an ASSIGN module assigns travel time to each vessel based on Table 5 and process time based on Table 3, then a DECIDE module determines different types of vessels traveling to Zone 4, based on data. Next, “scan for condition” type of HOLD modules keep vessels in sea buoy queues to check dock availability, channel closure and day light restriction constraints. The details of two constraints, closure constraints and dock availability, are presented in Table 8. For the sake of waiting time analysis, a RECORD module (named LPG tracking) is used to record time between a vessel is sent back to the sea buoy until it travels to above the bridge. The LPG tankers daylight restriction is modeled using “CalHour” function in a HOLD module to check simulation clock time, where the details are mentioned in Table 9. Similar to sub-model 1, a HOLD module is employed to scan channel closure constraints at the time of vessels returning to sea buoy, where bulk vessels HOLD module is specified in Table 10 as an example of these constraints. Similar to sub-model 1, to model the service time of vessels at zones 4 to 6, this study takes advantage of the separated SEIZE, DELAY and RELEASE modules. Using separate modules allow authors to put the RELEASE module after the HOLD module so that as long as the channel is closed, the resource is seized by the vessel, and once the condition becomes true, the RELEASE module releases the corresponding resource (dock).

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99

Fig. 9. Identifying warm-up period based on 3 resources utilization.

Table 11 Appropriate number of replications. Replications 1

2

3

4

5

xm

SD

0.23

0.2

0.2

0.25

0.23

0.22

0.02

t4,1− α2 2.776

Nm 13.376

6. Warm-up period, replications, verification and validation In this section warm-up period, number of replications, verification and validation of the model are studied. It should be noted that while the HSC operates 24/7 the simulation model starts with no vessel in the system and all the dock resources idle, thus the simulation results need to be collected after the warm-up period. This allows the queues, dock resources, and the whole system reaches the steady state condition. In order to determine a satisfactory warm-up period, the model is run for 1200 h and three response variables; pilot at sea buoy, TNK dock at zone 6 and CON dock at zone 1, are monitored over time. Fig. 9 demonstrates the utilization of these variables, where utilization is calculated by the average number of busy resources divided by the average number of resources that are available. It can be seen that the three response variables begin to exhibit steady state behavior after 850 h of warm-up period, which we consider throughout the paper. Next, an appropriate number of replications is calculated to assure the accuracy of the results with minimum effort. If too few replications are selected then the accuracy is lost, and if too many is done then it is costly and time consuming. Here, using the half width method first m = 5 number of initial replications is performed, where the waiting times are presented in Table 11. Accordingly, the sample mean xm , standard deviation SD(m) and student T-distribution quantile tm−1,1− α with significance level of α = 5% is calculated. Using Eq. (3) the appropriate number of replication is calculated [5,28].

 Nm =

SD(m ) × tm−1,1− α2 xm × 

2

2 (3)

As can be seen by Table 11, the appropriate number of replications is Nm = 13.376, and throughout this paper, we will replicate the model for 14 times. In order to ensure that the model is correct and the flowchart logic is correctly implemented, we conduct model verification and validation, using a few different approaches. First, given that vessels getting service at zones 1, 2 and 3 are not affected by the channel closure, we tested the waiting times of such vessels with different closure scenarios. As expected, the output waiting time were zero under all closure scenarios. Next, knowing that, with no channel closure, the total waiting time of all vessels should be around 15 min, for pilot assignment, we run the model for such scenario and reported the waiting time for 14 replications in Table 12. As can be seen at significance level of 10% the T-test p-value is .211, which implies that the null hypothesis μsimulation = μHSC = 15min is not rejected, and this test validates the model, as well. We further checked the operational behavior of the system by graphically observing the vessels movements through the time, and the animation approved the correct implementation of the model, as well. And finally, by increasing the closure hours, the model resulted in longer total vessel waiting time.

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B. Rahimikelarijani et al. / Simulation Modelling Practice and Theory 80 (2018) 89–103 Table 12 Waiting time (h) with no channel closure. Replications No closure

1

2

3

4

5

6

7

8

9

10

11

12

13

14

0.23

0.2

0.2

0.25

0.23

0.67

0.15

0.73

0.18

0.29

0.34

0.62

0.24

0.15

Table 13 Vessel waiting time (h) as a result of channel closure in a 12-day cycle. 3 − 2 − 3 Scenario

Replications

Closure

Opening

Closure

1

2

3

4

5

6

7

8

9

10

11

12

13

14

06–09 07–10 08–11 09–12 10–13

09–11 10–12 11–13 12–14 13–15

11–14 12–15 13–16 14–17 15–18

8.59 25.46 24.86 19.13 09.97

13.5 12.93 25.94 27.85 47.07

8.26 13.99 11.06 6.70 6.64

5.04 5.88 11.15 17.27 10.95

10.78 43.45 30.52 10.83 22.46

28.66 07.9 44.68 39.12 45.72

23.24 14.12 45.24 11.13 14

5.04 4.26 18.09 17.69 27.5

4:00 3.85 10.84 45.97 76.83

25.47 11.09 31.32 17.81 9.25

13.49 30.34 31.45 28.61 32.37

13.12 13.82 10.88 34.17 35.44

21.47 21.82 4.71 104.5 107.26

27.69 27.75 30.66 48.34 44.98

3 − 5 − 3 Scenario

Replications

Closure

Opening

Closure

1

2

3

4

5

6

7

8

9

10

11

12

13

14

06–09 07–10

09–14 10–15

14–17 15–18

9.11 6.38

15.29 22.24

6.37 5.58

4.1 16.94

7.16 14.55

11.08 19.32

9.08 5.36

6.95 19.83

21.68 15.52

9.19 26.18

8.34 13.44

8.91 2.42

16.97 10.26

10.71 9.4

No closure

Replications 1

2

3

4

5

6

7

8

9

10

11

12

13

14

0.23

0.2

0.2

0.25

0.23

0.67

0.15

0.73

0.18

0.29

0.34

0.62

0.24

0.15

Table 14 Closure waiting time with 90% confidence interval. 3 − 2 − 3 Scenario Closure

Opening

Closure

Mean

StDev

90% CI

06–09 07–10 08–11 09–12 10–13

09–11 10–12 11–13 12–14 13–15

11–14 12–15 13–16 14–17 15–18

14.88 16.90 23.67 30.65 35.03

8.76 11.46 12.9 24.95 28.64

(7.58, 22.18) (9.61, 24.20) (16.37, 30.97) (23.35, 37.95) (27.73, 42.33)

3 − 5 − 3 Scenario Closure

Opening

Closure

Mean

StDev

90% CI

06–09 07–10

09–14 10–15

14–17 15–18

10.35 13.39

4.68 7.11

(3.06, 17.65) (6.09, 20.68)

7. Results The model presented in Section 5 is run, and the total waiting times of all the vessels affected by the channel closure are presented in this section. Waiting times (h) are calculated for a 12−day cycle (see Fig. 1) for five different alternatives of 3 − 2 − 3 scenario and two alternatives of 3 − 5 − 3 scenario (see Table 1), each with 14 replications. First, vessels’ waiting time as a result of just channel closure is presented in Table 13, and next the waiting time of LPG tankers as a result of day light restriction is added and results are presented in Table 17. Table 13 shows vessels waiting time in three different cases: 3 − 2 − 3 scenario, 3 − 5 − 3 scenario, and no closure. The negligible waiting time with no closure affirms that the waiting time reported in 3 − 2 − 3 and 3 − 5 − 3 scenarios are actually the result of just channel closure. The mean and standard deviations of alternative cases are presented in Table 14, and it can be seen that as closure time moves to noon the average waiting time increases. Fig. 5 supports this conclusion, since as can be seen in this figure traffic of the channel increases in the noon, which increases the waiting time of vessels affected. Table 15 compares all 7 different alternatives of both scenarios at significance level of 10%. This table shows that the null hypothesis is rejected, and there is a significant difference between mean waiting time of different closure alternatives. The p-value of the test equal to zero confirms that the effect of different closure scenarios on the waiting time is significant, so Fisher least significant difference (LSD) method of multiple pairwise comparison is then constructed to analyze the difference between each alternative scenario mean and to find the best closure scenarios [29].

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Table 15 Analysis of variance for different closure alternatives. Source

DF

Adj SS

Adj MS

F-Value

P-Value

Case Error Total

6 91 97

7309 24,567 31,876

1218.1 270

4.51

.0 0 0

Table 16 Fisher pairwise comparison of alternatives at significance level of 10%. Alternative

Scenario

Closure

Opening

Closure

Mean

Grouping

5 4 3 2 1 6 7

3−2−3 3−2−3 3−2−3 3−2−3 3−2−3 3−5−3 3−5−3

10 − 13 09 − 12 08 − 11 07 − 10 06 − 09 06 − 09 07 − 10

13 − 15 12 − 14 11 − 13 10 − 12 09 − 11 09 − 14 10 − 15

15 − 18 14 − 17 13 − 16 12 − 15 11 − 14 14 − 17 15 − 18

35.03 30.65 23.67 16.9 14.88 13.39 10.35

A A

B B

C C C C

D D D D

Table 17 Waiting time (h) considering both channel closure and day light restriction in a 12-day cycle. 3 − 2 − 3 Scenario

Replications

Closure

Opening

Closure

1

2

3

4

5

6

7

8

9

10

11

12

13

14

06–09 07–10 08–11 09–12 10–13

09–11 10–12 11–13 12–14 13–15

11–14 12–15 13–16 14–17 15–18

8.59 89.74 89.14 83.41 74.25

67.98 97.59 110.6 112.51 131.73

56.65 62.38 59.45 55.09 55.03

64.09 17.97 70.2 76.36 70

29.25 61.92 48.99 39.13 41.88

28.66 32.17 68.95 49.73 59.7

93.25 84.13 115.25 56.61 59.48

47.74 30.16 43.99 55.85 59.06

97.16 97.01 104.17 81.67 80.37

90.57 101.43 121.66 93.35 104.71

83.22 88.56 89.67 86.6 90.36

60.19 60.89 57.95 81.24 82.51

50.04 50.39 33.28 128.11 130.87

91.07 86.51 89.42 107.1 103.14

3 − 5 − 3 Scenario

Replications

Closure

Opening

Closure

1

2

3

4

5

6

7

8

9

10

11

12

13

14

06–09 07–10

09–14 10–15

14–17 15–18

31.04 70.66

99.95 106.9

54.76 53.97

63.19 75.99

37.1 44.54

11.08 43.59

79.09 75.37

32.85 55.65

97.6 91.44

85.38 164.06

77.71 81.72

55.98 49.49

40.58 33.87

74.09 68.16

3 67.28

4 51.09

5 6.66

6 50.44

7 35.14

8 29.71

9 16.57

10 27.13

11 51.58

12 55.11

13 41.64

14 38.65

Replications 1 33.98

2 69.59

Table 16 presents Fisher pairwise comparison results. This table puts the alternatives with no significant waiting time difference in the same group and sorts them decreasingly. In other words, difference between mean waiting times of alternatives that share the same letter are not statistically significant. As can be seen, both alternatives of the 3 − 5 − 3 scenario are sorted in group D and have the least mean waiting time. The results show that the 3 − 5 − 3 scenario outperforms the 3 − 2 − 3 considerably. For example, alternative 7 (3 − 5 − 3) has 70% shorter total vessels waiting time than alternative 5 (3 − 2 − 3), and alternative 7 (3 − 5 − 3) has 30% shorter waiting time than alternative 1 (3 − 2 − 3). Fig. 10 is the graphical representation of Fisher pairwise comparison for the 7 alternatives, where all the 21 possible pairs are displayed on y-axes. The intervals containing zero show no difference between pairs of mean waiting times. Next, in Table 17 the waiting time of LPG tankers due to day light restriction is added to vessel’s waiting time (h) when different closure alternatives are imposed to the channel, and the results of the three different cases (3 − 2 − 3 scenario, 3 − 5 − 3 scenario, and no closure) are presented. The mean and standard deviations of alternative cases are presented in Table 18, as well. A one-way Anova is performed to compare the mean difference between waiting times under different alternatives of the 3 − 2 − 3 and 3 − 5 − 3 scenarios, and the results are resented in Table 19 for significance level of 10%. As can be seen by the table, the null hypothesis is not rejected, which means there is not a significant difference between the mean waiting time in the these alternatives. Our result show that while LPG tankers are just a small percent, 7.1%, of the vessels getting service at HSC, their waiting time due to daylight restrictions are that long that the closure schedule doesn’t make a significant difference for them. In other words, including the LPG tankers long day light restriction waiting time in decision making, there is no statistical significant difference between different closure alternatives. 8. Conclusion Congestion avoidance studies allow waterways to operate with shortest waiting time and highest throughput. In this paper we examined the congestion and waiting time caused by bridge-construction closures at the Houston Ship Channel.

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Fig. 10. Fisher pairwise comparison graph with 90% confidence interval. Table 18 Waiting time considering both channel closure and day light restriction with 90% CI. 3 − 2 − 3 Scenario Closure

Opening

Closure

Mean

StDev

90% CI

06–09 07–10 08–11 09–12 10–13

09–11 10–12 11–13 12–14 13–15

11–14 12–15 13–16 14–17 15–18

62.03 68.63 78.77 79.05 81.65

27.43 27.70 28.16 25.84 27.69

(49.5, 74.57) (56.10, 81.17) (66.23, 91.30) (66.52, 91.59) (69.11, 94.18)

3 − 5 − 3 Scenario Closure

Opening

Closure

Mean

StDev

90% CI

06–09 07–10

09–14 10–15

14–17 15–18

60.03 72.53

26.97 33.19

(47.49, 72.56) (59.99, 85.06)

Table 19 Analysis of Variance of day light restriction. Source

DF

Adj SS

Adj MS

F-Value

P-Value

Scenario Error Total

6 91 97

6198 72,488 78,686

1032.9 796.6

1.3

.267

We developed a generic discrete event simulation model for operations at different channel zones, that can be applied to determine the performance of the system under different decision making frameworks. We exposed the channel to different closure scenarios and statically compared the waiting time of different scenarios. We categorized the closure alternatives that have statistically significant difference in mean waiting time and determined the alternatives with shortest waiting time. In particular, our result show that the optimal closure alternative can result up to 70% shorter total waiting time. We also studied the effect of closures on daylight restricted vessels, such as LPG tankers. Our result show that while LPG tankers are just a small percent (7.1%) of the vessels getting service at HSC, their waiting time due to daylight restrictions are so long that including it in calculations results in no statistically significant difference between different closure alternatives. While this paper focuses on daytime closures (060 0–180 0), in order to recommend a closure scenario to HSC for implementation, it is interesting to evaluate the nighttime closures, considering all safety aspects and costs such as lighting costs. Further studies can be done for resources as such tugs, which can cause considerable waiting time for vessels getting service both above and below bridge. Another extension is to consider effect of other channel closures such as vessel collisions, fog, and oil spills on the construction closures. Beside, substituting current FIFO queue policy, Opt-Quest (an optimization toolkit integrated with Arena) can be used to determine a priority policy for vessels in queue to minimizes waiting time.

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Acknowledgment This work is supported by Center of Advances in Port Management (CAPM), Lamar University. The authors deeply appreciate Captain J.J. Plunkett and Captain George Pontikos from Houston Pilots for providing the data and their constructive feedbacks and comments throughout development of this paper. The authors also appreciate all the technical support and encouragement they have received from Mr. Erik Stromberg, director of CAPM. References [1] M. Associates, The 2014 economic impact of marine cargo activity at the port of houston on the state of texas and the united states (2015). URL www.portofhouston.com. [2] T. Pejovic, R.B. Noland, V. Williams, R. Toumi, A tentative analysis of the impacts of an airport closure, J. Air Transp. Manage. 15 (5) (2009) 241–248. [3] W. David Kelton, R.P. Sadowski, D.T. Sturrock, Simulation with Arena, McGraw Hill, 2008. [4] W. Zhang, Y. Qi, Y. Yan, J. Tang, Y. 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