The data collected on second-to-second operations of large-scale freight and logistics systems have increased in recent years. Data analytics can provide valuable insight and improve efficiency and reduce waste of resources. Understanding sources of uncertainty, including emergent and future conditions, is critical to enterprise resilience, recognizing regimes of operations, and to decision-making for capacity expansions, etc. This paper demonstrates analyses of operations data at a marine container terminal and disaggregates layers of uncertainty and discusses implications for operations decision-making and capacity expansion. The layers arise from various sources and perspectives such as level of detail in data collection and compatibilities of data sources, missing entries in databases, natural and human-induced disruptions, and competing stakeholder views of what should be the performance metrics. Among the resulting observations is that long truck turn times are correlated with high traffic volume which is distributed across most states of operations. Furthermore, data quality and presentation of performance metrics should be considered when interpreting results from data analyses. The potential influences of emergent and future conditions of technologies, markets, commerce, environment, behaviors, regulations, organizations, environment, and others on the regimes of terminal operations are examined.

## Introduction

There are critical needs to develop innovative methods for risk analysis and management of civil, infrastructure, and mechanical engineering systems. Large-scale disruptions call attention to uncertainty surrounding current models and their assumptions. Maritime container ports are an essential part of global supply chains and are typically a cost-effective option for shipping commodities over long distances [1]. These ports are typically owned or operated by consortia of industry and/or government and have missions that serve the public interest. They operate through economic and natural disruptions. Conditions at global levels (e.g., climate, macroeconomic trends, disruptive technological innovation) and regional/local levels (e.g., demographic shifts, region-level funding) affect the ability of ports to achieve their missions [2]. There is a need to find efficiencies, economies of scale, and innovations that allow these ports to achieve improved outcomes with fewer resources. Ports across the world are searching for innovative methods for obtaining financing, maximizing land use, and reducing risk through diversification of cargo types. It is important that capital expenditures are leveraged in ways that provide an acceptable return on investment with predictable levels of cost and schedule risk.

Port operations involve multiple groups and stakeholders, including port owners and operators, shipping lines, trucking companies, stevedores, rail companies, and others. The various stakeholders all contribute to the overall performance of the port, and interdependencies can cause disruptions in one area, e.g., vessel arrivals, to propagate to another area, e.g., trucking. Vessel berthing and allocation of equipment to load and unload vessels have been studied extensively, e.g., see Refs. [310]. However, the landside part of operations, moving cargo from the terminal yard to locations further down the supply chain, has been identified as an understudied area [11]. Port drayage refers to the transport of cargo between a port terminal and an inland location [12]. This paper will confine the term to container transport, although methods and conclusions are generalizable to other types of commodities.

Port drayage operations have received attention in recent years due to complaints of truck drivers about congestion within terminals as well as queueing at terminal gates [13,14]. Harrison et al. [11] conducted a survey among truck drivers receiving or delivering containers at the Port of Houston, TX, and found that 45.7% of drivers were unsatisfied with the efficiency of terminal operations, compared to 22.3% being satisfied or very satisfied. In addition to decreasing terminal efficiency with associated cost and less customer satisfaction, congestion also has negative effects on air quality, increases polluted runoff, and contributes to congestion on hinterland roads. In order to increase the efficiency of operations and reduce other indirect negative effects, it is important to identify and resolve bottlenecks in truck throughput at terminals. Innovative methods such as webcam image processing [15,16] and data mining [17] have been used to analyze gate queues and identify certain types of transactions that have abnormally slow processing times. However, there is a need to investigate further the specific contributions of activities such as queueing at gates, waiting for service at stacks, and receiving a chassis inspection to the overall performance of drayage operations.

There is a variety of methods for handling uncertainty in the modeling of engineering systems [18]. Uncertainty has been specifically accounted for in risk and decision models for infrastructure climate adaption [19,20], asset management of canal systems [21], watershed management [22], vessel berth scheduling [10], and highway access safety [23]. In many cases, expert elicitation [2426] is required to assess and evaluate uncertainties. Morgan et al. [27] and Haimes [28] propose classification schemes for different types of uncertainty.

This paper demonstrates a framework for disaggregation of uncertainties of operations of freight logistics systems into several layers, including a characterization of operations data for a container terminal on the U.S. East Coast, shown in Figs. 1 and 2. It delineates layers of uncertainty in data analytics that can be generalized to a variety of advanced logistics systems. It identifies metrics for port drayage efficiency and proposes new ones. A method for analyzing the spatial and temporal stress on various areas within the terminal is developed, and factors driving this stress are delineated. The paper is organized as follows. First, port drayage operations are briefly outlined and conventional performance metrics described. Second is a case study on data analytics methods in the setting of a semi-automated container terminal. Third is a discussion on layers of uncertainty. Last is the discussion on results and conclusions.

## Background

The efficiency of port drayage is in the industry typically measured by the truck turn time, that is how long it takes trucks to enter a terminal, perform required transactions, and leave the terminal. There is some variability between agencies how turn time is measured. In some cases, it includes time waiting in line outside the terminal or if it includes the processing time at the gate entering. In this paper, traditional turn time is defined as the time from when a truck enters the terminal yard until it leaves through the gate, whereas expanded turn time includes the time a truck spends queueing before entering the yard [29]. Figures 3 and 4 illustrate the definitions and illustrate the layout of the terminal and where time stamps are collected. While making a visit to the terminal, trucks can perform several types of transactions. Ingate transactions involve presenting necessary paperwork and entering the terminal yard. Stack transactions involve delivering containers for export or receiving containers for import. Chassis transactions involve getting a chassis inspected or repaired, picking up or dropping off an empty chassis. Outgate transactions involve presenting paperwork and leaving the terminal yard.

This paper characterizes operations data on truck visits at the Virginia International Gateway terminal. The terminal is one of the five terminals of the Port of Virginia and is located in Portsmouth, VA. Various data are collected on truck visits to the terminal. Using RFID readers, several time stamps pertaining to the truck visit are recorded. Table 1 expands on Fig. 3 and describes the time stamps. These time stamps are used to model the flow of truck traffic through the terminal. During a visit, a truck can make multiple stack transactions, each with its own LTADATE, LTACRANESTARTED, and LTACRANEFINISHED. It should be noted that a given truck visit might not perform all types of transactions.

The relevant data collected at the terminal describe individual transactions. In order to get information about the various states of the system while operating in different regimes, the data must be transformed from the transactions domain to a turn-time domain. An entry in the database is created every 10 min during the study period (entries can be adjusted to a shorter or longer period based on preferences of stakeholders). At the instance of the entry, the number of trucks in each state is recorded and the time the trucks currently in the system spend in their respective state as well as their traditional and expanded turn times. Thus, it is possible to correlate the time and occupancy of states with the overall turn time. States that are robust to variations in turn times can be expected to have a similar mean and variance in time and occupancy for different regimes of turn times.

To gain further insight into the behavior of the flow of trucks through the terminal, the transitions between states are modeled as a Markov chain. All trucks enter the system through the ingate and leave through the outgate but visits to chassis area and stacks can be in any order and multiple visits to these states are possible. In the demonstration presented, the number of visits to the chassis area and cranes does not exceed two. A key aim of the following analysis is to compare and contrast the prevalence of certain activities and their respective duration for different regimes of overall terminal drayage performance. The aim is to identify factors that drive long turn times and opportunities to improve operations, lower cost, and improve customer experiences. The main distinction in the analysis is made between long turn times, where the traditional turn time is over 60 min and short turn times with traditional turn times are under 60 min.

## Demonstration Part 1: Port Operations

This section describes a demonstration of the methods described in the Background section. The setting of the demonstration is the Virginia International Gateway, a container terminal operated by the Port of Virginia in the Hampton Roads region of Virginia. The terminal has the capacity to process over 1 million 20-foot equivalent unit containers annually and is the first and one of very few operational automated container terminals in the Western Hemisphere, with semi-automatic rail mounted gantries moving containers between stacks and trucks [30]. The terminal experienced significant congestion in early 2015 with excessive turn times and customer dissatisfaction [14]. Extended gate hours and several other measures were implemented and average turn times became shorter in the summer of 2015. A variety of macroscale events have been tied to the period of excessive turn times, such as winter weather slowing down operations and labor disputes on the U.S. West Coast driving more business to East Coast ports. However, analysis on a within-terminal scale bottlenecks or distribution of service demand serves an important purpose to improve efficiency and being able to recognize warning signs for long turn times.

The daily average turn time for the study period, January–September 2015, is illustrated in Fig. 5. There is an apparent seasonal behavior as Saturdays have shorter turn times than weekdays. During the study period, the terminal was closed to truck traffic on Sundays. After turn times peak around March 1 (day 60), there is a downward trend for the rest of the period. There are, however, still days toward the end of the period that exceed the operational goal of having turn times under 60 min. Figures 6 and 7 illustrate the number of trucks and time spent in each state at a given instance. The stacks is the state that has the highest median number and time in state. Comparing the number of trucks with the time spent in states, there are generally parallels. Stacks, ingate, and stacks queue have the greatest spread, in terms of interquartile range, for both measures. The chassis state takes the shortest time and has the fewest trucks present. A noteworthy difference is that in the time view there are more outliers, observations that are further than 1.5 times the interquartile range from the 75th percentile.

Figures 810 compare and contrast the distributions of times and numbers in the several states between periods where average turn times are under and over 60 min. The distributions are generated using a Kernel estimator on the entire dataset [31]. Outliers are included since a goal of the analysis is to identify conditions that lead to long turn times or periods with a high occurrence of outliers. Generally, when turn times are over 60 min the distributions are shifted to the right, meaning there are more trucks in each of the states and they spend longer time in states. Furthermore, the distributions for longer turn times have larger variances. This means that when making predictions about the number of trucks and time in states, there will be a larger uncertainty when the overall turn time is longer.

The distributions of truck numbers and times for turn times under and over 60 min can be formally compared using a dissimilarity measure [3235]. The dissimilarity measure between two continuous probability distributions, $f1$ and $f2$, is defined as
$D=1−∫−∞∞minf1t,f2tdt$
Similarly, for discrete distributions, the dissimilarity measure is defined as
$D=1−∑imin(f1(i),f2(i))$

The dissimilarity measure can be interpreted as the long tun proportion of instances, where the two conditions have different outputs. $D=0$ implies that the distributions are identical whereas $D=1$ means there is no overlap. Similar measures have been used to compare income distributions of demographic groups [33], eco-diversity [35], author co-citation analysis [34], and in other applications.

The dissimilarity measures for comparison of turn times under and over 60 min are described in Table 2. The chassis area has the lowest dissimilarity for both the number in the state and the time spent there. The stacks queue is the state most disrupted when turn times are over 60 min. With the exception of the chassis area, the time in state is more disrupted than the number of trucks in the state.

Trucks entering the terminal can either go to the stacks to receive or deliver a container or to the chassis area to receive or deliver a chassis, have a chassis inspection or repair. Trucks can perform multiple transactions in each state in a single visit, e.g., deliver a 20-foot container to the stacks, go to the chassis area to get a 40-foot chassis, and then back to the stacks to receive a 40-foot container. In this case, each transaction is recorded. The order in which transactions are performed is decided by the driver. Sometimes, like in the example before, there is a natural order, while other times the driver can decide where to start. Table 3 illustrates the transitions between states, modeled as a Markov chain. It is possible to go straight from ingate to outgate, implying that neither the stacks nor the chassis area was visited. The reasons for such behavior are several and are addressed later in this paper. A majority of trucks entering through the ingate to the stacks, while the majority of trucks at the stacks or in the chassis area head for the outgate. Movements between the chassis area and stacks are not symmetrical as a higher proportion of trucks at the stacks go to the chassis area than trucks at the chassis area move to the stacks.

## Demonstration Part 2: Uncertainty Analysis

The identification of factors that contribute to long turn times requires processing large amounts of operational data. The data are drawn from multiple sources, each collected for its own purposes. The outcomes or performance is measured using specific metrics which may not consider the perspectives of all stakeholders involved. This section identifies eight layers of uncertainty encountered that are summarized in Table 4. The layers arise in the analysis of a variety of advanced logistics systems. Challenges are caused by different standards between databases, different scope of data collection for similar systems (two terminals with different data management systems), and other issues where the data collected are accurate but scope or format is inadequate to fulfill requirements. Bad data, e.g., where values are recorded wrong into a database are another source of uncertainty. This can result in infeasible results, such as a truck having a negative turn time. Finally, the performance metrics, and their user interface and visualization should address the goals and objectives of the analysis and stakeholders should be able to easily interpret and understand the outcomes.

### Data Gaps.

The uncertainty layer addresses that data are not recorded fully for all activities. For the VIG container terminal, time stamps are recorded when (1a) a truck enters the ingate queue, (1b) they enter terminal through the ingate, (2a) they are admitted to a spot by the stacks, (2b) transaction finishes at the stacks, (3a) they enter chassis area, (3b) they leaving chassis area, and (4) they leave through the outgate. In the analysis presented, the ingate, stacks, and chassis area states can be accurately defined by these time stamps. The remaining states, stacks queue, chassis queue, and outgate, are estimated by interpolating between the truck leaving one from a transaction and starting another. Thus, the term queue is not necessarily accurate. For example, while a driver is in the state stacks queue, they might be parked for a meal break or having an issue resolved.

Driver's assistance is a state that is not recorded in a database. When there is a complication with a transaction, such as mistakes on paperwork, containers are damaged or dislocated, the truck driver visits driver's assistance to have the complication resolved. Experience has taught that a visit to driver's assistance can take anywhere from a few minutes to a couple of hours. At VIG, the driver's assistance building is located outside the gates so the driver has to exit the terminal and re-enter following a visit. Thus, it creates an additional record for the same requested transactions. As illustrated in Table 3, 13% of trucks go from ingate to outgate without visiting stacks and chassis area. A possible explanation is that some of these trucks have trouble with their transactions, have to go to driver assistance and subsequently re-enter the terminal. Since a visit to driver assistance is not recorded in a database, it is excluded from any analysis and can affect performance measures.

### Comparability Across Terminals.

The Port of Virginia operates three container terminals. In addition to VIG, there are Norfolk International Terminals (NIT) and Portsmouth Marine Terminal (PMT). The latter two are currently not automated to the same extent as VIG and therefore their operations are slightly different. Furthermore, data (specifically time stamps) collected for truck visits are different. Figure 11 illustrates the differences in time stamp collection between VIG and NIT. Due to different layouts and operations systems, chassis area data are not collected in the same manner. Rather than recording enter and exit times, the gate processing times are recorded. Once the trucks enter the chassis area, no further time stamps are recorded. The gate processing times are also recorded for ingate and outgate. This provides more detail about gate transactions than at VIG, where only the time a truck is finished processing is recorded. An implication of this is that at NIT it is possible to distinguish a long ingate (or outgate) queue due to traffic from a long queue due to slow processing by gate operators.

### Comparability Within Terminal.

Revisiting Fig. 11, there is no information about stacks or chassis queue times at NIT. This is due to incompatibility between databases for truck visits at the terminal. Two databases contain information about truck visits. One has information collected at the ingate, outgate, and chassis gates. The other has information from the stacks. A unique identifier for each truck visit links the two databases at VIG. However, at NIT the truck visit identifier is not the same for the two databases and therefore it is not possible to link stack transactions to gate transactions. Furthermore, since chassis area and stacks transaction can be performed in any order, the chassis queue state cannot be extracted from the data and state transitions cannot be computed.

### Data Accuracy.

Time stamps are recorded in various formats in each database. Most are recorded correctly and do not cause any problems but, however, there are instances where recorded time stamps are not accurate. As an example, of roughly 300,000 truck visits to VIG during the study period, about 30,000 (10%) have time stamps such that when calculating turn times, the turn time is either negative, over 12 h, or either ingate or outgate time is missing. When computing average turn times and state transitions, these instances can be filtered out since it is obvious that a truck cannot spend negative time at the terminal or leave without entering. However, there are issues with any filtering approach. The most important one is that even though data collected on these visits were bad, it was still an actual visit with the port personnel providing services to the driver. The experience of these drivers contributes to the terminals overall customer experience. The reasons for bad data can be various and difficult to track. In a worst-case scenario, the bad data are due to anomalies in the visit, such as trouble with paperwork or cargo and a need for drivers to seek assistance. In that case, these 10% of visits might have a disproportionally high effect on overall customer experience as drivers tend to weigh a long and complex visit heavier than a shorter business-as-usual visit. Still, these visits are not included in performance measurements meant to represent the efficiency of operations, such as daily average turn time.

### Data Completeness.

The data utilized to analyze factors contributing to the length of turn times were not exclusively collected for this purpose. Some of the data were in the past collected for a purpose but have since become obsolete. A field for the information still exists in the database and is sometimes filled out and sometimes not, based on whoever is entering the information. When an analyst who is not necessarily in direct communication with the persons entering the data, this might create confusion when data are treated as they were accurate while they are in fact only partially complete. This issue has been addressed by other researchers in the field of risk and uncertainty [36].

### Deficient Metrics.

As discussed before, the daily average turn time is the main performance metric used for port drayage operations. The metric is good to exemplify daily throughput but falls short on being a comprehensive representation of terminal efficiency. There are two main perspectives to consider when measuring truck operations at marine terminals: the perspective of the terminal operator and the perspective of the truck driver. Both benefit from a fast throughput and as few trouble visits as possible. A good performance metric should represent the goals and objective of the system it represents [37]. Using the average of turn times presents several considerations. The turn times are not symmetrically distributed around the average since they are bounded below by zero but can take values several hours longer than the average of around 60 min. This means that the median, which can be thought to represent a typical visit, is lower than the average. More concerning is that it is possible that the satisfaction of drivers is not driven by a typical visit but rather an atypical visit. The average does not distinguish between a hypothetical day where all trucks have turn times close to the average and one where half of the trucks have a very short turn time and the other half have a very long one. If a goal of operations is to improve customer satisfaction, the performance metrics need to address these longest turn times.

### Choosing New Metrics.

The uncertainty incurred by using the average as a performance metric can be partially addressed by adding another metric or metrics and considering the combinations of performance metrics. A metric that is less sensitive to large outliers while still addressing the goal of keeping turn times under 60 min is the proportion of turn times under a threshold value. The benefit of proportion under/over a threshold value is that it gives a clearer indication of how many visits meet the criterion for what could be considered an efficient visit, and complementary, how many visits did not meet the criterion. On the other hand, if the goal is to portray a typical visit, the median could be a better option. Another downside is that when more performance metrics are added, ranking based on the metrics gets more complicated and tradeoffs between metric might be necessary to establish a preference order.

### User Interface.

The performance metrics discussed so far, average, proportion under/over a threshold, and median are limited by their dimensionality as they aggregate data into a single number. Various forms of visualization can provide more complete insight into truck turn times. Figure 12 illustrates a sample interface for turn-time efficiency. The interface shows three numeric metrics: the average turn time, the proportion of truck visits with turn times under 60 min, and the proportion of trucks with turn times under 75 min. The 60 min threshold is chosen to represent the goal of turn times being less than an hour. The 75 min threshold is chosen to account for turn times that do not meet the 60 min threshold but might still not be considered excessively long, thus eliminating some of the ambiguity in the choice of thresholds. In addition, the interface has two graphics. The first is a histogram showing the distribution of turn times and the second shows the average turn time per hour. For the sample day in Fig. 12, the histogram reveals that the most populated bin was 24–36 min, which is lower than the daily average of 39 min. 84% of visits were under an hour and 93% under 75 min. There are, however, a few very long turn times and details on these visits should be investigated. The second graphic shows that turn times were fairly stable from the morning until midafternoon when decreasing until gates close at 18:00.

## Discussion

International trade has been estimated to account for close to a third of the U.S. economy [1]. A majority of imports and exports go through ports and in this sense, they are vital to a sustainable economy. In the Commonwealth of Virginia alone, a study has found that in 2013, the Port of Virginia supported 374,000 jobs or over 9% of the total state workforce and the total economic impact attributed to port activities was 60 billion USD [38]. Container shipping volumes are projected to multiply in the coming decades [39]. Addressing challenges coming with increasing volume and larger ships, data analytics play an important role and ways must be found to leverage data in the most effective ways [40].

This paper has characterized uncertainty of drayage operations data at a container terminal. Table 5 summarizes the key insights from the effort. Comparatively to other literature on the topic, the level of detail on activities performed, state occupancy, time spent in states and transition between states, is a significant contribution. The results of the characterization of long turn times confirm that as a general rule, congestion is spread across most states. An exception is the chassis service area which appears to be more resilient to higher traffic volume. The uncertainty layers touch on a variety of issues that are shared with other infrastructure and logistics systems such as highways [41,42], airports [43], and hydropower, navigation, and flood control [36].

This paper contributes to building a comprehensive discussion on each of the layers or all significant factors driving long turn times of trucks at container terminals. It has described several lessons learned on disaggregating layers of uncertainty in data analytics problems. Even though a large amount of operations data were available, prerequisites for meaningful analyses were often weak or lacking. Uncertainty is often classified into two broad categories, knowledge uncertainty and stochastic variability [28,44]. In this paper, the categories are both represented. Stochastic variability appears in the distribution of turn times, exemplified by Figs. 610. Even though trucks largely perform similar activities they can take a wide time range. This can be related to location of containers in stacks, weather, productivity of workers, and other factors. Knowledge uncertainty pertains to layers of data gaps, comparability across terminals, comparability within terminal, data accuracy, and data completeness. Data are partially missing, either by construct of the collection process or by individual errors. Another source of knowledge uncertainty is the relationship between customer satisfaction and turn times. The assumption is made that shorter turn times are a major improvement in the experience of drivers receiving and delivering cargo. However, it is unclear whether external factors such as hinterland traffic are a major contributor as well.

Future work might include an in-depth study on the regimes of operations identified in this paper, when turn times are under 60 min and when turn times are over 60 min. This includes, in addition to relating turn times to individual activity time components, considering information such as vessel arrivals, weather, seasonal variations in retail, and others. Strategic planning of expansion efforts should consider uncertainty layers of underlying assumptions and inputs to models. Discrete-event simulation has been used to analyze decision-making for both truck [17,45] and vessel [3,7] operations at container terminals. Simulation quantifies uncertainty and helps in evaluating the effect of uncertain inputs on outputs, for instance, truck turn times. The aggregated perspective of uncertainty (simulation) and the disaggregated perspective (delineating layers of uncertainty) complement each other as unexpected or unrealistic findings in one perspective can in many instances be accounted for by considering the other perspective. For instance, the fact that data are not collected on visits to driver's assistance might help explain if simulation results do not show very long turn times that are known to occur.

## Conclusions

The previous methods, results, and lessons learned should be of interest to researchers in the field of uncertainty and data analytics, logistics agencies, and private enterprises that collect large quantities of operations data. The need for multiple performance metrics and improvements in data collection and quality control should be accompanied by a periodical revision of goals, objectives, and methods. Risk management should consider the effect of emergent and future conditions on the evolving priorities of the systems of interest [46,47]. Conditions such as the proliferation of large container vessels, causing fewer but busier demand peaks at container terminals might change the behaviors in the drayage industry and call for a revision of performance measurement and associated data collection.

## Acknowledgment

This effort was supported in part with funding from Virginia International Terminals, LLC (VIT), a single-member limited liability company wholly owned by the Virginia Port Authority (VPA). In addition, Hampton Roads Chassis Pool (HRCP II), on behalf of and wholly owned by VIT, operates and manages the intermodal chassis and empty container yards. Collectively, the three entities are marketed as The Port of Virginia and referred to as such in this paper. The authors are grateful for support of the Commonwealth Center for Advanced Logistics Systems and Mark C. Manasco, President and Executive Director. This effort was supported in part by a grant from the National Science Foundation, 1541165 "CRISP Type 2: Collaborative Research: Resilience Analytics: A Data-Driven Approach for Enhanced Interdependent Network Resilience.

## Funding Data

• National Science Foundation (1541165).

• Commonwealth Center for Advanced Logistics Systems.

• Virginia International Terminals.

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