Measuring capacities in multimodal maritime port systems with anchorage queues

Abstract

This paper presents a framework for estimating the capacity of a multimodal maritime port system handling vessels of multiple classes. Port system capacity can be categorized into two distinct types: operating capacity, defined as the maximum number of vessels that can be processed over an extended period under stable operating conditions, and ultimate capacity, defined as the absolute maximum vessel throughput achievable irrespective of stability. Distinguishing between these two capacity measures is critical for long-term planning and resilience analysis, as ports may temporarily operate above sustainable levels following disruptions or during demand surges. Despite the importance of this distinction, existing port capacity models generally do not provide methods to compute port-level capacity estimates that clearly differentiate between operating and ultimate capacity. We introduce methods to estimate both capacity measures for seaport systems. We apply the proposed framework using the Port of Houston, Texas as a case study. Operating capacity is estimated using a parsimonious queueing-theoretic model, while ultimate capacity is estimated by fitting an ordinary differential equation model to simulation outputs. We estimate an operating capacity of approximately 0.9 vph and an ultimate capacity of approximately 1.4 vph for the Port of Houston. Sensitivity analysis of key port resources indicates that liquid-bulk terminals constitute the primary bottlenecks under stable operating conditions, whereas pilot availability becomes the dominant bottleneck following disruptions. These methods can be used in port planning to determine the expected operational and resilience gains of a given infrastructure intervention, or to identify bottlenecks in a complex, multimodal port environment.

Figures (6)

• Figure 1: Different anchorage queue dynamics over time.
• Figure 2: Capacity regimes (not to scale). The figure illustrates how the rate of anchorage exits changes with the arrival rate. In the uncongested phase, the rates of entry and exit are equal, reflecting sustainable conditions. Beyond the uncongested phase, the rate of exits falls below the rate of entries, causing persistent queue growth over time. The operating, ultimate, and saturated capacities are marked.
• Figure 3: Structure of port queueing model.
• Figure 4: Anchorage queue dynamics and channel occupancy observed over a six-month simulation horizon, based on six replicate runs.
• Figure 5: Anchorage queue behavior at different arrival rates over a six-month time horizon aggregated across six random seeds (exits counted after the warmup period). Subfigures (a) and (b) show bounded anchorage queues when arrival rates are below operating capacity, while subfigures (c) and (d) show unbounded queue growth beyond operating capacity. Subfigures (c) and (d) further motivate the concept of ultimate capacity, as vessel throughput into the port continues to increase despite unbounded queues.

Theorems & Definitions (3)

• Definition 1: Operating capacity
• Definition 2: Ultimate capacity
• Definition 3: Saturated capacity