58 waiting cost, and explore gate system optimization. The paper is divided into five sections. A literature review regarding MCT truck delivery and gate operations is provided in the next section. The methodology and a case study are then presented. Finally, a summary and a conclusion are presented. LITERATURE REVIEW MCT operation has been a research subject for many years. Researchers study issues of the MCT operation from different per- spectives and use many different techniques to improve MCT effi- ciency and performance. The literature review is concentrated on MCT gate operations and related issues. Literature addressing MCT receipt and delivery operations is rare, especially on truck waiting times at the gate; there are only a few studies. Ballis and Abacoumkin (3) and Kim et al. (4) have investi- gated the receipt and delivery operation in the yard. The former investigators developed a computer program with animation capabil- ities to simulate container yard operation that serviced outside trucks. Kim et al. recognized that truck turnaround time is one of the impor- tant indicators of the customer service level of a container terminal (4). A reinforcement learning technique was used to address the question of how a learner might choose optimal actions in an envi- ronment that was highly uncertain. Simulations were performed to evaluate the different sequencing rules. To deal with the problem of a truck queue at an MCT gate com- plex, Wantanabe (5) investigated the environmental impact of trucks waiting at the port entrance gate. In that report, the author pointed out that none of the available literature applied to his study. Experiments were carried out to measure the amount of noxious emissions of trucks in the Port of Yokohama in Yokohama, Japan. However, the author stated that no international regulations that governed such air pollution problems existed and suggested that further study was necessary to tackle the issue. Rail and truck intermodal terminals have some similar features in terms of receipt and delivery operations and terminal layout. Rizzoli et al. investigated the operation of an intermodal terminal using simulation (6). Train arrivals and truck arrivals were modeled as a deterministic input. By using a discrete-event simulation model and observed data, rail corridor and rail networks, truck arrivals at the gate, and terminal processes were simulated to evaluate operational performance. In particular, the relationship between gate processing time and truck waiting time was analyzed. To alleviate problems of traffic congestion, environment, energy, and labor costs, Taniguchi et al. proposed a concept of public logis- tics terminals (7 ). The objective was to establish a more efficient Modeling Gate Congestion of Marine Container Terminals, Truck Waiting Cost, and Optimization Chang Qian Guan and Rongfang (Rachel) Liu As a consequence of the continuing growth of container volume and the introduction of 13,000 containerships carrying 20-ft-equivalent-unit (TEU) containers into major trade routes, the port industry is under pressure to come up with the necessary capacity to accommodate the increasing freight volume. One critical issue is the gate capacity of marine container terminals. Limited gate capacity leads to congestion. The harbor trucking industry operates in a competitive environment, and gate congestion is detrimental to its economic well-being. This paper applies a multiserver queuing model to analyze gate congestion and to quantify the truck waiting cost. An optimization model was developed to minimize the total gate system cost with data from field observations. A case study was applied to analyze gate congestion behavior and the truck waiting cost. The sensitivity of the model is discussed. With optimization, the truck waiting cost can be drastically reduced. Several congestion mit- igation alternatives can be derived from the optimization model; the use of a truck appointment system seems to be the most viable way to reduce gate congestion and increase system efficiency. A marine container terminal (MCT) serves a critical node in the global supply chain. As container volume growth continues, compounded by the introduction of 13,000 vessels carrying 20-ft-equivalent-unit (TEU) containers into major trade routes in the past few years and a drastic increase in fuel price, these factors make the truck waiting time at the MCT gate a serious issue. World container port throughput grew to 440 million TEUs in 2006, 2.7 times the volume of 1997 (1), whereas U.S. container port throughput volume reached 27.5 million TEUs in 2006, almost dou- ble the volume in 1997 (2). The continuing growth in container volume and the increasing containership size put the port industry under tremendous pressure to come up with the necessary capacity to accommodate the demand. One critical issue is the gate capacity; limited gate capacity leads to gate congestion. However, harbor truckers undertaking local drayage are paid by trip and not by the number of hours that they drive. Therefore, congestion at the MCT gate is detrimental to their economic well-being and the local envi- ronment. The objectives of this paper are to apply queuing theory to model the MCT gate congestion of inbound trucks, quantify the truck C. Q. Guan, Department of Marine Transportation, U.S. Merchant Marine Academy, Kings Point, NY 11024. R. Liu, Department of Civil and Environmental Engineer- ing, New Jersey Institute of Technology, Newark, NJ 07090. Corresponding author: C. Q. Guan, guanc@usmma.edu. Transportation Research Record: Journal of the Transportation Research Board, No. 2100, Transportation Research Board of the National Academies, Washington, D.C., 2009, pp. 58–67. DOI: 10.3141/2100-07