Approximate Delays Caused by Lock Service Interruptions

The lock structures in the inland waterway system have become major constraints to navigation as a result of increased traffic and facility deterioration, leading to costly delays. Most of the locks have exceeded their design life, and service interruptions occur quite frequently, causing increasing delays to traffic. Hence, a reliable model is necessary to estimate the delay caused by lock service interruptions. In this paper, a model is developed in the form of one relatively simple equation to estimate tow delays caused by a single lock service interruption. A basic equation is derived on the basis of continuous flow theory. Because the waterway flows consist of discrete vessels, an appropriate discrete adjustment factor is developed. To account for the stochastic characteristics of actual waterway operations, an adjustment factor is estimated statistically from simulation results. The resulting model provides accurate estimates of delays far more quickly and inexpensively than simulation. The simple model developed in this paper should be useful in future studies of capacities, delays, service reliability, maintenance policies, and general waterway economics. Inland waterways are an important part of the transportation network in the United States. They provide low-cost, energy-efficient and safe transportation of heavy or bulky commodities. The National Waterways Study (1) identified the structural reliability of the inland waterway system as a major constraint in the system's ability to handle commercial waterborne traffic. More than 100 locks will have exceeded their 50-year design life by 2003 (1). Locks and dams are essential for creating stepped navigational pools with reliable depth for navigation. However, many of these facilities have become major constraints to inland navigation because of increased traffic and facility deterioration, leading to costly delays. The objective of this paper is to develop a inodel that estimates the delay caused by a single lock service interruption (i.e., a ''stall''). An equation is derived using the principles of continuous flow theory. Because the flow in real waterways consists of discrete tows or other vessels, an adjustment factor is developed on the basis of the assumption that the flow is discrete and uniform. Furthermore, the arrival and service distributions at waterway locks are probabilistic. Hence the equation developed using continuous flow is combined with an adjustment factor estimated statistically from the simulation results. This equation provides accurate estimates of delay caused by a lock service interruption. LITERATURE REVIEW Prediction of lock delays is essential for evaluating and scheduling waterway investments. Two models based on queueing theory V. Ramanathan and P. Schonfeld, Transportation Studies Center, University of Maryland, College Park, Md. 20742. have been found for estimating lock delays. DeSalvo and Lave (2) model lock operation as a simple single server queueing process with Poisson distributed arrivals and exponentially distributed service time. The assumption of Poisson distributed arrival and exponentially distributed service time does not fit every lock in the waterway system. Wilson's model (3) extends DeSalvo's model by treating the service processes as general distributions. Both models are designed for analyzing single lock delays. Neither of these models explicitly accounts for stalls. Also, the delays estimated with these models did not consider the interdependence between locks, which is highly significant in waterway locks. Kelejian's (4) efforts to model stall frequencies and duration have not yet yielded strong results despite the rigorous statistical method employed. Dai and Schonfeld (5) developed a microscopic simulation model that accounts for generally distributed arrivals and service times and interdependence between locks and stalls. As usual with microscopic simulation models, a significant amount of computer time is required for variance reduction to obtain reliable delay estimates. May and Keller ( 6) used the continuous flow theory to estimate the effects of road capacity changes at bottlenecks on delays to users. The continuous flow theory has also been used for various other highway applications. In this paper, a simple model is developed to estimate delay caused by a lock service interruption using continuous flow theory and an adjustment factor estimated from simulation results. The model is a reliable substitute for expensive simulation. PROPOSED MODEL In this section, a general equation is derived that provides a good estimate of the delay caused by a single lock service interruption based on the assumption that the arrival and service rates are uniform and continuous. The effect of a single stall, assuming uniform continuous flow, is shown in After the. end of the stall, the queue will start decreasing at a rate equal to the difference between the volume v and capacity c, and would finally become zero. The time s required to dissipat

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