Sizing of pipeline capacities in processing systems under stochastic operation conditions

Mathematical models and model-based methods are presented for reliability-based design of the capacity of pipelines aiming to transfer material or energy in batches under stochastic operation conditions. The occurrence times of the transfers are assumed to be described by Poisson processes, while the duration of the material and energy transfers may be constant or may vary randomly according to general probability distributions. Approximating analytical solutions are derived for constant duration batches, developed in terms of scan statistics, based on which two heuristics are formulated for sizing the pipeline capacities for constant batches. In the case of transferring random distribution batches described by general distribution functions, solutions are obtained by means of stochastic simulation based on an algorithm developed for that purpose. It is shown that the pipeline with random duration of batches becomes oversized using the heuristics of constant batches the extent of which depends on the standard deviation of the corresponding distribution. Combining the approximating formulae and the algorithm, a heuristic is formulated for sizing the pipeline also for random batches. A number of simulation experiences with exponential, normal, log normal and uniform distributions of the transfer sizes are presented and analyzed. The method works satisfactorily even in the case of bimodal distribution of batch sizes. Examples are presented to illustrate the proposed methodology. (c) 2005 Elsevier Ltd. All rights reserved.