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Mathematical Problems in Engineering
Volume 2017 (2017), Article ID 6380521, 18 pages
Research Article

A Two-Stage Queue Model to Optimize Layout of Urban Drainage System considering Extreme Rainstorms

1Shanghai Maritime University School of Economics and Management, Shanghai 201306, China
2Tongji University School of Economics and Management, Shanghai 200092, China

Correspondence should be addressed to Wenfa Hu

Received 27 August 2016; Revised 31 December 2016; Accepted 5 February 2017; Published 19 March 2017

Academic Editor: Mauro Gaggero

Copyright © 2017 Xinhua He and Wenfa Hu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Extreme rainstorm is a main factor to cause urban floods when urban drainage system cannot discharge stormwater successfully. This paper investigates distribution feature of rainstorms and draining process of urban drainage systems and uses a two-stage single-counter queue method to model urban drainage system. The model emphasizes randomness of extreme rainstorms, fuzziness of draining process, and construction and operation cost of drainage system. Its two objectives are total cost of construction and operation and overall sojourn time of stormwater. An improved genetic algorithm is redesigned to solve this complex nondeterministic problem, which incorporates with stochastic and fuzzy characteristics in whole drainage process. A numerical example in Shanghai illustrates how to implement the model, and comparisons with alternative algorithms show its performance in computational flexibility and efficiency. Discussions on sensitivity of four main parameters, that is, quantity of pump stations, drainage pipe diameter, rainstorm precipitation intensity, and confidence levels, are also presented to provide guidance for designing urban drainage system.