随机过程与排队论大作业

随机过程与排队论

大作业

姓名：李嘉文

学号：1150349310087

日期：2016-01-12

指导教师：石剑虹老师

The Application of Stochastic Process in

Transportation System

1.Intruduction

Economic and social factors haveprofound influences on the level and pattern of travel demand and the choices of travelerswithin a given transport infrastructure. They also impact on the ability of responsibleauthorities to fund the maintenance and improvement of infrastructure, and to conducteffective travel demand management and control policies. It is just at such stages of majorchange and uncertainty that those planning future transport policies most need support inmaking their decisions, but in general this is exactly when most of the modelling tools weadopt fail to offer support, with their assumptions based on either an unchanging world, orone in which the future follows deterministically from the present. Even in periods ofrelative economic/social stability, such assumptions are increasingly difficult to support;this is most notable in cities where continued demand growth has outpaced the expansionin capacity of the transport infrastructure, with the transport system highly sensitive todaily and seasonal fluctuations in demand and capacities.

The question then arises as to how we might develop modelling approaches to better deal with such situations. One approach to such problems is that of ‘worst-case planning’whereby the models suggest actions for a planner to take so as to minimize the impacts under a worst-case scenario.

At its simplestmost stripped down level the Stochastic Process SP) approach could besaid to comprise three main elements for representing the epoch-to-epoch changes in atransport system:

1. A learning model, to describe how travellers learn from their travel experiences in pasttime epochs.

2. A decision model, to describe how travellers make decisions, given their learntexperiences.

3. A supply model, to describe the experiences of travellers in a particular time epoch.

2.Model Establishment

The elements that described in the previous section are described by probability statements or probabilitydistributions, and when brought together they provide a single, self-consistent frameworkfor representing the mutual interactions between the uncertain components of thetransport system. Just as we demand of equilibrium transportation analysis, we can ask towhat extent this combination of elements may produce a well-defined and unique ‘output’(if the long-run is indeed what interests us), but whereas in equilibrium systems we referto a unique flow state, in the SP approach we refer to a unique probability distribution offlows. That is to say, the result of the modelling approach is to