應用馬可夫鏈探討駕駛人在車內導引資訊下之逐點動態路徑選擇行為

Applying Markov Chain to Study the Node-to-Node Dynamic Route Choice Behavior under the influence of In-Vehicle Guidance

姜禹辰(Yu-Chen Chiang)

指導教授 ： 董啟崇

淡江大學/管理學院/運輸管理學系碩士班/碩士(2005年)

https://doi.org/10.6846/TKU.2005.00232

摘要

馬可夫鏈為隨機過程中特殊型態，乃應用於處理動態預測分析，其基本定義包括狀態、轉移機率與轉移矩陣，將隨機過程透過轉移機率從一狀態轉移至另一狀態定義，藉由狀態間之轉移機率構成轉移矩陣，可見應用於許多領域預測分析上，如於路面工程、動態交通量指派等。

在交通資訊影響下駕駛者路徑選擇行為之研究中，過去多以個體選擇模式為基礎，通常以羅吉特模式處理靜態型式問題，或運用普羅比模式處理靜態或動態型式問題。在本研究之前系列研究中以多項式普羅比模式描述駕駛者路徑選擇行為，並定義其行為稱為逐點動態決策行為，即以無異帶的觀念構建，並延伸發展包含路網特性、用路者認路行為與空間能力等進階模式。此系列研究將駕駛者變換行為分為三類基準包括動態路徑基準、習慣（行前）路徑基準與建議路徑基準，並將實驗對象分為高能力與低能力，再依實驗地區分為熟悉與不熟悉地區等，可成功描述駕駛者在全程路徑中連續個別決策點路徑選擇機率，具有相當成果。

檢視逐點動態決策行為乃指駕駛者於整個行程中連續決策點實現路徑變換之動作，其型態表示決策對決策間關係與馬可夫鏈狀態至狀態轉換型式類似，因此描述逐點動態決策行為是否符合馬可夫鏈乃為本研究課題。

本研究以馬可夫鏈探討逐點動態決策行為可分為三階段，第一階段根據馬可夫鏈狀態定義，定義在每一個別決策點駕駛者路徑變換行為屬於馬可夫鏈之狀態，並沿用系列研究之動態模擬器實驗與模式，推算駕駛者於每一個別決策點變換或不變換路徑機率。第二階段定義馬可夫鏈，描述逐點決策狀態，並推算馬可夫鏈轉移機率而構建馬可夫鏈轉移矩陣。第三階段根據所構建之轉移矩陣作馬可夫鏈的假設檢定，以歸納分類出不同類型駕駛者在熟悉與不熟悉地區之決策型態屬於一階馬可夫鏈，最後利用馬可夫加上動態規劃方式構建駕駛者最佳路徑初步模型。

經高能力熟悉、高能力陌生、低能力熟悉與低能力陌生之實驗者所構建轉移矩陣，以馬可夫鏈檢定結果發現，利用動態路徑基準描述此類駕駛者轉移矩陣為佳，因此可說明在動態路徑基準構建前提下，逐點動態決策行為符合馬可夫鏈之型式。

關鍵字

逐點動態決策行為 ； 馬可夫鏈 ； 轉移機率

並列摘要

Markovian Decision Process can be referred to a series stochastic decision with a number of states. The transition probabilities between the states are described by a Markov chain. The applications of Markov Decision Process or the related concept of Markov Chain can therefore be found in wide range of problems including these in Transportation such as Dynamic Traffic Assignment (DTA), dynamic analyses in Pavement Management System (PMS) and other problems with state-dependent nature. Of particular importance is the application of dynamic programming to obtain the optimal solution of stochastic Markovian decisions.

The node-to-node dynamic route choice behavior is of the most interest to study the individual driver’s route choices under the influence of the route guidance information where individual driver makes consecutive route switch decisions along with the traveling route. This particular issue has been successfully modeled with various forms and extensions under the notion of the “Indifference Bands” applied with Probit model specifications by Tong and his students at Tamkang University in recent years. The probability of “swithching” or “route choice” at each decision node along the route can therefore be estimated under these model specifications.

The analogy seems quite attractive to examine the so-called “node-to-node” dynamic decision to the state-to-state Markovian Decision Process. In this thesis, the “state” was defined at each decision node and the transition probabilities and the associated transition matrices were derived from the probabilities estimated from the node-to-node behavior model under three various definitions of dynamic switches at each node. A statistical test was performed to evaluate the hypothesis of first order Markov Chain.

The data bases for this thesis were compiled from two previous experiments under simulated environment using a special purpose in-vehicle guidance simulator applied to Taipei metropolitan area. The statistical tests results have confirmed that the node-to-node decision can be successfully referred to fit into a first-order Markovian Process at individual level. In addition, the study has also demonstrated the application of dynamic programming to obtain an optimal cause of routing decision for the individual driver. These results have suggested the further study to develop the dynamic route guidance strategies based on the current modeling treatments and findings. The analysis of aggregate behavior based on similar concept can be encouraged as well.

並列關鍵字

Node-to-Node Dynamic Route Choice Behavior ； Markovian Decision Process ； Markov Chain ； Transition Probability

參考文獻

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