Dynamic Equilibrium and Optimal Solution to the Bottleneck Queuing Pricing Model

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Project title

Code/計畫編號

MOST106-2410-H019-026

Translated Name/計畫中文名

瓶頸等候定價模式之動態均衡與最佳解

Project Coordinator/計畫主持人

Chen-Hsiu Laih

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Merchant Marine

Website

https://www.grb.gov.tw/search/planDetail?id=12283454

Year

2017

Start date/計畫起

01-08-2017

Expected Completion/計畫迄

31-07-2018

Bugetid/研究經費

465千元

ResearchField/研究領域

經濟學

"傳統的瓶頸等候定價模式，旨在探討固定數量且時間價值相同之使用者，需在特定時刻到達目的地，但受限瓶頸場域容量低於使用者到達量，因而造成使用者排隊等候之現象。瓶頸等候定價模式透過收費金額取代等候時間成本，導致使用者分散其原本的出發時刻，進而達到消除或減少排隊等候時間之目的。該模式之發展已趨完整且頗具規模，並應用在實務上，如新加坡電子道路收費(ERP)以及倫敦市中心的擁擠收費等。然而現今交通運輸的快速進步與發展，對於傳統瓶頸等候定價模式之假設，產生以下之質疑： (1).使用者之時間價值可能不盡相同，(2).使用者數量可能不固定，(3).使用者之預計到達時刻可能非固定。本研究放寬上述假設狀態，改良傳統的瓶頸等候定價模式，並推導出動態均衡與最佳解。首先考量不同時間價值之使用者出發時刻偏好性，並將預計到達時刻由傳統模式之固定時刻放寬至彈性到達時段，建立異質使用者到達模式；亦修正傳統模式中固定數量使用者之假設，建構動態數量異質使用者之成本函數。接著計算動態數量異質使用者之均衡成本，並推導出該改良模式的最佳收費架構。最後比較改良前、後瓶頸等候定價模式之排隊等候消除效果與使用者到達分散行為，並進行改良模式之實例應用，以探究該模式的可行性。改良後的瓶頸等候定價模式更加符合實務現況，可有效減少尖峰需求使用者排隊等候之時間成本損失，進而提升瓶頸場域之服務品質與相關產業之競爭力。""The traditional bottleneck queuing pricing model is to explore a fixed number of homogeneous users with the same time value and need to arrive at the destination at a specific time, but the restricted capacity of the bottleneck field is lower than the user's arrival, thus causing the user to wait in line. The queuing time cost is completely replaced by the equivalent charge amount in the bottleneck pricing model, which causes the users to disperse their original departure time, so as to eliminate or reduce the queuing time. The development framework of this model has become more complete and scale, and applied in practice, such as the Singapore Electronic Road Pricing (ERP) and the road congestion tolling in the central area of London. However, the rapid progress and development of transportation today have created some doubts about the assumptions of the traditional bottleneck pricing model as follows: (1) the user's time value may not be the same, (2) the number of users may not be fixed, (3) the expected arrival time of the user may not be fixed. This study relaxes the above assumptions, improves the traditional bottleneck pricing model, and derives the dynamic equilibrium and optimal solution. Firstly, consider the heterogeneous user’s preference of departure time with flexible working hours to establish the model of the heterogeneous user’s departure patterns. Secondly, relax the assumption that the number of users is fixed in the traditional model to construct the user’s dynamic queuing cost function. Thirdly, calculate the heterogeneous user’s dynamic equilibrium cost, and then deduce the optimal tolling structure for the improved model. Finally, compare effects of the bottleneck pricing models on queuing reduction and departure behavior before and after improvement of the traditional model. In addition, simulate the practical case of the improved model to explore the feasibility of the model. The improved bottleneck queuing pricing model, which is more in line with the actual situation, will reduce the efficiency loss of user’s queuing time through the peak demand period, and enhance the service quality of the bottleneck field and the competitiveness of the related industries."

Keyword(s)

瓶頸
排隊等候
出發時刻
動態均衡
最佳收費
bottleneck
queuing
departure time
dynamic equilibrium
optimal tolling

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Dynamic Equilibrium and Optimal Solution to the Bottleneck Queuing Pricing Model

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