Study status and prospect of traffic signal control for over-saturated intersection
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摘要: 为应对日益严峻的信号交叉口拥堵, 总结了过饱和交叉口交通信号控制研究的发展历程和研究现状, 并分析了未来发展趋势。介绍了过饱和交通流信号控制的多个目标, 包括最小化延误、最大化通行能力、排队长度约束等。分析了过饱和交叉口交通信号控制的多种模型与求解算法, 例如线性规划与优化模型、混合整数规划模型、基于软计算技术和人工智能技术的模型等。总结了典型交通仿真平台和信号控制优化软件对过饱和交通信号控制的支持, 以及现有多个典型信号控制系统中对过饱和交通流状态的控制方法。分析结果表明: 由于过饱和交叉口的交通流特性, 当前过饱和交叉口信号控制方法需要解决变量过多、计算复杂、计算效率低等问题; 过饱和网络的交通流特性、集成优化模型、高效求解算法与技术、仿真平台和示范应用是未来需要关注的研究趋势。Abstract: In order to relieve the serious congestion at signalized intersections, the development course and research status of traffic signal control at over-saturated intersection were summarized, and future development trend was analyzed. The various control objectives of over-saturated traffic flow were introduced, including the minimum delay, the maximum capacity and the queue limitation etc. Several kinds of traffic signal control models and algorithms at over-saturated intersection were analyzed, such as linear programming and optimization models, mixed integer linear programming models and other models based on soft computing and artificial intelligence techniques etc. The traffic signal control under over-saturated condition which was supported by the typical traffic simulation platform and signal control optimization software was summarized, as well as the traffic signal control methods at over-saturated intersection in some typical traffic control systems. Analysis result indicates that according to the traffic flow characteristics at oversaturated intersection, some problems need to be solved by the control methods, including too much parameters, computational complexity and lower computation efficiency etc. In oversaturated network, traffic flow characteristics, integrated optimization model, highly efficient solving algorithm and technology, simulation platform and demonstration application are the future research trends which need to concentrate on.
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价格理论和运输经济学是经济学的两个重要分支。关于运输价格的理论学说观点较多, 大概分三类[1]: 运输成本理论、运输价值论和边际成本论。运输成本理论亦即总收入必须足以支付运输业务一切成本, 运价必须反映价值, 否则运输业的经营活动无法维持, 更不可能扩大再生产。可是交通运输业, 尤其是铁路建设需巨额投资, 分对象所耗费成本很难计算, 总的运输收支的平衡就更难得到, 因此运输成本理论在现实中会遇到很多困难。运输价值理论被称为负担力主义, 根据运输对象的负担能力决定运价, 主张运价上的差别[2]。本文通过讨论不同市场结构中独立的运输公司运用差别价格产生的利益, 探讨其对于铁路运输价格决策的意义。
1. 差别价格与市场权力
1.1 差别价格的含义及存在的条件
厂商如果在同一时期对同一种商品向不同的购买者或购买不同数量的购买者索取两种或两种以上不同价格, 这就是差别化价格。即使商品不完全相同, 如果其价格差别不能反映成本差别, 也称为差别价格[3]。它遵循支付意愿原则, 因而与不同水平的弹性相关。在完全竞争环境下, 大量公司生产完全相同的产品, 资源是完全可移动的, 消费和生产决策的信息是完全的, 所有市场环节都是可以自由出入的, 供应商是价格接受者。运输商不仅没有可行的经济上的战略选择, 也无法设定最优价格。只有那些有能力将价格定在边际成本之上的厂商才有可能实施差别价格策略。
1.2 垄断者与不完全竞争者的市场权力
垄断者和不完全竞争者将价格定在边际成本之上的能力也被称为市场权力。是什么决定了垄断者的市场权力呢?一个垄断者会将其产量增加到单位产品的边际成本等于其边际收益的那一点[4,5]。边际收益是增加一个单位产品给总收益带来的变化, 并可一般性地表示为
式中: MR为边际收益; P、T分别为价格和交通需求量; ETP为交通需求的价格弹性。边际成本与边际收益的交点决定了垄断者的最佳产量
式中: STVC为短期变动总成本; w、r分别为劳动和资本的价格; γ为技术水平的指数; K为总投资水平; k为固定总投资不变; MC为边际成本。
式(2)的左边表示价格高出边际成本的部分占价格的比例, 反映了垄断者将价格定在高于边际成本处的能力, 也是市场权力。从式(2)可看到, 市场权力依赖于需求的价格弹性, 市场需求越是缺乏弹性, 垄断者的市场权力越大, 因此那些决定市场需求价格弹性的因素也就决定了市场权力, 相近的替代品数量和该公司的市场份额是两个因素。一般相近替代品数量越大和公司占有的市场份额越少, 需求的价格弹性越高, 应用到完全竞争中, 就得到了需求完全弹性的预期结果, 因每个完全竞争的公司占有总市场的份额都很小, 并且生产无差异产品。在另一个极端, 垄断者的市场份额为1, 它的价格弹性完全取决于其产品与可能的替代品的差别, 几乎没有替代品时, 价格弹性几乎为零。寡头和垄断竞争者的需求弹性位于两个极端之间, 其市场权力也位于两者之间[6]。
不管产生垄断的原因是生产的经济性还是政府管制, 对于讨论的问题都一样, 只要论述完全垄断者的价格差别策略效果, 就能说明寡头与垄断竞争者的行为, 因为其市场权力介于前两者之间, 在高于边际成本处定价的能力也处于两者之间。
2. 价格差别策略对利润的影响
垄断者常被当成唯一价格设定者。模型还假设一个群体中每个消费者为交通产品T支付相同的价格[7], 另一方面, 假设垄断者拥有选择差别价格的权力。尽管垄断者可以以不同的价格出售产品, 这种价格差异不是基于成本的, 那么垄断者能用差别价格使其收益增加吗?
2.1 统一生产成本时的价格差别
为了能比较独立地分析这个问题, 举一个实例[8]。假设一条固定航线上有一家垄断公司提供旅客运输服务, 以较高价格向商务人员, 较低价格向私人提供客运服务, 据此, 航空公司的差别价格是建立在旅行目的上。航空公司的理由是私人旅行者在旅行时间、旅行方式和目的地上都有较多的替代品可选择, 他们将要比那些没有多少替代品可选择的公务旅行者对价格更敏感。一名商务人员常常要在特定时间到达指定目的地。航空公司真的可以通过向商务旅行者收取比私人旅行者更高价格获得利润最大化吗?公司的利润最大化的战略又是什么呢?根据式(1)
式中: b、v分别为商务和私人旅行者。假设再生产单位商务旅行与休闲旅行的边际成本相同, 利润最大化的垄断者一定使与商务和休闲旅行相关的边际收益相同[3], 即当
时利润达到最大。假设航空公司的价格策略是商务旅行价格高于休闲旅行价格, 即Pb > Pv, 为了保证式(4)成立, 必须要使
考虑到ETP < 0, 式(5)说明垄断者给更具刚性的细分市场设置一个更高的价格, 也就是说不太敏感的市场用较高的价格[7]。另一种说法是, 市场对价格越敏感, 边际成本与价格的差就越小, 那么所采用的向商务旅行者以更高价格出售旅行产品的价格策略是合乎垄断利润最大化理性的, 用图 1可阐述这种战略。假设旅行边际成本是不变的, 并且等于商务和私人休闲旅行的边际成本, 其他因素相同时, 私人旅行者对价格更敏感, 不太愿意接受偏离边际成本许多的价格; 商务旅行者的敏感度较低, 他们比前者更愿为同样的旅程支付更高的价格。
图 1中两个关于差别价格的必要条件是绝对的, 首先需求市场的价格弹性要能相互区分。在上例中, 若两类旅行者对价格变化的敏感度相同, 即ETPb=ETPv, 则每个细分市场的价格必须一样, 差别价格将不会增加利润。第二, 两个市场要分开, 就是说叫高价市场里的人不可能买到低价市场的物品。一般情况下, 航空公司无法把商务旅行者与私人旅行者区分开。有的公司通过强行限制停留时间把两者分开, 因为大多数商务旅行都是一个较短的时期, 这就有效地阻止商务人员到较低的价格市场中来[8]。另一项策略是预定票制度。西方国家很多航线要求乘客至少提前14 d预定, 而改变预定计划要受重罚, 这也是为了限制商务人员进入低价市场, 因为商务人员常常在临走之前没多长时间才能决定, 而度假者是早就计划好了的。不过货运市场要作到这两点较容易。式(4)中的利润最大化平衡条件说明了若垄断者设置价格时忽略了两个市场的需求弹性, 其利益就达不到最优。
2.2 不同边际成本时的差别价格
上例说明同一边际成本但不同价格对利润正的影响。如设垄断者面临着不同的边际成本, 可以通过设置统一价格提高其利润的。由于每个细分市场利润在边际收益等于边际成本处最大, 而假设提供一个商务人员旅行的边际成本要小于给私人旅行者的, 则式(4)就变成
式中: P没有下标, 是因为假设垄断者给两个市场制定一样的价格。将式(6)重写为
这与式(5)是一样的条件, 但不要把统一价格与没有差别价格相混淆。当边际成本不同, 而以同样价格出售时就与相同成本不同价格的差别价格是等同的, 因为在更富于弹性的市场里的价格与边际成本之差要小于较缺乏弹性的市场里的价格与边际成本差(图 2)。因此, 与单一价格策略相比, 垄断者可通过利用市场之间需求价格弹性差别来提高利润。通过这种方式, 价格与边际成本的差与相关市场的需求价格弹性成反相关关系。
图 2 不同边际成本统一价格的差别价格策略Figure 2. Discriminate price of different marginal cost and unified price2.3 与行业生存相关的价格差别
虽然关于价格差别的争论没有最后定论, 竞争者不断制造产品差异以保持和加强市场权力[9]。不过有时候某些商品和服务也只有在实行价格差别下才能生产出来, 即当市场上存在两种差别较大的需求市场, 且需求曲线都位于平均总成本曲线之下时, 若不实行价格差别, 就不存在任何使价格大于等于平均总成本的产量, 若实施价格差别就可能使两个细分市场的综合平均价格大于等于平均总成本。
3. 对铁路运输行业的启示
铁路运输的投资额巨大, 但是短期变动成本占总成本的比例远低于除了管道运输以外的其他运输方式。因此铁路运输的长期平均成本曲线(LAC)相对于其他运输方式的来说离原点要远得多, 也平坦得多, LAC的最低点处产量很高, 一般情况下很难达到。所以铁路公司大多数都运行在LAC最低点的左边, 也就是说继续增加产量会使其平均成本下降。
为了简单说明问题, 将铁路货物运输市场初步分为低值散装货物运输和制造品运输两个细分市场。尽管这两个细分市场的单位运输成本不一样, 但是价格差别策略的思想还是可以在此得到应用。见图 3, 假设制造品运输需求曲线D2穿过LAC, 说明在单一价格策略下行业仍然是可以生存的, 但是散装货物运输需求曲线D1大部分位于平均成本曲线下, 却大部分位于边际成本曲线Mc1之上。只要需求曲线位于边际成本曲线以上, 增加散装货物运输量就可以补偿全部变动成本和部分固定 成本, 使总产量T3产生的平均价格P3大于平均成本, 并增加了运输公司总利润。因此那些面临市场竞争的铁路运输企业制定价格策略时至少要考虑如下几项工作。
(1) 将市场进一步细分。
(2) 估计短期生产函数与成本函数。
(3) 估计每个细分市场的需求函数, 获得各细分市场的需求弹性(含对相近替代品的交叉弹性)。
(4) 针对需求弹性和需求曲线有差别地细分市场, 制定不同价格。
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