JP4481235B2 - High-precision estimation method of generated / concentrated traffic volume and OD traffic volume by zone - Google Patents
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Description
本発明は、観測リンク交通量を用いたゾーン別発生・集中交通量及びゾーン間OD交通量を高精度に推定する方法に関する。 The present invention relates to a method for accurately estimating the generated / concentrated traffic volume by zone and the OD traffic volume between zones using observed link traffic volume.
従来、道路交通量の推定は段階推定法で行われていた。段階推定法とは、先ずゾーン別の発生・集中交通量を社会経済指標データから推定し、次にゾーン別発生・集中交通量に一致するように各ゾーン間のOD(Origin-Destination)交通量を推定し、最後にOD交通量を道路ネットワーク上に経路配分して、各道路区間（リンク）上の交通量を推定しようとするものである（特許文献１、非特許文献１−３）。
Conventionally, estimation of road traffic volume has been performed by a stage estimation method. The stage estimation method first estimates the generated / concentrated traffic volume by zone from the socio-economic index data, and then the OD (Origin-Destination) traffic volume between each zone to match the generated / concentrated traffic volume by zone. Finally, the OD traffic volume is routed on the road network to estimate the traffic volume on each road section (link) (
しかし、この段階推定法で推定された道路区間交通量は、実際の交通量と大きな差を生じることがあった。その理由の一つは、対象地域におけるゾーン分割と道路ネットワーク記述が整合していないことにある。 However, the road segment traffic volume estimated by this stage estimation method may have a large difference from the actual traffic volume. One of the reasons is that the zone division in the target area and the road network description are not consistent.
道路ネットワークの一例を図１に示す。道路ネットワークは、道路区間を表すリンクと、リンクを結合するノードで記述される。また、ノードはゾーンにおける交通量の発生・集中が行われるセントロイド（●）と、交通量の分岐及び通過が行われるノード（○）に分類される。 An example of a road network is shown in FIG. The road network is described by a link representing a road section and a node connecting the links. The nodes are classified into a centroid (●) where traffic volume is generated and concentrated in the zone and a node (◯) where traffic volume is branched and passed.
対象地域におけるゾーン分割は、交通発生・集中量を推定するための社会経済指標データとの関係から、一般的には行政区単位で行われている。従って、一つのゾーン内に多数のセントロイドが含まれることが多く、段階推定法で得られたゾーン間OD交通量をセントロイド間OD交通量に修正することが必要となる。 Zone division in the target area is generally performed in units of administrative districts because of the relationship with socio-economic index data for estimating traffic generation and concentration. Therefore, many centroids are often included in one zone, and it is necessary to correct the OD traffic volume between zones obtained by the stage estimation method to the OD traffic volume between centroids.
この修正作業は、各ゾーンにおける発生・集中交通量をセントロイド数で按分するような簡易な方法で行われており、セントロイド間OD交通量は現実の道路ネットワークに整合していない。このため、道路ネットワーク上で厳密な経路配分によるセントロイド間OD交通量を推定計算しても、結果としてリンク交通量は実際観測値とは大きく異なりうる。これは配分理論の非現実性とも関係している。 This correction work is performed by a simple method that apportions the generated / concentrated traffic volume in each zone by the number of centroids, and the OD traffic volume between centroids is not consistent with the actual road network. For this reason, even if the OD traffic volume between centroids is estimated and calculated by strict route allocation on the road network, as a result, the link traffic volume may greatly differ from the actual observed value. This is also related to the unreality of distribution theory.
本発明が解決しようとする課題は、このような従来法の欠点を排し、より信頼性の高い新しい道路交通量推定法を提供することである。本発明により、現実の道路ネットワークに対応した高精度のゾーン別発生・集中交通量、ゾーン間OD交通量、OD別リンク交通量を推定することができ、新規道路の建設効果や各種交通規制・誘導策の実施効果を、事前事後の交通流変化を比較分析することにより的確に検証評価することができる。 The problem to be solved by the present invention is to eliminate such drawbacks of the conventional method and to provide a new road traffic volume estimation method with higher reliability. According to the present invention, it is possible to estimate the generation / concentrated traffic volume by zone, the OD traffic volume between zones, and the link traffic volume by OD corresponding to the actual road network, the construction effect of the new road, various traffic regulations, The implementation effect of the guidance measures can be verified and evaluated accurately by comparing and analyzing the traffic flow changes after the ex-ante.
上記課題を解決するために成された本発明に係る道路交通量の推定方法は、
a)現実の道路ネットワークに対応して対象域内と域外のゾーン分割を行うと共に、各ゾーンに対応するノードと、各ノードを結ぶリンクと、を定め、
b)域外及び域内の各ノードを結ぶリンクの観測リンク交通量v * を用いて、域内ノードiにおける集中交通量Aiを発生交通量Giの関数として定式化し、
c)定式化された各ノードの集中交通量Aiに基づき、域内−域内、域外−域内のOD交通に関する発生ノード別目的地選択確率m, qを算出し、一方、域外ノードlにおける観測集中交通量D l に基づき、域内−域外、域外−域外のOD交通に関する発生ノード別目的地選択確率n, rを算出し、
d)予め与えられた、域内ノードにおける発生交通量の域内集中確率τ及び域外ノードにおける発生交通量の域内集中確率λに対し、ノード別発生交通量G i とその域内域内集中確率τ及び前記発生ノード別目的地選択確率m, nを用いて、内内OD交通量X及び内外OD交通量Yを推定し、さらに、域外ノードkから域内への観測発生交通量S k とその域外域内集中確率λ及び前記発生ノード別目的地選択確率q, rを用いて、外内OD交通量Uと外外OD交通量Wを推定し、
e)前記各OD交通量X, Y, U, W、及び、i-jノード間OD交通が特定リンクaを利用する予め与えられたリンク利用確率Pij aを用いて各リンク交通量を推定し、
f)推定リンク交通量と観測リンク交通量の差の平方和Φが最小となる発生交通量Giを決定し、
g)決定した発生交通量Gi (t)とb)において用いた発生交通量Gi (t-1)の差が所定値ε以下となるまで発生交通量G i の修正及びb)〜f)の計算を繰り返す
ことにより、域内ノードの発生交通量と集中交通量、及び、域内と域外におけるすべてのノード間OD交通量を推定する。
The road traffic volume estimation method according to the present invention made to solve the above problems is as follows.
defined a) real road network line zoning of the target region and outside in response to Utotomoni, a node corresponding to each zone, and a link connecting each node, and
b) Using the observed link traffic v * of the links connecting nodes outside and within the region, formulate the concentrated traffic A i at the node i in the region as a function of the generated traffic G i ,
c) On the basis of the concentrated traffic volume A i of each node , the destination selection probability m, q for each source node for OD traffic within the region and within the region and outside the region is calculated. Based on the traffic volume D l , the destination selection probability n, r for each source node related to OD traffic within the region and outside the region and outside and outside the region is calculated,
d) With respect to the intra-regional concentration probability τ of the generated traffic volume in the regional node and the intra-regional concentration probability λ of the generated traffic amount in the outside node given in advance, the generated traffic volume G i by node , the intra-regional regional concentration probability τ and the occurrence using the node-specific destination selection probability m, n, the estimate of the inner in the OD traffic volume X and the inner and outer OD traffic volume Y, further observation generated traffic S k and its outside region concentrate probability to the region from outside the node k Using λ and the destination node-specific destination selection probabilities q and r, the outside / outside OD traffic volume U and the outside / outside OD traffic volume W are estimated,
e) Estimate each link traffic volume using the link usage probability P ij a given in advance for each OD traffic volume X, Y, U, W and ij inter-node OD traffic using a specific link a,
f) Determine the generated traffic volume G i that minimizes the sum of squares Φ of the difference between the estimated link traffic volume and the observed link traffic volume,
g) Correction of the generated traffic volume G i until the difference between the determined generated traffic volume G i (t) and the generated traffic volume G i (t-1) used in b) is equal to or less than a predetermined value ε, and b) to f ) Is repeated , the generated traffic volume and concentrated traffic volume of the nodes in the area, and all the inter-node OD traffic volumes in and outside the area are estimated.
ここで、上記推定目的地選択確率mは、ノード間距離tijの関数としてもよい。 Here, the estimated destination selection probability m may be a function of the inter-node distance t ij .
その場合、前記関数は例えばtij -γ（γはパラメータ）とすることができる。パラメータγは、観測値と合うように調整することができる。 In this case, the function can be, for example, t ij -γ (γ is a parameter). The parameter γ can be adjusted to match the observed value.
上記f)において、推定リンク交通量と観測リンク交通量の差の平方和と、域内ノードにおける推定発生交通量Giと観測値Ggi *の差の平方和の合計値が最小となるように発生交通量Giを決定するようにしてもよい。 In the above f), the sum of the sum of squares of the difference between the estimated link traffic volume and the observed link traffic volume and the sum of squares of the difference between the estimated generated traffic volume G i and the observed value Gg i * in the regional node is minimized. it may be determined to occur traffic volume G i.
また、f)において決定された発生交通量Giが負になる場合、非負制約条件を入れることができる。 Also, when the occurrence traffic volume G i determined in f) is negative, it is possible to put a non-negative constraint.
さらに、一部のノードに接続する各リンクを通る車両番号の照合を観測することにより、対象域全体の方向別の対象ノード通過推移確率と対象ノード集中（流入）確率、および対象ノードから隣接ノードへの発生（流出）推移確率を推定して、OD交通量を推定することができる。
しかし、観測ノード数を多くすることは実際上困難なため、これだけでは十分な精度を出すことができない。その場合には、観測値から求められた対象ノード通過推移（分岐）確率を利用し、対象ノードへの集中確率θを未知変数として内生化して、後述の方法により、高精度の推定を行うことができる。
Furthermore, by observing the verification of vehicle numbers that pass through each link connected to some nodes, the target node passage transition probability and target node concentration (inflow) probability for each direction of the entire target area, and the target node to the adjacent node OD traffic volume can be estimated by estimating the occurrence (outflow) transition probability.
However, since it is practically difficult to increase the number of observation nodes, this alone cannot provide sufficient accuracy. In that case, the target node passage transition (branch) probability obtained from the observed value is used, the concentration probability θ on the target node is endogenousized as an unknown variable, and high-precision estimation is performed by the method described later. be able to.
本願発明は次のような考えを元になされた。
第１に、対象地域のゾーン分割を現実の道路ネットワークと整合する形で行うこととした。本方法では、従来のようにノードとセントロイドを区別することはせず、ノードをすべてセントロイドして扱う。そして、１つのノード毎に１つのゾーンを設けることとした。これにより、ゾーン間OD交通量が現実的なノード間OD交通量として推定されることになる。
ただし、道路ネットワークは実際のネットワーク形状を現実どおりに詳細に記述する必要はなく、利用目的に応じて道路リンクの統合・省略を行って簡略的に模式表示してよい。
The present invention has been made based on the following idea.
First, the zone division of the target area is performed in a manner consistent with the actual road network. In this method, the nodes and centroids are not distinguished as in the prior art, and all nodes are handled as centroids. One zone is provided for each node. As a result, the inter-zone OD traffic volume is estimated as a realistic inter-node OD traffic volume.
However, the road network does not need to describe the actual network shape in detail as it is, and may be schematically displayed by integrating and omitting road links according to the purpose of use.
第２に、従来の段階推定法とはまったく逆の発想で、道路上を走行している実際交通量の観測値から、各ゾーンの発生交通量を推定することとした。ゾーン別発生交通量が推定されると、ゾーン別集中交通量は、観測リンク交通量を用いて、ゾーン別発生交通量の関数で記述できる。発生ゾーン別目的地選択確率は、目的地選択確率が目的地ゾーンの集中交通量に依存することから、発生交通量の関数として推定できる。OD交通量は、ゾーン別発生交通量に発生ゾーン別目的地選択確率を乗じることで推定される。また、リンク交通量は、OD交通量にOD別リンク利用率を乗じ、リンクごとに加算することで得られる。OD交通量には対象域の内内、内外、外内、外外の４種類あるが、これらのOD交通に対するリンク交通量の推定値と観測値の誤差（残差平方和）を最小化することで、対象域内のゾーン別発生交通量を推定するのが、本発明の考え方である。この残差平方和を最小化するモデルは、連立方程式の繰り返し計算により、精度の高いゾーン別発生交通量が推定できる。このことにより、従来の配分結果であるリンク交通量が現実値と大きな差異を生じるという問題はなくなる。 Secondly, the generated traffic volume in each zone is estimated from the observed value of the actual traffic volume traveling on the road, with the idea opposite to the conventional stage estimation method. When the generated traffic volume by zone is estimated, the concentrated traffic volume by zone can be described as a function of the generated traffic volume by zone using the observed link traffic volume. The destination selection probability by generation zone can be estimated as a function of the generated traffic volume because the destination selection probability depends on the concentrated traffic volume of the destination zone. The OD traffic volume is estimated by multiplying the generated traffic volume for each zone by the destination selection probability for each generated zone. The link traffic volume is obtained by multiplying the OD traffic volume by the OD-specific link usage rate and adding it for each link. There are four types of OD traffic within the target area: inside, inside, outside, outside, and outside, and the error (estimated sum of squares) of the estimated and estimated link traffic for these OD traffic is minimized. Thus, the idea of the present invention is to estimate the generated traffic volume by zone in the target area. The model that minimizes the residual sum of squares can estimate the generated traffic volume by zone with high accuracy by iterative calculation of simultaneous equations. This eliminates the problem that the link traffic volume, which is the conventional distribution result, has a large difference from the actual value.
第３に、上の方法とは別に、ノードに接続する各リンクを通る車両番号の照合により、方向別の対象ノード通過推移確率と対象ノード集中（流入）確率、および対象ノードから隣接ノードへの発生（流出）推移確率を推定して、ノード別発生交通量Giと発生ノード別目的地選択確率m, n, ｑ, ｒを算出し、これらからOD交通量を推定する方法がある。
ただし、このような車両番号照合法の適用が困難な場合は、観測された対象ノード通過推移（分岐）確率を利用し、また対象ノードへの集中確率θを未知変数として内生化して推定する方法も用いることができる。 この方法では、θに対するノード別発生交通量Gi ~をノード別発生・集中交通量条件式から算出し、一方でθに対するノード別推移確率から発生ノード別目的地選択確率を算出して残差平方和モデルでノード別発生交通量Gi ^を推定し、両者の差|Gi ~−Gi ^|が所定の収束基準値ε以下となるまでθの修正を繰り返すことで、ゾーン別発生交通量とOD交通量を推定することができる。
Thirdly, apart from the above method, by comparing the vehicle number passing through each link connected to the node, the target node passage transition probability and target node concentration (inflow) probability by direction, and from the target node to the adjacent node There is a method of estimating the occurrence (outflow) transition probability, calculating the generated traffic volume G i for each node and the destination selection probability m, n, q, r for each generated node, and estimating the OD traffic volume from these.
However, when it is difficult to apply such a vehicle number verification method, the observed transition probability (branch) probability of the target node is used, and the concentration probability θ on the target node is endogenously estimated as an unknown variable. Methods can also be used. In this method, the node-generated traffic volume G i ~ for θ is calculated from the node-specific generated / concentrated traffic volume conditional expression, while the destination selection probability for each source node is calculated from the node-specific transition probability for θ and the residual is calculated. Estimate the generated traffic volume G i ^ by node with the sum of squares model, and repeat correction of θ until the difference | G i ~ −G i ^ | Traffic volume and OD traffic volume can be estimated.
これらの方法により、車両番号照合法を適用できるノードと適用困難なノードを組み合わせて、ゾーン別発生交通量とOD交通量を高精度に推定することができる。 By these methods, it is possible to estimate the generated traffic volume and OD traffic volume by zone with high accuracy by combining nodes that can be applied with the vehicle number matching method and nodes that are difficult to apply.
本発明に係る方法を用いることにより、ゾーン別発生・集中交通量、ゾーン間OD交通量、OD別経路交通量の現状値が高精度で推定できるので、これらを社会経済指標データと関連付けることにより、将来推定値の精度向上が実現できる。 By using the method according to the present invention, it is possible to estimate the current values of the generated / concentrated traffic volume by zone, the OD traffic volume between zones, and the route traffic volume by OD with high accuracy. In the future, the accuracy of the estimated value can be improved.
従来の段階的推定法では困難であった時間帯毎のゾーン別発生・集中交通量やゾーン間OD交通量、OD別リンク交通量も容易に推定でき、道路ネットワークにおける時間帯ごとの効果的な交通規制・誘導策が計画できる。 Occurrence / concentrated traffic by zone, OD traffic between zones, and link traffic by OD for each time zone, which was difficult with the conventional stepwise estimation method, can be easily estimated. Traffic regulation and guidance measures can be planned.
リンク交通量を車種別に観測することにより車種別の各ノードの発生交通量と集中交通量を推定できる。対象道路ネットワークが広域になった場合、対象域を分割統合することにより本手法が適用できる。 By observing the link traffic volume for each vehicle type, it is possible to estimate the generated traffic volume and the concentrated traffic volume for each node of the vehicle type. When the target road network becomes a wide area, this method can be applied by dividing and integrating the target area.
すべてのリンク交通量がその容量限界まで流れると仮定することにより、各ゾーンにおける発生・集中交通量の上限が推定できるので、ゾーンごとの発生・集中交通量に対する適正な規制・誘導策を計画することができる。 Assuming that all link traffic flows to its capacity limit, the upper limit of generated / concentrated traffic in each zone can be estimated, so plan appropriate regulations and guidance measures for generated / concentrated traffic in each zone. be able to.
道路ネットワークにおけるリンク交通量を継続的に観測することにより、本モデルを用いて時間帯別のゾーン別発生・集中交通量、ゾーン間OD交通量、OD別リンク交通量をデータ蓄積できるので、これより道路ネットワーク交通流の変動特性が分析解明できる。また、これらの交通量データとプローブなどによる走行時間データを結合することにより、走行移動時間の安定性を目指した先進的な動的交通管理運用策が実現できるようになる。また、大規模なイベント時や突発事象発生時における道路ネットワーク交通量の動態変化も把握できることから、いわゆる非常時の交通管理対策が計画可能となる。 By continuously observing the link traffic volume in the road network, this model can be used to accumulate data on generated / concentrated traffic volume by zone, OD traffic volume between zones, and link traffic volume by OD. It is possible to analyze and clarify the fluctuation characteristics of road network traffic flow. In addition, by combining these traffic volume data and travel time data by a probe or the like, an advanced dynamic traffic management operation policy aiming at stability of travel time can be realized. In addition, since it is possible to grasp the dynamic change of the road network traffic volume at the time of a large-scale event or sudden occurrence, so-called emergency traffic management measures can be planned.
道路ネットワークにおける動的交通流シミュレーションモデルは近年急速に発展してきたが、ゾーン別発生・集中交通量及びノード間OD交通量に関するインプットデータの作成は依然として課題として残されている。本モデルと動的交通流シミュレーションモデルを結合することにより、シミュレーションモデルの現実性を格段に高めることができる。 Although dynamic traffic flow simulation models in road networks have been rapidly developed in recent years, the creation of input data regarding the generated / concentrated traffic volume by zone and the OD traffic volume between nodes remains a problem. By combining this model with the dynamic traffic flow simulation model, the reality of the simulation model can be greatly enhanced.
この方法では、現実道路ネットワークに対応してゾーン別発生交通量やOD交通量が推定できるので、GIS（Geographical Information System）による土地利用データと結合させて、街路整備計画や市街地再開発計画、容積率制限などに対する有用な都市計画データとして利用することができる。 Since this method can estimate the generated traffic volume and OD traffic volume by zone corresponding to the real road network, it is combined with land use data by GIS (Geographical Information System), and it is combined with the street improvement plan, urban redevelopment plan, volume It can be used as useful city planning data for rate restrictions.
(1) 本発明の概要
現実道路ネットワークに対応した各ゾーンの発生交通量と集中交通量を路上観測交通量（リンク観測交通量）を用いて高精度で推定する方法を開発した。従来の残差平方和モデル（非特許文献２）では目的地選択確率の過去データあるいはサンプル調査データが必要であるが、本発明では目的地選択確率を未知変量として改良し、過去データが存在しなくても推定できるようにした。
(1) Outline of the present invention A method for estimating the generated traffic volume and the concentrated traffic volume of each zone corresponding to the real road network with high accuracy using the road observation traffic volume (link observation traffic volume) was developed. The conventional residual sum of squares model (Non-Patent Document 2) requires past data of the destination selection probability or sample survey data. In the present invention, the destination selection probability is improved as an unknown variable, and past data exists. I was able to estimate without it.
対象域内と対象域外の道路ネットワークの一例を図２に示す。まず、対象域内を、現実の道路ネットワークに対応してゾーン分割する。図２の例では単純化のために対象域内を３×３の９ゾーンに分割している。次に、境界の域内ゾーンに隣接する対象域外をそれぞれ域外ゾーンとする。そして、各ゾーンに１つのノードを対応させる。 An example of a road network inside and outside the target area is shown in FIG. First, the target area is divided into zones corresponding to the actual road network. In the example of FIG. 2, the target area is divided into 3 × 3 9 zones for simplification. Next, the outside of the target area adjacent to the in-zone zone of the boundary is set as the outside zone. Then, one node is associated with each zone.
観測リンク交通量を用いて各ノードiの発生交通量と集中交通量の関係を定式化し、集中交通量を発生交通量と観測リンク交通量の関数で記述する。目的地選択確率は、目的地集中交通量の関数と考えられることから、ノード別発生交通量の関数で記述する。ゾーン別発生交通量は、ゾーン間OD交通量の経路配分によるリンク交通量の推定値と観測値の残差平方和を最小化することで推定されるので、推定モデルの未知変数はゾーン別発生交通量のみとなる。 The relationship between the generated traffic volume and the concentrated traffic volume at each node i is formulated using the observed link traffic volume, and the concentrated traffic volume is described as a function of the generated traffic volume and the observed link traffic volume. Since the destination selection probability is considered as a function of the destination concentrated traffic volume, it is described as a function of the generated traffic volume by node. Since the generated traffic volume by zone is estimated by minimizing the residual sum of squares of the estimated value of the link traffic volume and the observed value by the route allocation of the OD traffic volume between zones, unknown variables of the estimation model are generated by the zone. Only traffic volume.
最適解を得る方法として、連立一次方程式の繰り返しによる実用的な計算法を開発した。また、ノード別発生交通量の推定値が負とならないようKuhn-Tucker条件式を考慮した計算方法を開発した。ノード別発生交通量が推定されると、リンク観測交通量からノード別集中交通量が得られる。また、モデルで推定された目的地選択確率からゾーン間OD交通量が求められる。OD別リンク交通量はOD別リンク利用率を乗じることで推定できる。 As a method to obtain the optimal solution, a practical calculation method by repeating simultaneous linear equations was developed. We have also developed a calculation method that takes into account the Kuhn-Tucker conditional expression so that the estimated traffic volume by node does not become negative. When the generated traffic volume by node is estimated, the concentrated traffic volume by node can be obtained from the link observed traffic volume. In addition, the OD traffic volume between zones is obtained from the destination selection probability estimated by the model. Link traffic volume by OD can be estimated by multiplying the link utilization rate by OD.
(2) ノード（ゾーン）における発生・集中交通量と観測リンク交通量の関係
Giを対象域内部ノードiからの発生交通量、Aiを対象域内部ノードiへの集中交通量、vij *をノードiからノードjへ向かうリンクij（場合に応じてリンクaと記述する）上の観測交通量とするとき、
Gi−Ai = Σjvij *−Σjvji * = Σj(vij *−vji *) = Δvi * （１）
である。すなわち、
Ai = Gi−Δvi * （２）
である。このように、ゾーン集中交通量はゾーン発生交通量の関数として記述される。この関係を図３に示した。また、本発明に現れる各パラメータを図４に整理して示したので、以下の説明において参照されたい。
(2) Relationship between generated / concentrated traffic volume and observed link traffic volume in node (zone)
G i is the traffic generated from node i inside the target area, A i is the concentrated traffic volume to node i inside the target area, and v ij * is the link ij going from node i to node j. Yes) when the above observed traffic volume
G i −A i = Σ j v ij * −Σ j v ji * = Σ j (v ij * −v ji * ) = Δv i * (1)
It is. That is,
A i = G i −Δv i * (2)
It is. Thus, the zone concentrated traffic volume is described as a function of the zone generated traffic volume. This relationship is shown in FIG. In addition, the parameters appearing in the present invention are shown in FIG. 4 in order to refer to them in the following description.
(3) 目的地選択確率の定式化
対象域内OD交通の各発生ノードからの目的地選択確率は目的地ゾーンの集中交通量Ajに比例すると仮定する。対象域が狭いときはこの仮定は概ね妥当であるが、対象域が広くなると距離抵抗f(tij)を組み込むことが考えられる。
(3) Formulation of destination selection probability It is assumed that the destination selection probability from each source node of OD traffic in the target area is proportional to the concentrated traffic volume A j of the destination zone. This assumption is generally valid when the target area is narrow, but it can be considered that the distance resistance f (t ij ) is incorporated when the target area becomes wide.
すなわち、対象域内から域内への内内OD交通量の目的地選択確率mijは、次のように仮定する。
対象域が狭い場合、
mij = Aj/ΣjAj = (Gj−Δvj *)/{Σj(Gj−Δvj *)} （３）
対象域が広い場合、
mij = Ajf(tij)/ΣjAjf(tij) = (Gj−Δvj *)f(tij)/{Σj(Gj−Δvj *)f(tij)} （４）
That is, the destination selection probability m ij of the internal OD traffic volume from the target area to the internal area is assumed as follows.
If the target area is narrow,
m ij = A j / Σ j A j = (G j −Δv j * ) / {Σ j (G j −Δv j * )} (3)
If the target area is wide,
m ij = A j f (t ij ) / Σ j A j f (t ij ) = (G j −Δv j * ) f (t ij ) / {Σ j (G j −Δv j * ) f (t ij )} (4)
距離抵抗f(tij)は、例えば、
f(tij) = tij -γ （５）
とすることができる。ただし、tijはij間の距離、γはパラメータである。
The distance resistance f (t ij ) is, for example,
f (t ij ) = t ij -γ (5)
It can be. Where t ij is a distance between ij and γ is a parameter.
同様に、対象域外から対象域内への外内OD交通量の目的地選択確率qkj、対象域内から対象域外への内外OD交通量の目的地選択確率nil、及び対象域外から対象域外への外外OD交通量（通過OD交通）の目的地選択確率rklはそれぞれ次のように表される。
qkj = Aj/ΣjAj = (Gj−Δvj *)/{Σj(Gj−Δvj *)} （６）
nil = Dl/ΣlDl （７）
rkl = Dl/ΣlDl （８）
ここに、Dlは外部ノードｌへの集中（流出）交通量である。
以上の４つの目的地選択確率mij、qkj、nil、rklを図５及び図６にまとめて示した。
Similarly, the destination selection probability q kj of outside / inside OD traffic from outside the target area to inside the target area, the destination selection probability n il of inside / outside OD traffic from inside the target area to outside the target area, and from outside the target area to outside the target area The destination selection probability r kl of outside / outside OD traffic (passing OD traffic) is expressed as follows.
q kj = A j / Σ j A j = (G j −Δv j * ) / {Σ j (G j −Δv j * )} (6)
n il = D l / Σ l D l (7)
r kl = D l / Σ l D l (8)
Here, D l is the concentrated (outflow) traffic volume to the external node l.
The above four destination selection probabilities m ij , q kj , n il , and r kl are collectively shown in FIGS.
内外交通及び外外交通の目的地選択確率nil及びrklの決定については、別の方法として、前述の車両番号照合観測値を用いたノード推移確率計算法により行うことができる。 The determination of the destination selection probabilities n il and r kl of the domestic / external traffic and the external / external traffic can be performed by the node transition probability calculation method using the vehicle number collation observation value as another method.
(4) OD交通量の数式表示
域内ノードiにおける発生交通の域内集中確率及び域外集中確率をそれぞれτ及び1−τとすると、内内OD交通量は次のように算出される（0<τ<1）。域内ノードにおける発生ノード別の域内集中確率及び域外集中確率の過去データあるいはサンプル調査データが存在する場合はτiとする。
Gi I = τGi （９）
Xij = Gi Imij = τGimij (10)
ΣjXij = Gi I, ΣiXij = Aj I （11)
ここに、Xijは内部ノードiから内部ノードjへの内内OD交通量、Gi Iは内内OD交通に対する内部ノードiからの発生交通量、Aj Iは内内OD交通に対する内部ノードjへの集中交通量である。
(4) Mathematical expression of OD traffic volume When the intra-region concentration probability and the out-of-region concentration probability of generated traffic at intra-region node i are τ and 1-τ, respectively, the internal OD traffic volume is calculated as follows (0 <τ <1). If there is past data or sample survey data of intra-regional concentration probability and out-of-region concentration probability for each generation node in the regional node, τ i is set.
G i I = τG i (9)
X ij = G i I m ij = τG i m ij (10)
Σ j X ij = G i I , Σ i X ij = A j I (11)
Where X ij is the internal OD traffic volume from internal node i to internal node j, G i I is the generated traffic volume from internal node i for internal OD traffic, and A j I is the internal node for internal OD traffic. It is the concentrated traffic volume to j.
内外OD交通量は次のように算出される。
Gi E = (1−τ)Gi (12)
Gi I + Gi E = τGi + (1−τ)Gi = Gi (13)
Yil = Gi Enil = (1−τ)Ginil (14)
ΣlYil = Gi E, ΣiYil = Dl I (15)
ここに、Yilは内部ノードiから外部ノードlへの内外OD交通量、Gi Eは内外OD交通に対する内部ノードiからの発生交通量、Dl Iは内外OD交通に対する外部ノードlへの集中交通量（対象域外の流出ノードlへの内部ノード群からの流出交通量）である。
Domestic and foreign OD traffic is calculated as follows.
G i E = (1−τ) G i (12)
G i I + G i E = τG i + (1−τ) G i = G i (13)
Y il = G i E n il = (1−τ) G i n il (14)
Σ l Y il = G i E , Σ i Y il = D l I (15)
Where Y il is the internal / external OD traffic from internal node i to external node l, G i E is the generated traffic from internal node i for internal / external OD traffic, and D l I is the external node l for internal / external OD traffic. Concentrated traffic (outflow traffic from internal node group to outflow node l outside the target area).
外内OD交通量は、外部ノードにおける発生交通の域内集中確率及び域外集中確率（通過確率）をそれぞれλ及び1−λとすると、次のように算出される(0<λ<1)。外部ノードにおける発生ノード別の域内集中確率及び域外集中確率の過去データあるいはサンプル調査データが存在する場合はλkとする。
Sk I = λSk (16)
Ukj = Sk Iqkj = λSkqkj (17)
ΣjUkj = Sk I, ΣkUkj = Aj E (18)
ここに、Ukjは外部ノードkから内部ノードjへの外内OD交通量、Sk Iは外内OD交通に対する外部ノードkからの発生交通量（対象域外の流入ノードkからの内部ノード群への流入交通量）、Aj Eは外内OD交通に関する内部ノードjへの集中交通量である。
The outside OD traffic volume is calculated as follows (0 <λ <1), where λ and 1−λ are the local concentration probability and the external concentration probability (passing probability) of the generated traffic at the external node, respectively. If there is past data or sample survey data of intra-regional concentration probability and out-of-region concentration probability for each generation node in the external node, λ k is set.
S k I = λS k (16)
U kj = S k I q kj = λS k q kj (17)
Σ j U kj = S k I , Σ k U kj = A j E (18)
Where U kj is the outside / inside OD traffic volume from the external node k to the internal node j, and S k I is the traffic volume generated from the external node k for the outside / inside OD traffic (internal node group from the inflow node k outside the target area). A j E is the concentrated traffic volume to the internal node j for the outside / inside OD traffic.
外外OD交通量は、次のように算出される。
Sk E = (1−λ)Sk (19)
Wkl = Sk Erkl = (1−λ)Skrkl (20)
ΣlWkl = Sk E, ΣkWkl = Dl E (21)
ここで、Wklは外部ノードkから外部ノードlへの外外OD交通量、Sk Eは外外OD交通に対する外部ノードkからの発生交通量（対象域外の流入ノードkからの外部ノード群への流出交通量、すなわち通過OD交通量）である。
The outside / outside OD traffic volume is calculated as follows.
S k E = (1−λ) S k (19)
W kl = S k E r kl = (1−λ) S k r kl (20)
Σ l W kl = S k E , Σ k W kl = D l E (21)
Here, W kl is the external / external OD traffic volume from external node k to external node l, and S k E is the generated traffic volume from external node k for external / external OD traffic (external node group from inflow node k outside the target area) Spilled traffic volume (ie, passing OD traffic volume).
(5) 目的関数（その１−非負制約条件がないリンク交通量モデル）
推定OD交通量をネットワークに経路配分した推定リンク交通量と、観測されたリンク交通量の現実値の差の平方和が最小になるようにゾーン別発生交通量を推定する。
(5) Objective function (1-Link traffic volume model without non-negative constraints)
Estimate the generated traffic volume by zone so that the sum of squares of the difference between the estimated link traffic volume that distributes the estimated OD traffic volume to the network and the actual value of the observed link traffic volume is minimized.
非負制約条件がないモデルにおいては、残差平方和Φは次のように定式化され、その最小値を求めることになる（図７）。
Φ = Σa[(ΣiΣjXijPij a + ΣiΣlYilPil a + ΣkΣjUkjPkj a + ΣkΣlWklPkl a)−va *]2
= Σa[{ΣiΣjτGimijPij a + ΣiΣl(1−τ)GinilPil a + ΣkΣjλSkqkjPkj a
+ ΣkΣl(1−λ)SkrklPkl a}−va *]2 → Min (22)
ここに、Pij aはノードiからノードjへのOD交通ijがリンクaを利用する確率（リンク利用確率）である。Pij aの求め方としては、前述の車両番号照合観測値を用いたノード推移確率計算法（ただし、対象範囲が広くなると精度が低下する）やDialによる確率経路選択法を用いて外生的に求める方法がある。
In a model without a non-negative constraint, the residual sum of squares Φ is formulated as follows, and its minimum value is obtained (FIG. 7).
Φ = Σ a ((Σ i Σ j X ij P ij a + Σ i Σ l Y il P il a + Σ k Σ j U kj P kj a + Σ k Σ l W kl P kl a ) −v a * ] 2
= Σ a [{Σ i Σ j τG i m ij P ij a + Σ i Σ l (1−τ) G i n il P il a + Σ k Σ j λS k q kj P kj a
+ Σ k Σ l (1−λ) S k r kl P kl a } −v a * ] 2 → Min (22)
Here, P ij a is a probability that the OD traffic ij from the node i to the node j uses the link a (link usage probability). P ij a can be obtained exogenously using the node transition probability calculation method using the vehicle number verification observations described above (however, the accuracy decreases as the target range becomes wider) and the stochastic route selection method using Dial. There is a method to ask for.
(22)式の解は、各発生ゾーンに対する∂Φ/∂Gi = 0から得られる。
Σa[[{ΣiΣjτGimijPij a + ΣiΣl(1−τ)GinilPil a
+ ΣkΣjλSkqkjPkj a + ΣkΣl(1−λ)SkrklPkl a}−va *]
×[ΣjτmijPij a + Σl(1−τ)nijPil a}] = 0 (23)
The solution of equation (22) is obtained from ∂Φ / ∂G i = 0 for each generation zone.
Σ a [[{Σ i Σ j τG i m ij P ij a + Σ i Σ l (1−τ) G i n il P il a
+ Σ k Σ j λS k q kj P kj a + Σ k Σ l (1−λ) S k r kl P kl a } −v a * ]
× [Σ j τm ij P ij a + Σ l (1−τ) n ij P il a }] = 0 (23)
ここで、Jia及びHaを
Jia = ΣjτmijPij a + Σl(1−τ)nilPil a = Jia (24)
Ha = ΣkΣjλSkqkjPkj a + ΣkΣl(1−λ)SkrklPkl a (25)
と表記すると、(23)式は各iについて次のように書ける。
Σ a [{ΣjGjJja + Ha−va *}Jia] = 0 (26)
Where J ia and H a
J ia = Σ j τm ij P ij a + Σ l (1−τ) n il P il a = J ia (24)
H a = Σ k Σ j λS k q kj P kj a + Σ k Σ l (1−λ) S k r kl P kl a (25)
(23) can be written as follows for each i.
Σ a [{Σ j G j J ja + H a −v a * } J ia ] = 0 (26)
式（26）の連立一次方程式の繰り返し演算により解を求める。この繰り返し演算において、t-1回目の計算のGiをGi (t-1)、t回目の計算のJia及びHaをそれぞれJia (t), Ha (t)とする。 The solution is obtained by iterative calculation of the simultaneous linear equations of Equation (26). In this repetitive operation, the G i of t-1 th calculation G i (t-1), the J ia and H a of t th calculation each J ia (t), and H a (t).
まず、前回の演算で決定されたJia (t)及びHa (t)を確定値として、次の各iについての連立一次方程式からGi (t+1)を求める。
Σa{ΣjGj (t+1)Jja (t) + Ha (t)−va *}Jia (t) = 0 (27)
First, G i (t + 1) is obtained from simultaneous linear equations for each of the following i using J ia (t) and H a (t) determined in the previous calculation as definite values.
Σ a {Σ j G j (t + 1) J ja (t) + H a (t) −v a * } J ia (t) = 0 (27)
次に、前回のGi (t)の値との差|Gi (t)−Gi (t+1)|を計算し、その差が収束基準値εを超えるときは、t→t+1として再度Gi (t+2)の設定を行って計算を繰り返す。
差|Gi (t)−Gi (t+1)|が収束基準値ε以下となれば、計算を終了する。これにより、最終的な解が求まる。
Then, the difference between the value of the last G i (t) | G i (t) -G i (t + 1) | was calculated, when the difference exceeds a convergence criterion value ε is, t → t + Set G i (t + 2) again as 1 and repeat the calculation.
If the difference | G i (t) −G i (t + 1) | is equal to or less than the convergence reference value ε, the calculation is terminated. As a result, a final solution is obtained.
(6) 目的関数（その２−非負制約条件を付したリンク交通量モデル）
上記のような非負制約条件がないモデルでは、発生交通量の推定値が負になることがある。これは非現実的であるので、非負制約条件を導入したモデルをここに提示する（図８）。このときのモデル式は、式(22)に以下の制約条件を付加して記述される。
G = ΣiGi (28)
Gi ≧ 0 (29)
(6) Objective function (Part 2-Link traffic volume model with non-negative constraints)
In the model without the non-negative constraint condition as described above, the estimated value of the generated traffic volume may be negative. Since this is unrealistic, a model that introduces non-negative constraints is presented here (FIG. 8). The model formula at this time is described by adding the following constraints to the formula (22).
G = Σ i G i (28)
G i ≥ 0 (29)
ラグランジュ関数を用いれば、目的関数は式(22)、(28)、(29)より次のように書き換えることができる。
L = Σa[{ΣiΣjτGimijPij a + ΣiΣl(1−τ)GinilPil a + ΣkΣjλSkqkjPkj a
+ ΣkΣl(1−λ)SkrklPkl a}−va *]2
+ μ(ΣiGi−G) → Min. (30)
If the Lagrangian function is used, the objective function can be rewritten as follows from the equations (22), (28), and (29).
L = Σ a [{Σ i Σ j τG i m ij P ij a + Σ i Σ l (1−τ) G i n il P il a + Σ k Σ j λS k q kj P kj a
+ Σ k Σ l (1−λ) S k r kl P kl a } −v a * ] 2
+ μ (Σ i G i −G) → Min. (30)
制約条件(29)及びKuhn-Tucker条件から、ラグランジュ関数の最適解は以下の条件を満足しなければならない。
∂L/∂Gi = 2Σa{ΣjGjJja
+ Ha−va *}Jia + μ = 0 (Gi > 0の場合)
≧ 0 (Gi = 0の場合) (31)
∂L/∂G = −μ = 0 (32)
∂L/∂μ = ΣiGi−G = 0 (33)
これより、
∂L/∂Gi = 2Σa{ΣjGjJja + Ha−va *}Jia = 0 (Gi > 0の場合)
≧ 0 (Gi = 0の場合) (34)
∂L/∂μ = ΣiGi−G = 0 (35)
を解けばよいことになる。
From the constraint condition (29) and the Kuhn-Tucker condition, the optimal solution of the Lagrangian function must satisfy the following condition.
∂L / ∂G i = 2Σ a {Σ j G j J ja
+ H a −v a * } J ia + μ = 0 (when G i > 0)
≥ 0 (when G i = 0) (31)
∂L / ∂G = −μ = 0 (32)
∂L / ∂μ = Σ i G i −G = 0 (33)
Than this,
∂L / ∂G i = 2Σ a {Σ j G j J ja + H a −v a * } J ia = 0 (when G i > 0)
≥ 0 (when G i = 0) (34)
∂L / ∂μ = Σ i G i −G = 0 (35)
If you solve the problem.
連立一次方程式(34)(35)の繰返し演算により解を求める。この繰返し演算において、t+1回目の計算のGiをGi (t+1)、t回目の計算のJia及びHaをそれぞれJia (t), Ha (t)とする。 The solution is obtained by iterative calculation of the simultaneous linear equations (34) and (35). In this iterative operation, G i of the t + 1-th calculation is G i (t + 1) , and J ia and H a of the t-th calculation are J ia (t) and H a (t) , respectively.
まず、前回の演算で決定されたJia (t)及びHa (t)を確定値として、各iについての次の連立一次方程式からGi (t+1)を求める。
Σa{ΣjGj (t+1)Jia (t) + Ha (t)−va *}Jia (t) = 0 (36)
First, G i (t + 1) is obtained from the following simultaneous linear equations for each i using J ia (t) and H a (t) determined in the previous calculation as definite values.
Σ a {Σ j G j (t + 1) J ia (t) + H a (t) −v a * } J ia (t) = 0 (36)
得られたGi (t+1)がGi (t+1)<0となるとき、Gi (t+1) = 0とおいて変数集合から取り除く。また、前回のGi (t) = 0なる変数Gi (t)に対して∂Φ/∂Gi≧0を満たさないとき、変数集合に新たにGi (t+1)を付け加える。このようにして更新された変数集合で次回連立方程式を解く。
すべての変数Gi (t+1)がGi (t+1)≧0及び∂Φ/∂Gi≧0を満たせば、このステップにおける最適解となる。
前回の算出値Gi (t)と今回の算出値Gi (t+1)の差｜Gi (t+1)−Gi (t)｜が所定の収束基準値εを超える場合、t→t+1として上記計算を繰り返す。
｜Gi (t+1)−Gi (t)｜が収束基準値ε以下になれば、計算を終了する。
When the resulting G i (t + 1) becomes G i (t + 1) < 0, removed from a set of variables at the G i (t + 1) = 0. Also, when not satisfied ∂Φ / ∂G i ≧ 0 with respect to the previous G i (t) = 0 becomes a variable G i (t), newly adds the G i (t + 1) to the variable set. The next simultaneous equations are solved with the variable set updated in this way.
If all the variables G i (t + 1) satisfy G i (t + 1) ≧ 0 and ∂Φ / ∂G i ≧ 0, the optimal solution in this step is obtained.
If the difference | G i (t + 1) −G i (t) | between the previous calculated value G i (t) and the current calculated value G i (t + 1) exceeds a predetermined convergence reference value ε, t → Repeat the above calculation as
If | G i (t + 1) −G i (t) | becomes equal to or smaller than the convergence reference value ε, the calculation is terminated.
(7) 目的関数（結合モデル）
推定OD交通量を、道路ネットワークに経路配分した推定リンク交通量と観測リンク交通量の残差平方和と、ゾーン発生交通量の推定値と現実値の残差平方和の両者を加えた合計値が最小となるようにゾーン別発生交通量を推定する。推定リンク交通量と観測リンク交通量の残差平方和のみで計算を繰り返した場合、その誤差が大きいと、ゾーン発生交通量の推定精度が不安定となる傾向があり、非負条件がないとゾーン別発生交通量が負になる場合が出てくるが、このようにゾーン発生交通量の推定値と現実値の残差平方和を加えることにより、ゾーン別発生交通量の推定値の精度が上がり、計算が安定するようになる。
(7) Objective function (joint model)
The sum of the estimated OD traffic volume and the residual sum of squares of the estimated link traffic and observed link traffic distributed to the road network, and the estimated sum of the zone-generated traffic volume and the residual sum of squares of the actual values Estimate the amount of traffic generated by zone so that is minimized. If the calculation is repeated only with the residual sum of squares of the estimated link traffic volume and the observed link traffic volume, if the error is large, the estimation accuracy of the zone traffic volume tends to become unstable, and if there is no non-negative condition, the zone In some cases, the generated traffic volume becomes negative, but adding the estimated sum of the zone generated traffic volume and the residual sum of squares of the actual values in this way increases the accuracy of the estimated traffic volume generated by the zone. The calculation will become stable.
非負制約条件があるモデルでは、目的関数は次の形を取る。
Φ = Σa[(ΣiΣjXijPij a + ΣiΣlYilPil a + ΣkΣjUkjPkj a + ΣkΣlWklPkl a)−va *]2
+ Σi[Gi−Ggi *]2
= Σa[{ΣiΣjτGimijPij a + ΣiΣl(1−τ)GinilPil a + ΣkΣjλSkqkjPkj a
+ ΣkΣl(1−λ)SkrklPkl a}−va *]2 + Σi[Gi−Ggi *]2 → Min (37)
For models with non-negative constraints, the objective function takes the form
Φ = Σ a ((Σ i Σ j X ij P ij a + Σ i Σ l Y il P il a + Σ k Σ j U kj P kj a + Σ k Σ l W kl P kl a ) −v a * ] 2
+ Σ i [G i −Gg i * ] 2
= Σ a [{Σ i Σ j τG i m ij P ij a + Σ i Σ l (1−τ) G i n il P il a + Σ k Σ j λS k q kj P kj a
+ Σ k Σ l (1−λ) S k r kl P kl a } −v a * ] 2 + Σ i [G i −Gg i * ] 2 → Min (37)
制約条件は次の通りである。
G = ΣiGi (38)
Gi ≧ 0 (39)
ここに、gi *は過去データあるいはサンプル調査データにより得られるゾーン別発生交通量の比率であって、ゾーン別の発生交通量の観測値(過去データあるいはサンプル調査データ)をGi *、その総和をG*とすると、gi * = Gi */G* である。
The constraint conditions are as follows.
G = Σ i G i (38)
G i ≥ 0 (39)
Here, g i * is the ratio of the generated traffic volume by zone obtained from past data or sample survey data, and the observed traffic volume by zone (past data or sample survey data) is G i * If the sum is G * , g i * = G i * / G * .
ラグランジュ関数を用いて上の目的関数(37)を以下のように書き換える。
L = Σa[{ΣiΣjτGimijPij a + ΣiΣl(1−τ)GinilPil a
+ ΣkΣjλSkqkjPkj a + ΣkΣl(1−λ)SkrklPkl a}−va *]2
+ Σi[Gi−Ggi *]2+ μ(ΣiGi−G) → Min. (40)
この解は次の連立方程式による繰り返し演算で求められる。Kuhn-Tucker条件からラグランジュ関数の最適解は以下の条件を満足しなければならない。
∂L/∂Gi = 2Σa{ΣjGjJja + Ha−va *}Jia
+ 2(Gi−Ggi *)+ μ = 0 (Gi > 0の場合)
≧ 0 (Gi = 0の場合) (41)
∂L/∂G = −2Σi(Gi−Ggi *)gi *−μ = 0 (42)
∂L/∂μ = ΣiGi−G = 0 (43)
Using the Lagrangian function, the above objective function (37) is rewritten as follows.
L = Σ a [{Σ i Σ j τG i m ij P ij a + Σ i Σ l (1−τ) G i n il P il a
+ Σ k Σ j λS k q kj P kj a + Σ k Σ l (1−λ) S k r kl P kl a } −v a * ] 2
+ Σ i [G i −Gg i * ] 2 + μ (Σ i G i −G) → Min. (40)
This solution can be obtained by iterative calculation using the following simultaneous equations. From the Kuhn-Tucker condition, the optimal solution of the Lagrangian function must satisfy the following conditions.
∂L / ∂G i = 2Σ a {Σ j G j J ja + H a −v a * } J ia
+ 2 (G i −Gg i * ) + μ = 0 (when G i > 0)
≥ 0 (when G i = 0) (41)
∂L / ∂G = −2Σ i (G i −Gg i * ) g i * −μ = 0 (42)
∂L / ∂μ = Σ i G i −G = 0 (43)
式(43)は、以下の連立方程式の繰り返しによりGi (t)を求めて解く。すでに記載したリンク交通量モデルの計算方法と同様に、Kuhn-Tucker条件式を満たすように解集合の削除と追加を行い、Gi (t)が収束するまで計算を続ける。
∂L/∂Gi (t) = 2Σa{ΣjGj (t)Jja (t-1) + Ha (t-1)−va *}Jia (t-1)
+ 2(Gi (t)−G(t)gi *)+ μ = 0 (44)
∂L/∂G(t) = −2Σi(Gi (t)−G(t)gi *)gi *−μ = 0 (45)
∂L/∂μ = ΣiGi (t)−G(t) = 0 (46)
Equation (43) is solved by obtaining G i (t) by repeating the following simultaneous equations. Similar to the calculation method of the link traffic volume model already described, the solution set is deleted and added so as to satisfy the Kuhn-Tucker conditional expression, and the calculation is continued until G i (t) converges.
∂L / ∂G i (t) = 2Σ a {Σ j G j (t) J ja (t-1) + H a (t-1) −v a * } J ia (t-1)
+ 2 (G i (t) −G (t) g i * ) + μ = 0 (44)
∂L / ∂G (t) = −2Σ i (G i (t) −G (t) g i * ) g i * −μ = 0 (45)
∂L / ∂μ = Σ i G i (t) −G (t) = 0 (46)
ゾーン別発生交通量は、次のような方法によっても推定することができる。以下、上記の方法を第１の方法とし、それ以外の４つの方法を第２〜第５の方法として説明する。 The generated traffic volume by zone can also be estimated by the following method. Hereinafter, the above method will be described as a first method, and the other four methods will be described as second to fifth methods.
第２の方法は、ノードに接続する各リンクを通る車両番号を実測し、それを各リンク間で照合する方法（車両番号照合法）である。この方法により、方向別対象ノードへの集中（流入）確率f、対象ノードから各リンクへの発生（流出）交通の推移確率e、及びノード別目的地選択確率が得られる。 The second method is a method (vehicle number verification method) in which the vehicle number passing through each link connected to the node is measured and verified between the links. By this method, the concentration (inflow) probability f to the target node by direction, the transition probability e of the generated (outflow) traffic from the target node to each link, and the destination selection probability by node are obtained.
各確率の導出方法は次の通りである。なお、現実的には全てのノード（すなわち、全てのリンク）において車両番号を観測し、照合することは難しい。このため、一部のゾーン又は時間において車両番号照合を行い、そのデータより得られたゾーン別発生交通量とゾーン間推移確率を用いて対象域全体のOD交通量を推定することになる。 The method for deriving each probability is as follows. Actually, it is difficult to observe and collate vehicle numbers at all nodes (that is, all links). For this reason, vehicle number collation is performed in some zones or times, and the OD traffic volume of the entire target area is estimated using the generated traffic volume by zone and the transition probability between zones obtained from the data.
・方向別ノード集中交通の推移確率
対象ノードの接続リンクにおける流入方向と流出方向の二地点の車両番号照合により、ノード通過の方向別交通量Fijが得られる（図９）。方向別交通量Fijの相対比率fijを求めることにより、対象ノードiの通過交通および集中交通の方向別推移確率が得られる。集中交通量Ajは、観測リンク交通量vijに集中交通量Fijの相対比率fijを乗じることで求めることができる。
-Transition probability of node-concentrated traffic by direction Traffic volume F ij by direction of node passage is obtained by collating vehicle numbers at two points of the inflow direction and the outflow direction in the connection link of the target node (FIG. 9). By obtaining the relative ratio f ij of the traffic volume F ij by direction, the transition probability by direction of the passing traffic and the concentrated traffic of the target node i can be obtained. The concentrated traffic volume A j can be obtained by multiplying the observation link traffic volume v ij by the relative ratio f ij of the concentrated traffic volume F ij .
対象ノードの或る接続リンクにおいて流入方向のみの車両番号が観測される場合（すなわち、所定時間内にその車両番号がそのノードから流出しない場合）、その交通量Fijはそのノードへの集中交通となる。 When a vehicle number in only the inflow direction is observed at a certain connection link of the target node (that is, when the vehicle number does not flow out of the node within a predetermined time), the traffic volume F ij is concentrated traffic to the node. It becomes.
・ノード別発生交通の推移確率
対象ノードの接続リンクにおいて、流出方向のみの車両番号が観測される場合は（すなわち、それ以前の所定時間内にその車両番号がそのノードに流入しなかった場合）、当該ノードからの発生交通量Eijが得られる（図１０）。Eijの相対比率eijにより、対象ノードから接続リンクへの発生交通に関する推移確率が得られる。ノードiからの発生交通量Giは、集中推移確率によるAiとノードごとの発生・集中交通量条件式（数式(2)）から得られる。
・ Transition probability of generated traffic by node When the vehicle number of only the outflow direction is observed at the connection link of the target node (that is, when the vehicle number did not flow into the node within the predetermined time before that) The generated traffic volume E ij from the node is obtained (FIG. 10). Based on the relative ratio e ij of E ij, the transition probability regarding the generated traffic from the target node to the connection link can be obtained. Generating traffic volume G i from node i is obtained from A i and generation-intensive traffic condition of each node due to the concentration transition probability (Equation (2)).
・発生ノード別目的地選択確率
一つの発生ノードから域内域外全ての集中ノードへの選択経路を考慮し、リンク通行方向を定める。なお、生起確率が微小とみなせるノード間OD交通は無視する（図１１、図１２では、域外ノード11からすぐ隣接する域外ノード13への選択の生起確率は無視される）。
・ Destination selection probability by source node Determines the link traffic direction in consideration of the selected route from one source node to all concentrated nodes inside and outside the region. Note that the inter-node OD traffic that can be regarded as having a very small occurrence probability is ignored (in FIGS. 11 and 12, the occurrence probability of selection from the out-of-
まず、車両番号照合法で得られたFijを用いて、隣接ノード間推移確率zijを求める（図１１）。次に、発生ノードから経路進行方向に沿って、ノード通過ごとに隣接ノード推移確率zijを逐次乗算することで、発生ノードからのリンク利用率Zijが得られる（図１２）。なお、経路が合流するノードでは、全リンク利用率Zijを加算する。このように計算した場合の終端リンクのノード間推移確率Zijが目的地選択確率となる。この演算は、吸収マルコフ連鎖を用いて行うことができる。 First, the transition probability z ij between adjacent nodes is obtained using F ij obtained by the vehicle number matching method (FIG. 11). Next, the link utilization rate Z ij from the generation node is obtained by sequentially multiplying the adjacent node transition probability z ij for each node passing along the path traveling direction from the generation node (FIG. 12). Note that the total link utilization rate Z ij is added at the node where the route joins. The terminal link transition probability Z ij of the terminal link in this case is the destination selection probability. This operation can be performed using an absorption Markov chain.
・OD別リンク利用率
発生ノードと集中ノードを一つのペアに限定すれば、隣接ノード間推移確率zijを用いて、同様の計算方法でOD別リンク利用率が求められる（図１３、図１４）。ただし、この方法は現実的な経路選択を記述しているとはいえず、便宜的方法である。むしろ、既存の経路選択手法を用いる方が実用的と思われる。
-Link usage rate by OD If the generation node and the concentrated node are limited to one pair, the link usage rate by OD can be obtained by the same calculation method using the transition probability z ij between adjacent nodes (FIGS. 13 and 14). ). However, this method does not describe realistic route selection and is a convenient method. Rather, it seems more practical to use the existing route selection method.
第３の方法は、車両番号照合の適用が困難な場合、観測ノード分岐確率を利用し、対象ノード集中確率を未知変数として内生化して決定する方法である（図１５）。まず、対象ノードから隣接ノードへの発生（流出）推移確率はリンク観測交通量に比例すると仮定する。一方、隣接ノードから対象ノードへの集中（流入）推移確率は、あらゆる方向に対し一定比率θであると仮定する。このとき、参考にできるデータがあれば利用してもよい。また、通過推移確率は現状比率とする。 The third method is a method in which when it is difficult to apply vehicle number verification, the observation node branch probability is used and the target node concentration probability is endogenously determined as an unknown variable (FIG. 15). First, it is assumed that the occurrence (outflow) transition probability from the target node to the adjacent node is proportional to the link observed traffic volume. On the other hand, it is assumed that the concentration (inflow) transition probability from the adjacent node to the target node is a constant ratio θ in all directions. At this time, if there is data that can be referred to, it may be used. The passage transition probability is the current ratio.
次に、二つの方法でノード別発生交通量を推定する。
a）ノード別推移確率及びOD別リンク利用確率を決定し、ゾーン別目的地選択確率を決定する。そして、上記の残差平方和モデルからノード別発生交通量Gi ^を推定する。
b）θに対するゾーン別集中交通量Ai ~を推定し、ノード別発生・集中条件式からゾーン別発生交通量Gi ~を推定する。
Next, the generated traffic volume by node is estimated by two methods.
a) Determine the transition probability by node and the link use probability by OD, and determine the destination selection probability by zone. Then, the generated traffic volume G i ^ for each node is estimated from the residual sum of squares model.
b) Estimate the concentrated traffic volume A i ~ for each zone with respect to θ, and estimate the generated traffic volume G i ~ for each zone from the generation / concentration condition formula for each node.
これら二つの方法で推定したゾーン別発生交通量Gi ^とGi ~の差が収束基準値ε以上であれば、θを修正する。この計算手続を、両ゾーン別発生交通量の差|Gi ^−Gi ~|が収束基準値ε以下となるまで繰り返す。 If the difference between the zone-specific generated traffic volumes G i ^ and G i ~ estimated by these two methods is equal to or greater than the convergence reference value ε, θ is corrected. This calculation procedure is repeated until the difference | G i ^ −G i ~ | of the traffic volume generated by each zone becomes equal to or less than the convergence reference value ε.
第４の方法は、プローブカーデータを利用する方法である。大量に蓄積されたプローブカーデータを用いることにより、発生ノード別目的地選択確率、ノード間推移確率及びOD別リンク利用確率を高い精度で得ることができる。これらの高精度の先決データを残差平方和モデルに投入することで、対象域内のノード別発生交通量及びノード間OD交通量をより高精度に推定することができる。 The fourth method uses probe car data. By using a large amount of probe car data accumulated, it is possible to obtain the destination selection probability by node, the transition probability between nodes, and the link usage probability by OD with high accuracy. By introducing these highly accurate prior data into the residual sum of squares model, the generated traffic volume by node and the inter-node OD traffic volume in the target area can be estimated with higher accuracy.
第５の方法は、以上の各方法の組み合わせによる方法である。残差平方和による方法、車両番号照合法、ノード別推移確率を内生化する方法、プローブカーデータを利用する方法をそれぞれ状況に応じて組み合わて用いることにより、柔軟な適用が可能となる。例えば、先決データの入手が可能なノードと困難なノードに対し、それぞれの部分ごとに最適な方法を組み合わせて用いることができる。また、複数の方法を用いることにより、互いに検証することもできる。 The fifth method is a method based on a combination of the above methods. By using a method based on residual sum of squares, a vehicle number matching method, a method for endogenously generating a node-by-node transition probability, and a method using probe car data, depending on the situation, it can be applied flexibly. For example, it is possible to use a combination of optimum methods for each part for a node from which pre-determined data can be obtained and a difficult node. Moreover, it is also possible to verify each other by using a plurality of methods.
Claims (8)
b)域外及び域内の各ノードを結ぶリンクの観測リンク交通量v * を用いて、域内ノードiにおける集中交通量Aiを発生交通量Giの関数として定式化し、
c)定式化された各ノードの集中交通量Aiに基づき、域内−域内、域外−域内のOD交通に関する発生ノード別目的地選択確率m, qを算出し、一方、域外ノードlにおける観測集中交通量D l に基づき、域内−域外、域外−域外のOD交通に関する発生ノード別目的地選択確率n, rを算出し、
d)予め与えられた、域内ノードにおける発生交通量の域内集中確率τ及び域外ノードにおける発生交通量の域内集中確率λに対し、ノード別発生交通量G i とその域内域内集中確率τ及び前記発生ノード別目的地選択確率m, nを用いて、内内OD交通量X及び内外OD交通量Yを推定し、さらに、域外ノードkから域内への観測発生交通量S k とその域外域内集中確率λ及び前記発生ノード別目的地選択確率q, rを用いて、外内OD交通量Uと外外OD交通量Wを推定し、
e)前記各OD交通量X, Y, U, W、及び、i-jノード間OD交通が特定リンクaを利用する予め与えられたリンク利用確率Pij aを用いて各リンク交通量を推定し、
f)推定リンク交通量と観測リンク交通量の差の平方和Φが最小となる発生交通量Giを決定し、
g)決定した発生交通量Gi (t)とb)において用いた発生交通量Gi (t-1)の差が所定値ε以下となるまで発生交通量G i の修正及びb)〜f)の計算を繰り返す
ことにより、域内ノードの発生交通量と集中交通量、及び、域内と域外におけるすべてのノード間OD交通量を推定する交通量推定方法。 defined a) real road network line zoning of the target region and outside in response to Utotomoni, a node corresponding to each zone, and a link connecting each node, and
b) Using the observed link traffic v * of the links connecting nodes outside and within the region, formulate the concentrated traffic A i at the node i in the region as a function of the generated traffic G i ,
c) On the basis of the concentrated traffic volume A i of each node , the destination selection probability m, q for each source node for OD traffic within the region and within the region and outside the region is calculated. Based on the traffic volume D l , the destination selection probability n, r for each source node related to OD traffic within the region and outside the region and outside and outside the region is calculated,
d) With respect to the intra-regional concentration probability τ of the generated traffic volume in the regional node and the intra-regional concentration probability λ of the generated traffic amount in the outside node given in advance, the generated traffic volume G i by node , the intra-regional regional concentration probability τ and the occurrence using the node-specific destination selection probability m, n, the estimate of the inner in the OD traffic volume X and the inner and outer OD traffic volume Y, further observation generated traffic S k and its outside region concentrate probability to the region from outside the node k Using λ and the destination node-specific destination selection probabilities q and r, the outside / outside OD traffic volume U and the outside / outside OD traffic volume W are estimated,
e) Estimate each link traffic volume using the link usage probability P ij a given in advance for each OD traffic volume X, Y, U, W and ij inter-node OD traffic using a specific link a,
f) Determine the generated traffic volume G i that minimizes the sum of squares Φ of the difference between the estimated link traffic volume and the observed link traffic volume,
g) Correction of the generated traffic volume G i until the difference between the determined generated traffic volume G i (t) and the generated traffic volume G i (t-1) used in b) is equal to or less than a predetermined value ε, and b) to f ) Traffic volume estimation method that estimates the generated traffic volume and concentrated traffic volume of nodes in the region and all inter-node OD traffic volumes within and outside the region by repeating the calculation of).
h)対象域内の各ノードにおいて、該ノードに接続する各リンクを通る車両番号を照合することにより得られた通過、集中、発生に関する方向別交通量の相対比率を、対象域全体の各ノードにおける方向別の対象ノード通過推移確率と対象ノード集中（流入）確率、および対象ノードから隣接ノードへの発生（流出）推移確率として用い、
i)前記の各ノードにおける通過、集中、発生の推移確率を用いた吸収マルコフ連鎖により、発生ノード別目的地選択確率m, n, q, rを推定する
ことを特徴とする請求項１〜３のいずれかに記載の交通量推定方法。 When estimating the destination selection probability m, n, q, r,
h) At each node in the target area, the relative ratio of the traffic volume by direction regarding passing, concentration, and generation obtained by checking the vehicle number passing through each link connected to the node is calculated for each node in the entire target area. direction different nodes pass the transition probabilities and the nodes concentrate (inlet) probability, and the generation of the target node to the adjacent node (outflow) used as the transition probabilities,
i) Destination selection probability m, n, q, r for each source node is estimated by an absorption Markov chain using transition probabilities of passing, concentration, and occurrence at each node. The traffic volume estimation method according to any one of the above.
k)対象ノードiに流入するリンクにおける観測リンク交通量v * にθ i を乗算することにより、集中交通量A i ~ を算出すると共に、該算出された集中交通量A i ~ とノード別発生・集中交通量条件式に基づいて、ノード別発生交通量Gi ~を推定し、
l)一方、対象ノードiから流出するリンクにおける観測リンク交通量v * に比例して与えた隣接ノードへの発生推移確率、該流出観測リンク交通量v * の現状比率で与えた通過推移確率、及び集中推移確率θ i を用いて、吸収マルコフ連鎖により発生ノード別目的地選択確率m, n, q, rを算出して、残差平方和モデルでノード別発生交通量Gi ^を推定し、
m)|Gi ^−Gi ~|が収束基準値ε以下となるまでθ i の修正を繰り返す、
ことにより、ノード別発生交通量及び集中交通量を推定することを特徴とする請求項１〜３のいずれかに記載の交通量推定方法。 j) Set the concentration (inflow) transition probability from the adjacent node in the target node i as an unknown variable θ i ,
k) Calculate the concentrated traffic volume A i ~ by multiplying the observed link traffic volume v * in the link flowing into the target node i by θ i , and the calculated concentrated traffic volume A i ~ and occurrence by node -Estimate the generated traffic volume G i ~ by node based on the concentrated traffic volume conditional expression ,
l) On the other hand, the occurrence transition probability to the adjacent node given in proportion to the observation link traffic volume v * in the link flowing out from the target node i , the passage transition probability given by the current ratio of the outflow observation link traffic volume v * , and using the concentration transition probabilities theta i, absorbing Markov chain by generating node by the destination selection probability m, calculate n, q, and r, is estimated by node generating traffic volume G i ^ in the residual sum of squares model ,
m) Repeat correction of θ i until | G i ^ −G i ~ | is less than or equal to the convergence reference value ε.
The traffic volume estimation method according to claim 1, wherein the generated traffic volume and the concentrated traffic volume are estimated for each node .
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