考虑拥堵空间排队和溢出的交通流用户均衡分配模型

doi:10.13229/j.cnki.jdxbgxb.20250287

Abstract

Abstract:

Aiming at the problem that the traditional user equilibrium assignment model is difficult to describe the phenomenon of congestion space queuing and spillover， in order to describe the macroscopic and overall traffic operation state of the road network， portray the impact of congestion spatial queuing and spillback phenomena on the traffic assignment of road network， and provide reference ideas for traffic planning， demand management and congestion mitigation， considering the general road network with both smooth and congested state， a novel traffic user equilibrium assignment model with congestion space queuing and spillover caused by the link capacity and storage capacity constraints was constructed. The equivalence of model with user equilibrium principle and the uniqueness of solution were proved. Moreover， mechanisms such as demand conversion， congestion backtracking， congestion area identification and demand loading of different traffic conditions were introduced， the calculation method of demand flow transfer coefficient was proposed， and an improved FW algorithm was constructed to solve the model. Finally， the effectiveness of the model and the algorithm was compared and analyzed by numerical examples. The error accuracy of the calculation results of the simple numerical example is $e = 1.044 ? 5 × 10 - 5$ ， and the routes with loaded traffic volume have equal travel times， which conforms to the user equilibrium principle. The results show that the model is an integration and expansion of the traditional smooth and fully congested user equilibrium assignment model， which can effectively calculate the equilibrium assignment results and the final equilibrium steady states of the road network under different traffic conditions， and describe the phenomenon of congestion space queuing and spillover. The assignment results can reflect the macroscopic and global traffic operation characteristics when the road network reaches the equilibrium state， identify bottleneck locations and congestion queuing areas， and provide basis for road network structure optimization， traffic guidance， demand management and congestion relief.

Key words: engineering of communications and transportation system, user equilibrium assignment model, traffic assignment, congestion space queuing, queuing spillover

CLC Number:

U491

Qi-yue ZHANG,Hao YUE,De-lin MENG,Qiu-shi QU. Traffic user equilibrium assignment model with congestion space queuing and spillover[J].Journal of Jilin University(Engineering and Technology Edition), 2026, 56(9): 2302-2316.

Figures/Tables 14

Fig.1

Table 1

Variable and parameter explanation"

序号	类型	参数	含义
1	路段属性	$X a$	路段 $a$ 上的需求流量，是计划分配并允许超过路段通行能力的流量，pcu/time
2		$x a$	路段 $a$ 上的流入流量，是考虑路段 $a$ 上游需求折算后流入路段 $a$ 并允许超过路段通行能力的流量，pcu/time
3		$y a$	路段 $a$ 上的流出流量，是考虑下游空间排队和溢出，进行需求折算和拥堵回溯后路段 $a$ 实际流出并不超过路段通行能力的流量，pcu/time
4		$y 1, a$	次生瓶颈路段 $a$ 上干扰流的流出流量，是经过路段 $a$ 的所有路径中，路段 $a$ 下游产生拥堵空间排队并蔓延溢出至路段 $a$ 的部分路径，通过路段 $a$ 的部分流出流量，pcu/time
5		$y 2, a$	次生瓶颈路段 $a$ 上被干扰流的流出流量，是经过路段 $a$ 的所有路径中，路段 $a$ 下游没有产生拥堵空间排队或没有蔓延溢出至路段 $a$ ，但受到其他产生拥堵空间排队并蔓延溢出至路段 $a$ 的路径干扰的部分路径，通过路段 $a$ 的部分流出流量，pcu/time
6		$y a ?, k r s$	出发地为 $r$ 、目的地为 $s$ 的OD间的第 $k$ 条路径上，路段 $a$ 紧邻的下游路段总流出流量，pcu/time
7		$N Q a$	路段 $a$ 下游出口处在路段 $a$ 上的待排队需求车辆数，是计划分配并允许超过路段存储容量的车辆数，pcu
8		$N Q 1, a$	次生瓶颈路段 $a$ 下游出口处在路段 $a$ 上的干扰流待排队需求车辆数，是经过路段 $a$ 的所有路径中，路段 $a$ 下游产生拥堵空间排队并蔓延溢出至路段 $a$ 的部分路径，在路段 $a$ 下游出口处产生的部分待排队车辆数，pcu
9		$N Q 2, a$	次生瓶颈路段 $a$ 下游出口处在路段 $a$ 上的被干扰流待排队需求车辆数，是经过路段 $a$ 的所有路径中，路段 $a$ 下游没有产生拥堵空间排队或没有蔓延溢出至路段 $a$ ，但受到其他产生拥堵空间排队并蔓延溢出至路段 $a$ 的路径干扰部分路径，在路段 $a$ 下游出口处产生的部分待排队需求车辆数，pcu
10		$N B a$	路段 $a$ 上游入口处排队溢出的需求车辆数，是路段 $a$ 待排队需求车辆数超过路段存储容量后从该路段溢出的需求车辆数，pcu
11		$N B a ?, k r s$	出发地为 $r$ 、目的地为 $s$ 的OD间的第 $k$ 条路径上，路段 $a$ 紧邻的下游路段入口处排队溢出总需求车辆数，pcu
12		$t a (Ω)$	路段 $a$ 的交通阻抗，根据路段的畅通拥堵状态、流入/流出流量和上游入口处排队溢出车辆数计算得出， $Ω$ 为自变量 $x a 、 y a 、 N Q a 、 N B a$ 的集合，time
13		$t 1, a (x a)$	路段 $a$ 以流入流量为自变量的畅通状态阻抗函数，由路段通行能力 $C a$ 、自由流通过时间 $t 0, a$ 等组成，畅通状态下流量增大、密度增大、速度减小、通过时间增加，故阻抗函数为单调递增函数
14		$t 2, a (y a)$	路段 $a$ 以流出流量为自变量的拥堵状态阻抗函数，由路段通行能力 $C a$ 、自由流通过时间 $t 0, a$ 等组成，拥堵状态下流量增大、密度减小、速度增大、通过时间减少，故阻抗函数为单调递减函数
15		$C a$	路段 $a$ 的通行能力，是通过该路段上瓶颈的最大流量，简化为该路段固定的出口容量，pcu/time
16		$γ a$	路段 $a$ 的需求折算系数
17		$γ a ˙, k r s$	出发地为 $r$ 、目的地为 $s$ 的OD间的第 $k$ 条路径上，导致次生瓶颈路段 $a$ 拥堵的下游最近物理瓶颈路段的需求折算系数
18		$K a$	路段 $a$ 的拥堵比例，是路段 $a$ 上拥堵排队部分占该路段的比例
19	路径属性	$F k r s$	出发地为 $r$ 、目的地为 $s$ 的OD间第 $k$ 条路径上的需求流量，pcu/time
20		$f m (r + s +)$	在局部畅通子网络中，起讫点分别为 $r +$ 、 $s +$ 的第 $m$ 条路径上的流量，pcu/time
21		$f n (r - s -)$	在局部拥堵子网络中，起讫点分别为 $r -$ 、 $s -$ 的第 $n$ 条路径上的流量，pcu/time
22		$δ a, k r s$	路段-路径相关变量，如果路段 $a$ 属于从出发地 $r$ 到目的地 $s$ 的OD间的第 $k$ 条路径，则 $δ a, k r s = 1$ ，否则 $δ a, k r = 0$
23		$μ a, k r s$	0-1变量，如果路段 $a$ 是从出发地为 $r$ 到目的地为 $s$ 的OD间的第 $k$ 条路径上的最上游首条路段，则 $μ a, k r s = 1$ ；否则 $μ a, k r s = 0$
24	OD属性	$q r s$	出发地 $r$ 和目的地 $s$ 间的OD交通需求流量，是道路网中 $r 、 s$ 间计划或预期分配的流量，pcu/time
25		$q r + s +$	在局部畅通子网络中，起讫点分别为 $r +$ 、 $s +$ 间的交通分配流量，pcu/time
26		$q r - s -$	在局部拥堵子网络中，起讫点分别为 $r -$ 、 $s -$ 间的交通分配流量，pcu/time
27		$N r s$	出发地 $r$ 与目的地 $s$ 间的OD交通需求车辆数，是道路网中 $r 、 s$ 间计划或预期分配的遇到瓶颈时产生空间排队的车辆数，pcu
28	节点	$N$	道路网中节点的集合
29		$R$	道路网中出发地的集合， $R ? N$
30		$S$	道路网中目的地的集合， $S ? N$
31	路段、路径集合	$A$	道路网中路段的集合
32		$A +$	每次迭代过程中需求折算和拥堵回溯后，道路网中完全畅通状态的路段集合， $A + ? A$
33		$A *$	每次迭代过程中需求折算和拥堵回溯后，道路网中 $x a > C a$ 时导致形成拥堵空间排队的完全拥堵状态的物理瓶颈路段集合， $A * ? A$
34		$A -$	每次迭代过程中需求折算和拥堵回溯后，道路网中 $x a ≤ C a$ 但由于物理瓶颈导致的拥堵空间排队进行蔓延溢出而形成的完全拥堵状态的次生瓶颈路段集合， $A - ? A$
35		$A ±$	每次迭代过程中需求折算和拥堵回溯后，道路网中 $x a ≤ C a$ 但由于物理瓶颈导致的拥堵空间排队进行蔓延溢出而形成的半畅通半拥堵状态的次生瓶颈路段集合， $A ± ? A$
36		$A k ˉ r s$	出发地为 $r$ 、目的地为 $s$ 的OD间的第 $k$ 条路径上的最上游首条路段集合， $A k ˉ r s ? A$
37		$A a ?, k r s$	出发地为 $r$ 、目的地为 $s$ 的OD间的第 $k$ 条路径上，路段 $a$ 的所有上游路段集合，其中不包括路段 $a$ ， $A a ?, k (r s) ? A$
38		$A a ˙ ?, k r s$	出发地为 $r$ 、目的地为 $s$ 的OD间的第 $k$ 条路径上，导致次生瓶颈路段 $a$ 拥堵的下游最近物理瓶颈的所有上游路段集合，其中不包括该物理瓶颈， $A a ˙ ?, k r s ? A$
39		$P r s$	出发地 $r$ 和目的地 $s$ 间的所有路径集合

Table 1

Fig.2

Fig.3

Fig.4

Fig.5

Table 2

Assignment results of the simple road network"

路段	$X a$	$x a$	$y a$	$K a$	$N Q a$	$N B a$	$t a$
A	8	8	8	0	0	0	5.635
B	4.13	4.13	2.58	0.11	61.18	0	38.824
C	3.87	3.87	2.42	0.53	580.43	0	255.128
D	4.13	2.58	2.58	1	619.57	61.18	216.301
E	8	5	5	1	1 250	1 200	10

Table 2

Fig.6

Fig.7

Fig.8

Table 3

Fig.9

Table 4

Fig.10

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模型算法	分配结果误差	算法计算时间/s
Beckmann模型	4.753 1×10^-6	2.881 6
非均衡分配算法^［19］	0.095 3	2.028 5
本文模型	1.044 5×10^-5	3.283 0

Traffic user equilibrium assignment model with congestion space queuing and spillover

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