ML20149E830
| ML20149E830 | |
| Person / Time | |
|---|---|
| Site: | Seabrook  |
| Issue date: | 11/05/1987 |
| From: | Ceder A TECHNION-ISRAEL INSTITUTE OF TECHNOLOGY, HAIFA, ISRAE |
| To: | |
| References | |
| OL-A-023, OL-A-23, NUDOCS 8802110290 | |
| Download: ML20149E830 (11) | |
Text
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Amdf Acd & Pw. Yd 14, W l.pp 31-44.kj
0MI 61ElEls-lesoHrd 4
rm ons au e um rees~ rma ig
.P bien of Res,euch &
2U DOCKETED h
USHR"'
enis. nn troc. 32, RELATIONSHIPS BETWEEN ROAD ACCIDENTS h N!!
i.11efCI. sc.6.
AND HOURLY TRAFFIC FLOW-il M
t97 4e day un au.
'88 FEB -2 A9 :28
.i Submiued to Accid.
PROBA!31LISTIC APPROACil T.
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,sure to rist Ph D.
W EICE F EIIIM #
Av!SnAl CEDER 00CKEI N A u. m.
e Querf. XXI,3 July Transportation Research Institute.Technion-IsraelInstitute of Technology,llajfa, Israel
'D
'Y (Reuired 15 April 1930;in rerludform 5 havary 1981) r b' k n of the relationship
/erkehr, March 19%.
i
- volume on a section Abstract-This is a cor.linuation of the investigation into relationships between accident rate and hourly
.h traffic flaw as outhned in Part i of the research. The underlying study attempts to determine approrriate y;
9, models for single and multi-schicle accideni rates in conjunction with free. frow and congested-flow condEons. For the free now data, the Ivtal accident rate-hourly now curve follows the lJ-shared 4
configuration. This form is the result of a consen downward and a conves upward curve for sirgle and rnulti schicle accidents, respectisely. For the corgested flow data (characterized by multi schicle ac.
f cidents). the accident rate increases sharply with hourly flow. The models are applied to probabilistic l f aspects with consideration of a fined, generalized (hourly flow defendent) bead *ay model. The headway
- i v.
model represents the probability that t*o vehicles which are, esen instantaneously, under a car follomirg y 6 mode are in a potentia!1y harardous situation. The approach investigated is beliesed to provide an essential
- W.'
iaput for both simulation studies and theoretical models of road traliic accidents.
%, y
.c h
- 1. INTRODUCTION This is the second part of a continuing study to explore the interrelationship between road 1/3
! b accidents and hourly trame flow. In the first part [Cedcr and Livneh,1981), the entite research g[{
based on nationwide data,is presented in four phases, with phase IV exhibited by this paper, The availability of data makes it possible to further separate the consideration of trame now p,
components according to the following chain: ADT-+llourly Flow-+11ourly Free and Con.
$@3 gested. Flow.1he latter separation, which is outlined here, may be approached from both deterministic and probabilistic viewpoints. The probabilistic aspects, which are emphasized in i$i this work, are both vindicated and based on determined dcterministic relationships between an accident measure and the hourly (free! congested) flow.
3[
gtt
- 2. DETERMIN ATION OF FREE FLOW AND CONGESTED-FLOW CONDITIONS f
At any instant, the driver of an automobile is confronted with a plethora of visual, aural,
~ ; f' sestibular and pressure stimuli. Though motion of his vehicle causes continuous changes in f
these stimuli, the driver cannot,and need not, evaluate each change in each stimulus dimension, j "k Of major interest are those stimuli which create a potential hazardous situation. One of the
{g known analytical tools used to assess the safety of individual cars is the car following
[
theoryllidie,1974].1his theory assumes that a driver will react to a stimulus generated by the I;Q c
nearest forward vehicle. The uniqueness of this theory is that it provides a bridge between the motion of individual cars and the entire traffic flowlCeder,1979). Ilowever, the car following k
h.t
' p!
rules are applicable only to those vehicles which are under the innuence of other vehicles in the stream-behaviour particularly noticeable under congested Dow conditions.
r.
Consequently,it is probable that as the trame now becomes more congested, the vehicles k
are more constrained and can hardly perform a desirable manoeuvre. Such situations have a 3
e direct bearing on rear-end and chain collisions, as they result from an inappropriate time lag of y
a following car response to a disturbance caused by the vehicle ahead.This argument leads to the separation of free-flow and congested flow condilions, since they have different efTects y$
upon single and culti-vehicle accidents. While free flow conditions are characterized by both 5
single and muiti vehicle accidents, congested conditions are particularly characterized by bf multi vehicle accidents.
N idI5 (It is dimcult to distinguish between free now and congested Dow periods when consideling i
on'y the hourly now variable) liven in a well deGned free-flow condition (say, from the traffic L kp now theory [Edie,19741), one can observe a platoon of vehicles moving under a congested
?p mode; and vice versa in a congested-dow condition. 'therefore, a safety based criterion is
,j Pgg W 8 2# 8Koa8 %
z3 i
t PDR 7
g;grrye..
verem
- w y.y pem mesewm m.,
m; c
4 I
h
'a b
M m/
A. CEDU established: The congested hourly flow periods are determined by those pcriods in which 95%
h<{
or more of the overall accidents are multi-vehicle accidents, and furthermore, the proportion of rear end collisins is 85% or more of total accidents.The remaining now periods are considered be Ih, Par free dow condtions. As indicated in the next part graph, this criterion determines the boundary 1
of now rate (r n an hourly basis period) between free and congested modes.
This criterion enables one to disregard single vehicle accidents (skids, roll over, running-off-00 ared 4
the road) in congested flow conditions, and to consider primarily rear end collisions (in com.
parison to head-on and angle collisions). The criterion has been applied to three four lane, k
divided roadway sections (13 3,13 5 and 13-6) mentioned in the first part of this study [ Ceder li t turns out that only for q = 1600 vehlhr per direction of travel (two lanes) i
]
and Livneh,1980){isfied3These congested hourly now periods were obser wh; this criterion is sat 4
1 roadway section (13-6). It is interesting to note that the criterion under consideratioii seems also Sin
]
1 to be adequate for high trafk flows on four lane autobahns in Germany [Leutzbach et al.,1970; f
, ley m
i
?
Briton,1976]
}
j The data considered in this paper are based on 8 year daylight (excluding night) accidents f
l and hourly Dow information for the above mentioned three roadway sectiors. Certainly, for the b
three sections no attempt is made to differen'iate between time-sequence and cross sectional whf analyses, as in Part I of this work, but rather to emphasize free flow and congested-now a,[
..k{
conditions. 'Ihe variable q is analyzed for free-flow periods, with 100 sch/br intervals within the s
range 0< q < l600; and for congested now periods, with 50vehlhr intervals within the range (3)g y
1600 5 q 51900 (the maximum measured hourly now on section 13 6 is 1900 vehlhr).
L A
f
.4 f.,
[
j
- 3. FREE FLOW AND CONGESTED FLOW MODELS
(
Under free-flow conditions, both single and multi vehicle accidents occur where the moi l
[
f proportion of single vehicle accidents is decreasing with q.13ased on the data exhibited in Part I
(
i of this work, it can be surmised that on four lane divided roadways, the majority of multi-y b
vehicle accidents are rear-end collisions over all q ranges. It is, therefore, reasonable to claim f
,d that a potential multi vehicle accident is associated with those trafric situations in which h < T, wh i
M; where h = headway in seconds (fronf bumper to front bumper) and T = a time lag of the co
[ f,.'j driver vehicle system in seconds (sufficient time in order to completely perceive, interpret, f
j
\\ 1,j decide and act, and for the schicle to respond).
f
- E /,H The time lag is an essential variable both in the event of an emergency deceleration (to void id,%
rear end collision), and in the event of a risky manoeusre (to avoid angle collision). On IS.
four lane divided roadways, head-on collisions rarely occur, and can be disregarded. llence, str;'
[M,M under free Dow conditions, the probability of a multi vehicle accident is particularly dependent thi.
j,5 F1 on the interaction of two events, A and B:
reg
.N;# < ]
Esent A: h < T in a car following mode; di Event B: a risky situation (e.g. the leading car performs a hazardous manoeuvre, or the
] h;)
driver of the following car drastically reduces his attention, or an etternal factor interferes with to aN;, f1 m
one of the vehicles).
7, h.,.
E According to the multiplicative law of probability:
.e z -
nn Ml P
= P(A n B) = p(A) p(BlA).
(1) di;d, p) h[
1he measure A,(q) which is the accident rate (acc/10'veh km)is explained in Part I of this wl b ' y.
work. 'lhis measure, divided by 10', can be used as a probability measure for an accident in h
i
{
cach veh km*within the interval q aq. It is certain that the event A is dependent on the hourly fu flow q and therciore, p( A)= p(h < Tlq). The expression p(BlA) in eqn (1) depends also on q q
g y
and it is represented by a power function. These interpretations lead, from eqn (1), to:
?
r.s k
'[
A;r(q) = p(h < Tlq) aig
(2) d v
[
p where A',,(q) 10 'is the (probability) measure for a multiochicle accident in each veh km and aig'i 10 ' represents the probability of a risky situation within the flow q iaq such that w'
7 4
h 4
S M
.t
.)
h j
=
-e8ff=T'p wYr, y a* -
3 m* **"P' V f W5"cF9 9,__
u g
,.. We onrra v?.,
N
. hhh hk i
(
)
)
h
"" '" '" " '# "#' "-U
>ds in chich 9h%
Y h < T; ai,si are constants and certainly all the probability expressions are constrained so as to Q.
he proportion of f
ds are c;n'sidered be less than I.
Another approach in the interpretation of p(BlA)is through the definition of As.(q), from nes the boundary Part I of this study, which is the accident density (accil(/ km) per nne hour exposure of traffic
,1
>ver. running off.
flows within the interval y aq. Under free flow of q vehlhr, the number of headways which
- f allisions (in com-are potential for accidents is q p(h < Tlq). Assuming a steady flow for one hour:
- 1[
' three four lane, As.(q) = q p(h < Tlq) y(q)
'[
this studylCeder i.t where it is clear that y(q) 10 is the probability for being in a risky situation when h < T.
l Iravel (two lanes) ved Inly on one Since A,.(q) 10 /q is the number of accidents per veh km,it turns out that y(g)= p(DlA).
L[.
4 ratiori seems also For single vehicle accidents under free-flo" conditions, one cannot assume a clear cut tbach el al.,1970; intersection between events. Equation (3) represents the power function for these accidents:
N. ]
4 night) accidents
,t ' ]
A*r " arq#'
(3) fert: inly, for the id cross sectional I
where A!r 10 is the (probability) measure for single-vehicle accidents in each veh.km and
)
d c:ngested flow I
n.F: are constants.1he total measure for free tlov -cidents is the summation of eqns (2) and 5.T; itervals within the r
aithin the range (3):
[6 veh/hr).
i
\\
A,r = p(h < Tlq)m 1 + atq.
(4) f@
%y For the complimentary congested flow conditions, a simple power fune: ion is selected as a q
i j
model(due to already determined criterion, mentioned in the previous section):
g occur obere the y
najority of multi.
A,c = u 39
(5) ifJ f cxhibited in Part !
Ef '
where A,c 10 ' is the measure for multi vehicle accidents in each sch km and a3,03 are h
- sonable to claim is in which h < T, in tirne lag of the constants.
Q, Wi i
erceive, interpret, j
- 4. G EN ER Al.lZED llE ADW AY MODEt.S The first expression in eqn (4) includes the headway probability distribution which basically h;
deration (to avoid is determined by measurements of headwa)s between successise vehicles in a single-lane s
Igle collision). On stream. While substantial literature has deseloped regarding the mathematical description of
),N stegarded. Ilence, this distributionlEdie,1974), only a few studies are concerned with model parametrization in g,
lcularly dependent
- k respect to different 9 values.
1he search for a generalized headway model in terms of q dependency has led to three
@qf difierent models-cach constructed with two components associated primarily with free and g,]
nanoeuvre, or the constrained schicles. The first, reported by Grecco and Sword [19681,is an empirically based h*/
tor interferes with model which considers Schuhl's distribution (best fitted distt:bution aneg: Schuhl, Gamma, Erlang and Pearson t)re 111). Their results, from measurements on four lace divided roadwa)s.
g.l include an hourly Cow variable on a per lane basis, qn and takes the Ictm.
4 qi e"-"" + (1 - 115 10 qi) e "'"e"'
(6)
,.5 4
n (1) p(h 2 f) = 15 ;0 iY:,
where t a i second and the parameters were derived according to the range 0 < qi s 700 vehlbr.
1he second study, reported by Dawson and Chiminil1968}, describes what th y call the J,l ed in Part i of this for an accident in h)rerlang headway model. lheir model is a linear combination of a translated exponential
' y ident on the hourly depends also on q function and a translated Erlang function:
{g
- qn (I), to:
(2) p(h :. g) e n, eismor 8 ' 4 n, ch 8 *h r,
2 (7) s 4
4 'e l
n each veh-km and where A,,3, are the minimum headwa)s and y,, y are average headways for free ana 4 2 49 such that constrained schicles, respeclisely; A is an index that indicates the degree of nonrandemney in y
(,.
lLr h
()
38 A. cwa i;
the constrained headway distribution; and ai,a denote the proportion of free and constrained vehicles, respectively (ni + a = 1). The parameters of eqn (7) were evaluated for one. lane flows f't (on a four lane divided roadway) ranging from 158 (k = li to 957 (k = 6) veh/hr. Though eqn (7) fL does not include the hourly now variable, the adjustable parameters for nine different flow E
q levels provide sufDciently adequate data for this work.
L The third work, recently reported by Wasielewskil1979J is based on the semi Poisson l
F headway distribution model. The estimate of the total headway probability density function, t
h
{
f(I),is given by:
l m
N
/(t) = +g(t) + AA e-^' f tg(u) d u, (8) j k
(
with 1
. *l
$ = l-A A f,e-'! f, f(u)du dt 10 JQ l
5 where + is the proportion of following (constrained) vehicles; g(t) is an estimate for g(t) and i
the latter is the probability density function of the constrained vehicles; A and A are parameters "I
d which are evaluated from the observed data (in those situations in which the vehicles are not f
h under the car-following mode). The findings of Wasiclewski introduce the function g(t) and f
ji indicate that no signincant disagreemert is fourv! beiween f(t) and the observed total headway 3y
[%
probability density function; also, it is interesting to note that the flow dependence is g
considered only through the parameters A and A.These findings are based on 42,000 observed l
5
)g headways regardini,12 groups of hourly nows ranging from 922 to 1985 vehlhr per lane on a j
y (f.$
sidlanc divided roadway.
.j r]lC The above three reviewed models are med heie to evaluate the expression p(h < Tlq)in j
g eqn (4). The value of T defined in the presicus section is censidered as 2 sec. Generally, T is a
{
E Sq, distributed variable and ranges fram 0.5 to even 4.Osce, depending on the complexity of the (j
p[g @ia[r 2.g.k driving situationlGieenshields,1901. Let m recall that h < T is considered as a potential c
situation for i n!aschicle accident where for h a T,it is improbable that such an accident will o
occur.1he vat e el T = 2 is whetituted in egns (6) and (7), and in the numerical integration of b
t i
'i.
d eqn (8), in order to obtain the functbn p(h < 2!q ) = 1 -p(h a 2lqi), where qi = the flow on a y@ty[?thd per Irne basis.
' M E.'
lhe results are demonshated in Fig.1. In the upper part of this figure the results of each d [h ' Y 8%
model. In the lower part of Fig.1, a regression line based on a power function is indicated for
?
model are exhibited separately where the flow levels correspond to the based-data of each v
J.g: m.7 all the models' results, namely:
t 34$'
p(h < 2lqi) = 0.01Iqid" (9)
MnF[t/. *
'N with standard error (SE) of 0.014 probability units. It is rather interesting to note that the M.L' Gb;fiiji[,.I regression line for the hyperlang and empirical based models only,in which q u957 vehlbr,is
.t 9
almost like eqn (9).1 hat is, p(h < 2lqi)= 0.0llq! whh SE = 0.024. The interpretation of the
.d, p ?r
', Q;.
latter result is that extrapolation of the fint two rnodels fits very well an independent model
.:. y eir @M
{ic'k.
shich is calibrated with data characterized by the ra.ge 922 4 q,41983 5ehlhr. This finding supports and strengthens the generality of eqn(9).
' h
('ly J Th
- 5. REGRESSt0N RESULTS AND NSCUSSION
. h,j.y 1he selected data are describ:d in Section 2 with !!- separation criterion between hourly gQ frce-dow and congeded flow periods. The fitted power function to multiochicle accident data ur. der free-(low cnnditions is:
g ed N b,e.m.s A'r(q) = 43 104 q' "
(10)
&~~'p.[N
- 5 with SE = 0.19(acc/10'veh km). The breakdown of eqn (10) in accordance with egns (2) and gp y
M
.)
M
, bI.
.E,,,7E$$. =m2T@,**"N.%"r,wEw@
e
==yrwm,,w $ @ M Mn ner -
er MS@
@%M h1
s
.x-
~
/~
- Q' 9
t f
s 39 Re $ ships between road accidents and hourly tra2e 65-11 l
ee and constrained oao
^,., 7 -.,
- N 7
I fo/ C ne l' ne llowl
~
a' #, c # ' * -
h
' A a
ihr.Though eqn (7) 030 g,,,,,, ice.8 ai. 4
/.
}
nine different flow p,,,,,,g,,,,
+
[
the semi Poi; son o.ro k
1 density funClion,
~
V Hypertong Model
-H f
y.\\o
(
~-o
( \\-
(8) o i
oAo
--4,,
w d
i A
{
. W.
M e
(
oJo o.20 1
s[
~
Mj
~
gi pf!
<timate for g(f) and l
s' p,0.ogi q *'s kh A are parameters J
03; -i s
e schicles are not J
Pd
(
function f(f) tnd f
,s i
i i
i 2rved tot:1 headway 1
- n coo soo soo 1000 1200 1400 1600 teco 2000 h! dependence is
\\
l'of f'C fl0* IV'h/h'u'I P" IO"'
ris.1. The rrobabiliiy of headway less than 2 see according to the empirical teed results of Grecco and
((I on 42,0C0 observed s.ordil9631. the ligerlang Model of Dawson and Chiminill94}. and the semi Poisson Model of sh/hr per (ane on a j
Weick ski [1979};in the lower figure. a regression modelis shown for the Gace sets of results.
[
'f ssi9n pun < T19) in i
Q
- c. Generally, T is a (9), reveals that ai = 5.42 10 and pe = 0.848: This breakdown presumes that eqn (9) can be (i
4 s cornplexity of the
,I i
sted as a potential applied to two-lane flows by considering separately each lane behaviour,i.e. p(h < 2[q)is t ased 7.
on eqn (9) with gi= lg. Consequently, ai and si of eqn (2) determine the expression p(BlA) uch an accident will ericalintegratio.. '
i belong to eqn (1).
qi = the 110w on a For single vehicle accidents, the following fornn.la is obtained through regression:
dn the results of each A!r(q) = 232.27 q-' '5 (H)
N f^
- based-data of each l
tion is indicated for l
with SE = 0.34 (acc/10' veh km). Equation (11) is associated with eqn (3: and eqn (4) is fuB! led l
through the summation of eqns (10) and (11),i.e. A,e = A;r + Air w hich is the total measure for b
free flow accidents.The lef t side of Fig. 2 illustrates both the data points and the free flow model.
7 (9) 5 p(b a
ei
_iue - tio -
ei
-j h
ng to note that the T-r-
T-i
- h q 5 957 vehlhr,is Y
+ im W -v'h't
h
.nterpretation of the
- [,"'~~---
j independent model j
.. - e.g.s i. e. v i.
f,i eo 5 ehlhr. 'Ihis finding j
j
. mviii...N <i.
v ei 1 is
)
m h
t z
g
- io p.
J pa between hourly 1
i erJct: accident data j
-
- s D...___,
.:. -f ft'-
ci ei h-d T
- Jt..' '.
t h
a o,.-.:'1
- _1. D.c'. c rt I,i 8 tm. A..,_.
o
..,a t.ci.t._ i 3
w
.ro xo exo,
m
.m emo
([0) s qtveh/hevri
{
q tveh/hov l e
Q
'e. tith eqns (2) and Tis 1. The data ard regression modeli.or free flow and contested ik. conditions.
E 9
t g,
(
y s
wam w w.
vp.vs,mwie v w.,,m.
, n vy,.
, m y.
yyvemy0
' f$
?
- g Y? 4 Y
40 (j
A. Crru i
The optimum conditions, by differentiating, yield q4r = 503 vehlhr, which is similar to that y
)
[
found in Part I of the work (for data composed also of night accidents and without separating t
Vi N
free and congested conditions).
t y
)
For congested How conditions, eqn (5) through regression, takes the form:
[
4 y
.y A,c = 7.21 10"' q""
(12)
}
7 g
l with SE = 0.06 (acell0' veh km),and is demonstrated on the sight side of Fig. 2. Despite the small
!l number of data points,it is possible to observe a sharp increase in A,e as q increases.
)
i in trame flow theories [Edie,1974), a congested dow behaviour refers particularly to a low,
{
,9 y
slow and congested stream of vehicles. Under these conditions, the time headway (not the I
spacing between vehicles) is usually higher than that observed under high flow levels and I
h'f:'gsk therefore, the probability of collisions is reduced. Perhaps this explanation can cast light on the 1.
results in Fig. 2 which show a diminishing tendency of A,e as q decreases. A study on the y,
j.'
attentional demands of driverslCeder,1977], also indicates the increase in collision risk under peak flow conditions. This study, based on a driver's uncertainty model, shows that under peak j
f.
'{
flow conditions (small spacing with relatively high speed), drisers tend to absorb information i
incompletely. This mode is characterized as overload attention. The latter might explain the
(
A h
relatively high probability of being involved in a collision at such now conditions, j
f$
Generally, trame engineers attempt to manage trame at high flows in order to enable N(%h movement of as many units of car as possible in a unit of time. Their belief in a productivity i
measure such as this results in nedect of the saf ety component,which is clearly indicated in Fig.2.
Q lt is desirable to approach a weighting objective function w hich will balance increased savings in trasel time with an increased accident rate as the flow level increases.
4.Wf
- 6. PROD ADtLISTIC ASPECTS i
This section further examines probabilistic interpretations of the accident measures.'!hese (ar'
{)5 ' h@k re aspects are an essential input for both simulation studies and theoretical models of trame
,,3
'A J
~N taccidents.
thi L
N.h Equation (1) considers the intersection between the two events A and B. While event A has
$ Eh been widely investigated, event B is a complex one and depends on the driver population, I
('fM human factors and other elements which can hardly (if at all) be predicted. An attempt is made here to examine event B given that event A occurs, based on the investigated data. The
[m.;W[.,f,
3 component p(B/A)in eqn (1) takes the form:
m
- L M) 4 p(BJ A) = 5.42 104 q' "'
(13)
{.[j Q,q)f 2,..
which is the probability of being in a risky situation given that the hcadway (between two ti 3 g, vehicles in a single lane)is less than two seconds. For example,if one counts 491 vehicles in a g
71 single lane during one hour, one can expect to observe (or measure) 100 out of 490 headways to an 3
.b/j be characterized by h < 2 sec (using eqn 9). The probability, for those vehicles insolved in these 4-
%7 h 100 headways, of being in a risky situation for one kilometer of driving is 1.87 104 (substitut.
fu lj ing q = 982 in eqn 13). In other words, this is the probability that the situation becomes an of
(?? M,f f actual accident from a potential accident, ac e,i q'l y " pl Two additional probabilistic aspects which can be hrived from the results of this study are:
ill f[V (i;5 (1) determination of the number of kilometers with an hourly flow q, for a given probability 95 hp such that (at least) one accident will occur.
p(
f (2) determination of the number of hours with an hourly flow q, for a given probability such (p ' W7![
f that (at least) one accident will occur.
Wi W
For both aspects, the determined quantity (kms or hrs) does not necessarily maintain the g{i continuity property (e g. for the first aspect it gives the number of kms exposed to q in one year f,6 p.
for a gisen probability).
In fact, for both aspects repeated independent trials (Bernoulli trials) are performed.
Q@, 4./
Q Considering the first aspect,one inspects w hether or not (at least) one accident will occur at each w
M hb sch km under the now q, presuming independence between each two inspections. For large numbers of veh-kms the description of the first aspect approaches the normal distribution
}!;
p']
m 7
ld kf,h.
e mym+mm w
w
. v.
. mmrynm%cm m7 W
?:
h.
("
p
\\
l N)
RetstbnsNps betrees road acddents and hourly traf5c fWa-It 41 h b similar to that 1 :ithout separating o[, [ '
[
m:
3, 3
..n,....,c.
1 ic.ng.u.a.n..
y (12) 3w l 4
2, Despite the small
$7 i
- '"[ 7 "
33,
/ increases.
articularly to a low, head: ray (not the 3.o g,
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r gight explain the f.
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in order 12 enable
,o
,o o
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,o cf in a productivity n oo%,
l {
7 indicated in Fig.2.
Increased savings in 4 3 * '""h'"' " b"'hir b" 'h' P'*b' bib' Y I '
l'' '"' id'"' # " I ' k"'
g(vehlhi)ialues.
y', '
nt measures. These (approximation to the binomial distribution). Also, since the analysis is not succersive with V/c,
'l models of traffic respect to q, a vehicle involved in an accident is, theoretically, not excided from further
)
examinations (otherwise, the appropriate distribution is geometric rather than normal). Thus,
{[,J While event A has the analysis of previous sections enables a definition:
driver population, A,(q) 10 = the probability of being involved in an accident in each veh-km within the flow An attempt is made rstigated data. The ranc q aq (Aq = 100 vehlbr) g X = number c! accidents-normally distributed (gi,al) n C
((
(lv
)
where h '4 4
16;.
cay (between two pi a n A,(q) 10; al = n A,(q) 10-'[1 - A,(q) 10-')
1
'is 491 vehicles in a h.,Q g
af 490 he dways to
?
ani n is the number of kilometers travelled by a vehicle at a given flow (within the range
- p q 2 aq). The investigated probability is p(X)llq). Figure 3 illustrates this probability as a if i@s involved in there l 7 10-' (substitut-I function on n for different flow lesels, based on eqns (10)-(12). For example, at the probability I
lation becomes an of 90%, a flow of 1000 vehlhr needs to cover 40 million km so that (at least) one single vehicle yl accident will occur, in comparison with 8.5 million km for a multi. vehicle accident. Figure 4 f
lcof this study are:
illustrates the functional dependency between n and q for three probability lesels: 30,70 and eff O given probability 951 That is, both Figs. 3 and 4 demonstrate the resultant relationship between n, q and
.c4 f)/j p(X a 1lq)-each in a different rnanner.
' n probability such Similarly, for the second aspect:
g, J
hl tarily rnaintain the A,.(q) = A,(q) q 10 = the probability of being involved in an accident on any kilometer I:d I q in one year j
exposed to one hour of flow within the range q + aq h.3 y = number of accidents-normally distributed (H2,al) j-)
[) are performed.
[g p
.I cill occur at each where Iections. For large 4
a = m A,,(q)[1 - A,,(q)]
h 3
ormal distribution pi = m A,,(q);
a f
t 2
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- s.,,..,... _ _.,, _
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41 A. Carrn 1-1 r-
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o
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,'8
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,4 q t v.h/bour i
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b I'ig. 4. The resuliant relationship between A and q for three fevels of probabdit'et (for at least one accident).
l;f
[
l. %,td
.m ag :
and m is the number of hours which experience a flow (within the range q Aq) at a given thesd
..:9hhh J.' '
kilometer. The investigated probability p(y ;r 1lg) is shown continuously in Fig. 5, and for only proba relatit three levels in Fig. 6.
- p D
~, g'f?,i free.f fQ
- 7. S U M M ARY l!.gGf.'
. This study which is the last, and phase IV of the entire research (shown schematically in the free f
/i k j first figure in Ceder and Livneh,1981), attempts primarily to consider accident data regarding resy
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e 4.m
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- e
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Cede m
O
'o b E b
$- E E~~Io Dam
.3 R
/
i m tto' b v.si Edie
? I.
il (f
Grec Fig 5. The resultant relatiochip betmeen the probabuiry for at least one accident and m for various 4 r.
t1:
3.'
'{
behlht) ulues.
,S' 4
t.
c.
,Y
- q...f...
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m - nwv.
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i Relat!x. ships betuten road acciJeds and hourly tramc N r-Il 41 4
f
~ T-~
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ts% probability _
s D
i 60
,,. - = =
-]
)
I do -/*
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g so y
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s y
o
-, -- p a _ 4 -_ _, _, _g. -
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y 2.
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q tveh/ houri I '
es (for at kast one f
Fig 6.1he resultant relationship betecen m and g for three leve's of probabilities (for at least one accident).
the separation between free. flow and congested. flow conditions. The adopted and deseloped ige q 2 Aq) at a given i
b r3 5, and for only probabilistic approach outlined in this paper is another way of tackling the determined l
relationships between the accident rate and the hourly traffic flow.
f Dased on a predetermined criterion, the c6itgested flow conditions are separated from the free flow conditions, and subsequently applied ai.J correlated to accident data in Fig. 2. For the
[
vn schematically in the i
free now data, the total accident rate curve follows the known U shaped configuration with l'
ecident data legarding j
respect to the hourly flow, which is the result of combining a convex downward and a convex j
upward curve for single and multi vehicle accidents, respectively. For congested flow data, the Y
j (multi vehicle) accident rate is sharply increased with hourly flow.This outcome suggests, from j
a safety viewpoint, avoidance of high flow levels in contrast to the general trallic engineers'
{
desire to move as many cars as possible in a unit of time (i.e. to approach a capacity level). A 6
.i balanced traflic productivity measure might then attempt to maintain the stream of schicles h
(assuming it is under control) at a buffer point below its maximum range.
(
1he probabilistic aspects utilize a generalized headway model litted to three different models r;
from the literature. This headway model is hourly flow dependent and it represents the
{J probability that two velicles which are, even instantaneously, under the car.following mode, j
are in a potentially hattrdous situation.The remaining underlying probability aspects are based 9
on the determined accident models for the free flow and congested flow conditions. It is i
i believed that such models are essential input both for simulation studies and for theoretical j
models of road trafhe accidents.
I REFERENCES Brilon W lJnfsPreschehen und Verkehrsabbuf. forst Annt Strassedan nad Strassenerrichtsreckna. lkft 201.1976.
l Ceder A., tXivets' en movements as related to attention in simulated trame now conditions. Unmen factors 19 6).
t 371-581. 1977.
Ceder A.. Stable phase piane and car following behaviour as applied to a macroscopic phenomenon. Trensra Sd 13(1).
g 64-79. 1979.
1 Ceder A.and Livneh M..Relationshipi beteeen road accidents and hourty trame he-l. Analpis and interpretation. Accid.
}
Anal. A Pers.14.14-M.19s2.
Danon R. F. and Chimini L Aslhe h>reilang probability distribulbn-a generalized bame he:Jeay model. Hignisy Res. Rec 1.s0. t-14.1%R.
Edie L C.. Dow theories in Trefc Scitare (Edited by Garis D. C 1 Waey. New Yo<k.1974.
.and a for sarbus t Grecco W. L and SeoiJ E. C.. Predxtbn of parameters for Schuhrs headmay distributba. Trafc Engng 3sd), %-38 1%8 g
a I
q I
.A M M M R i d...........
S,....,_,* @ n M S M i8? M
... ~
WsMI
[
%)
Mj' r.a 44 A. Ctern I
Greenshields B. D..lhe driier,in Trefc Enginemat flandbm4 (Edited by Daermaid J.W-). Insinuie of Trame Engineers.
j Washington, D C.,1%5.
Leutzbach W., Siegener W. and Wiedemann R. On the connection betm een tramc accidents and trame volume on a section f.
of a German Autotuhn. Accid. Anal. A her. 2,141-146 (in German),1970.
Wasielemski P., Car follo=ing headnays on freemays interpreted by the semi Poisson headasy distribution model.
j, Treups Sci. l.h!). W55,1979.
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UNITED STATES
[
NUCLEAR REGULATORY COMMISSION 7.
WASHINGTON, D. C. 205M liay 26, 1987 MEMORANDUM FOR:
John Milligan Technassociates FROM:
Emile L. Julian Weting Chief Docketing and Service Branch
SUBJECT:
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1 i
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