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Establishing relationships between accidents and flows at urban priority road junctions
Acrid. Anal. & Prm. Vol. 24, No. 6, pp. 689-694.1992 tinted in Great Britain.
00014575/92 $5.00 + .OO Q1992PnpmonRaLtd.
ESTABLISHING RELATIONSHIPS BETWEEN ACCIDENTS AND FLOWS AT URBAN PRIORITY ROAD JUNCTIONS Department
J. C. GOLIAS of Transportation Planning and Engineering, National Technical University of Athens, 5 Iroon Polytechniou, 15700 Zografou, Athens, Greece (Received 6 August 1990; in revisedfown 6 August 199 1)
Ahs#raet--This papers explores the effects of traffic stream flows on accident potential at urban priority-controlled (i.e. unsignalised), four-arm junctions. Forty-three urban priority junctions were carefully selected so that other than flow parameters expected to influence accident potential have similar values at the junctions considered. Using traffic accident data for five-year time periods and the corresponding 24-hour flows, a new exposure index is proposed consisting of an expression of the flows of the junction’s interacting traffic streams. The regression of this exposure index on the expected number of accidents per year at junctions of the type. examined yields a quite satisfactory correlation coefficient, better than those achieved when other proposed indices are used.
INTRODUCTION
The fact that more than half of all injury urban area accidents occur at road junctions is a well-known result from trafhc accident analyses in various countries (Smeed 1968; United Nations 1985; Department of Transport 1987; International Road Federation 1988). This rather large proportion of accidents concentrated at specific sites in the road network, has caused, as expected, much concern about this extremely important safety problem. It is obvious that the actual number of accidents at a junction in any year depends upon a large number of factors, road features and traffic characteristics being the most important. However, for road junctions at urban areas, where speeds are low, and given the junction type, traffic characteristics are expected to have the dominant significance (Ward et al. 1983). This paper attempts to establish relationships between the expected number of accidents and the flows of the traffic streams passing through the junction. Although the majority of accidents at junctions occur in urban areas, accident analysis in relation to existing traffic flows was initially attempted for rural junctions. In an early paper, Tanner (1953) showed that the number of accidents at three-way rural intersections was related to the square root of the product of the flows on the major and minor roads, a result reinforced later by more thorough research (Colgate and Tanner 1967). McDonald (1953) and Roosmark (1966) deduced similar relationships, the difference being in the power to which major and minor road flows are raised. Although a high proportion of all junctions in urban areas are priority controlled, research on safety at these junctions is rather limited. Grossman (1954) proposed the estimation of accident potential by use of the sum of the corresponding traffic flows only at junction points where these flows cross each other. Breuning and Bone (1959) and Surti (1969) rather than simply adding conflicting stream flows proposed an exposure index that is formed by use of the sum of the products of flows that cross or merge with each other. However, no functional relationship between this index and the expected number of accidents was given. The establishment of such a relationship was attempted in a later study (Hakkert and Mahalel1978), but priority junctions were treated together with those signal&d. The number of accidents at various types of urban intersections was also related (Leong 1973) to the product of the flows of the major and minor road, each one raised to a Rower less than one, but the results were not considered satisfactory as P was always well below 0.50, although the samples of junctions analysed can be considered homo689
690
BriefCommunicationsand ResearchNotes
geneous. Improvements in the way such an exposure can be derived are thoroughly discussed in a later paper (Hodge and Richardson 1978). In a more recent study (Ward et al. 1983) various log-linear models using expressions of the traffic stream flows were used to predict accident potential at three-arm, urban, uncontrolled road junctions. Analysis of the data was carried out using the generalised linear modelling system (Nelder and Wedderburn 1972; McCullagh and Nelder 1983). A log-linear model using as exposure index a function of the sum of the cross products of the flows of the traffic streams that cross, merge, or diverge was found to be the best estimator of the accident potential. However, the relation proposed does not explain more than 32% of the variability of accident numbers at the junctions examined. The use of generalised linear models for the prediction of accidents at junctions has also been adopted in more recent studies. Thus, Frith and Harte (1986) used such models for the assessment of the effects that control changes on urban junction have on junction safety. Maycock and Hall (1984) used the generalised linear modelling system to establish relationships for the prediction of accidents at four-arm roundabouts. They derived through regression analysis log-linear models, which use functions of the flows of the various traffic streams within a four-arm roundabout. A similar approach was followed in a later study for rural T-junctions (Pickering, Hall, and Grimmer 1986), which led to log-linear relations between the total accident frequency at the junction and various functions of the traffic flow through the junction. However, although some functions of flows were found to be highly significant predictors of accident frequency, the percentage of deviance (Baker and Nelder 1978) accounted for by the corresponding models does not exceed 40% in any case. The above review seems to indicate that the problem of the determination of an exposure index to be used as a basis for the prediction of the number of accidents at an urban junction has not been solved yet satisfactorily. The objective of this paper is to contribute towards the determination of a satisfactory exposure index for priority-controlled (i.e. unsignalised) road junctions. Data collection This study considers only four-arm, priority-controlled road junctions. Data on traffic flow and accidents were collected for 43 such urban junctions in the Greater Athens area. As this study aims to research the mechanisms of relationships between accidents and traffic flows of interacting streams, these 43 junctions were carefully selected so that all other parameters expected to have a contribution in accident occurence have similar values. Thus, all junctions have stop signs on the minor road arms and no speed limit signs on any direction. Unfortunately, there are no major road speed measurements for the time period considered at each junction. However, as major road mean speeds were found to be at present similar, ranging from 30 to 40 km/h during morning off-peak period at the 43 junctions, it was assumed that major stream, mean speeds were also of similar range in all 43 junctions for the time periods considered by this investigation. As far as layout is concerned, the effective carriageway width of the major road arms ranges from 4.2 to 5 m per direction, while that of the minor road arms ranges from 3.3 to 3.8 m. Gradients in all arms do not exceed 4%. There are no extra lanes for the left turn manoeuvre and no central or ghost islands at any of these 43 junctions. Visibility along major road arms from minor road arms was also of the same range in all junctions selected, and for a distance of 10 m from the stop line on the minor road arms ranged from 10 to 40. Traffic flow data were collected from existing sources for the above 43 junctions and for the corresponding five-year time periods. The annual average daily flow, expressed in passenger car units (pcu), was finally calculated and used for each traffic stream at each junction. Traffic growth figures of the study area were also used, when necessary, to scale the existing annual average daily flow estimates to represent average daily flows throughout the particular study period for each junction.
Brief Communications and Research Notes
691
The daily flows calculated for the traffic streams of the junctions considered covered, as expected, a very wide range. Thus, the major road traffic stream daily flows range from 3,000 to 25,000 pcus while the minor road traffic stream daily flows range from 1,200 to 3,000 pcus. It should be noted that the number of different traffic streams at the junctions examined is not constant, but ranges from 6 to 12. However, this is not expected to diminish the desired homogeneity of the junction sample, given that the effect of this number can be accounted for indirectly by considering the junction points of conflict, the number of which is directly related to the number of streams. Furthermore, it should be noted that for the five-year period considered at these junctions there were no counts for pedestrian flows, a dominant parameter for the occurence of pedestrian-involved accidents. Thus, it was decided that this analysis deals only with nonpedestrian accidents. However, as it was thought that the intensity of pedestrian activity at a junction may influence driver behaviour and consequently accident occurence, care was taken that it is of the same range at present in the junctions selected, assuming that this ensures that it was also of the same range during the fiveyear time period examined. Pedestrian activity intensity was expressed as the sum of pedestrian flow per hour in the four junction arms, and ranged from 50 to 100 pedestrians per hour for the junctions selected. Data on accident occurence in the 43 junctions finally selected were collected from police records. The number of accidents for the five-year period between 1983 and 1987 was recorded for each junction. Six of the 43 junctions were converted from priority to signalised junctions during this period and hence the five-year time period before the year of signalisation was used for these junctions. The use of a long time-period for the accident investigation in each junction is expected to have rendered negligible the regression to the mean effects (Hauer 1986; Golias 1988). The number of nonpedestrian accidents recorded for the five-year time period at each junction ranged from 5 to 33. More particularly, the above number ranged from 5 to 10 at 14 junctions, from 10 to 15 at 11 junctions, from 15 to 20 at 9 junctions, from 20 to 25 at 5 junctions and from 25 to 30 at 3 junctions, while there was also a junction with 33 accidents in the sample examined. Analysis Taking into account the results of similar research reviewed above, it was decided that for the formation of an exposure index, traffic flows of all streams entering the junction are used instead of total traffic flows per direction. The sum of the products of the flows of traffic streams that cross or merge with each other was initially investigated for the prediction of the accident potential. Therefore, this exposure index I, for a specific junction, is given by the following formula:
I =
2 2 Qi Qj i=l
j=l
(1)
where n: is the number of traffic streams entering the junctions Qi: is the traffic flow of stream i amongst the n traffic streams entering the junction I?z~:is the number of traffic streams of the junction crossing or merging with stream i Qj: is the traffic flow of stream i amongst the mi traffic streams of the junction crossing or merging with stream i. It should be noted that this exposure index is identical to that already used for a mixed sample of signalised and priority junctions (Hakkert and Mahalel 1978) except that the right turning traffic stream out of each arm is considered to merge not only with the straight-going stream of the vertical arm but also with the left-turning stream out of the opposite arm.
692
The regression equation:
Brief Communications and Research Notes
of this index upon the number
of accidents gave the following
Ai = 1.16 + 0.23 X lo-’ Zi
(2)
where Ai: is the mean number of accidents per year in the five-year period examined for junction i Zi: is the exposure index for junction i, given by equation (1). The correlation coefficent was found to be equal to 0.71, i.e. equation (2) explains about 50% of the existing variability, a rather unsatisfactory result. It should be noted that the regression analysis procedure followed in this study uses the weighted instead of the normal least square method so that the fact that accidents in a given period follow a Poisson distribution can be taken into account. (Jorgenson 1961; Weber 1971; Hakkert and Mahalel 1978). When the products used in equation (1) are raised to a power less than 1 and the resulting indices I are regressed upon the number of accidents, better results are achieved, although the improvement can be considered as marginal. The investigation towards this approach revealed that the best exposure index Z to be used, is given by the formula:
z= i
i=l
2 (Qi
Q,)".*
= i [Qp.5;
Qy.51
(3)
i=l
j=l
When this index is regressed upon the number of accidents the following equation derived Ai = 0.78 + 0.50 x 1O-4 Z,
is
(4)
with a correlation coefficient equal to 0.78. The above investigation indicated that if the interactions between the different conflicting traffic streams at a junction were better determined, the correlation coefficient could increase considerably. Thus, a number of different exposure indices, formed on the basis of various interaction assumptions, were regressed upon the number of accidents. The best results were finally obtained by use of an exposure index Z given by the formula:
i=l
L
j=l
_I
which, when regressed upon the average number Ai of accidents per year at junction i, gave the following equation: Ai = 0.37 + 0.60 X 10m3Zi.
(6)
The correlation coefficient was found to be equal to 0.89, i.e. about 78% of the variability of the number of accidents at a junction is explained by equation (6) on the basis of the exposure index proposed by equation (5). The results of the above analysis seem to suggest that the exponent to which traffic flows should be raised when exposure indices are formed should be less than 1 and preferably near 0.5. The most probable explanation for this conclusion, which agrees with results of previous research (Tanner 1953; Ward et al. 1983), is that drivers seem to be more cautious when implementing manoeuvres involved with high traffic flow streams, an explanation in accordance with risk compensation theory (Haight 1986).
Brief Communications
and Research Notes
693
Furthermore, it should be noted that all accident prediction equations established above through thorough regression analysis have constants that are not equal to zero. It is most probable that as drivers are less careful when traffic flows are low and as heavy traffic junctions are expected to have higher design standards, the constant in the prediction equation is required to take these factors into account for the range of values studied. CONCLUSIONS
The relationship between the number of nonpedestrian accidents and traffic flows of the various streams was investigated for 43 urban priority controlled road junctions. The 43 junctions were carefully selected to have similar road features and operational characteristics so that variation of accident number is mainly due to different traffic flows. Exposure indices formed by the sum of functions of cross products of traffic stream flows, which take into account the interaction between traffic streams, were regressed upon the number of accidents per junction and were found to give accident potential predicting equations explaining always more than 50% of the observed accident variability. The exposure index finally proposed after thorough investigation of different relationships among the conflicting streams is the sum of the square root of the product consisting of the flow of each stream entering the junction multiplied by the sum of the flows of the traffic streams crossing or merging with it (equation 5). This result, in combination with those related to the other indices examined, indicates the use of traffic flow exponents that are less than 1 when exposure indices are formed. The percentage of variability in the number of accidents explained by the finally proposed model (equation 6), which was found to be 78%, is considered satisfactory taking into account that the other factors influencing accident potential had values of the same range but not identical at the junctions examined. Furthermore, it should be noted that this percentage is much higher than those of previous similar research. As fas as the remaining variance is concerned for the type of junctions investigated, it is believed that it can be mainly explained by the minor differences in the values of the road feature factors. A model that would incorporate the effect of factors like approaching vehicle speed, visibility from the minor road, level of street lighting for accidents occuring during darkness, gradients would be expected to have greater explanatory power. Whether this improvement will be worth the increase of model complexity is yet to be researched. It is clear from this investigation that the dominant factor influencing the accident potential of an urban junction-at least for the type studied, although it is believed that this would be the case for any urban junction- is an expression of the interacting traffic stream flows. The results of the analysis is believed to have clarified issues concerning the mechanisms that determine this expression. It is obvious that more research is needed to validate these mechanisms in other types of junctions, too, and to establish more general accident prediction equations, applicable in various types of junctions and in different layouts for each type. REFERENCES Baker R. J.; Nelder, J. A. Generalized linear interactive modelling, the GLIM system Release 3, Harpenden, U.K.: Rothamsted Experimental Station; 1978. Breuning, S. M.; Bone, A. J. Interchange accident exposure. Highway Research Board Bulletin 240:44-52; 1959. Colgate, M. G.; Tanner, J. C. Accidents at rural three-way junctions. RRL Report LR87. Crowthorne, U.K.: Transport and Road Research Laboratory; 1967. Department of Transport. Road accidents Great Britain 1986. The Casualty Report. London: H.M.S.O.; 1987. Frith, W. J.; Harte, D. S. The safety implications of some control changes at urban intersections. Accid. Anal. Prev. l&183-192; 1986.
694
Brief Communications
and Research Notes
Golias, J. C. Techniques for the control of the regression-to-mean effect in before-and-after accident studies. Technika Chronica, Scientific Journal of the Technical Chamber of Greece, Section A, 8(2):7-30; 1988. Grossman, L. Accident exposure index. Highway Research Board Proceedings, 33:129; 1954. Haight, F. A. Risk, especially risk of traffic accident. Accid. Anal. Prev. 18:359-366; 1986. Hakkert, A. S.; Mahalel, D. Estimating the number of accidents at intersections from a knowledge of the traffic flows on the approaches. Accid. Anal. Prev. 10:69-79; 1978. Hauer, E. On the estimation of the expected number of accidents. Accid. Anal. Prev. 18:1-12; 1986. Hodne, G. A.; Richardson, A. J. A study of intersection accident exposure. Proceedings of the Australian goid Research Board 9(5):151-160; 1578. International Road Federation. World road statistics 1983-1987. Washineton. DC: International Road Federation; 1988. Jergenson, D. W. Multiple regression analysis of the Poisson process. Journal of American Statistical Association 56:235-245; 1961. Leong, W. H. J. Relationship between accidents and traffic volumes at urban intersections. Journal of Australian Road Research Board, 5(3):72-90; 1973. Maycock, G.; Hall, R. D. Accidents at 4-arm roundabouts. TRRL Report LR 1120. Crowthorne, U.K.: Transport and Road Research Laboratory; 1984. McCullagh, P.; Nelder, J. A. General&d linear models; Londqn, U.K.: Chapman and Hall Ltd; 1983. McDonald, J. W. Relation between number of accidents and traffic volume at divided-highway intersections. HRR, Bulletin 74:7-17; 1953. Nelder, J. A.; Wedderburn, R. W. M. Generalized linear models. Journal of Royal Statistical Society A 135:370-384; 1972. Pickering, D.; Hall R. D.; Grimmer, M. Accidents at rural T-junctions. TRRL Report RR 65 1986. Roosmark, P. 0. Traffikolyckor trevagskorsningar Statens Vaginstitut Preliminary Report 22. Stockholm, Sweden: 1966. Smeed, R. J. Variations in the pattern of accident rates in different countries and their causes. Traff. Eng. Control 10(7):364-371; 1968. Surti, V. H. Accident exposure and intersection safety for at-grade, unsignalised intersections. Highway Research Record 286:81-94; 1969. Tanner, J. C. Accidents at rural three-way junctions. Journal of the Institution of Highway Engineers II(ll):5667; 1953. United Nations. Statistics of road traffic accidents in Europe 1984. New York: United Nations; 1985. Ward, H.; England, L.; Murphy, R. S. D.; Moore, R. L. Accident occurence, traffic and road features at urban priority type road junctions. Report to Accident Investigation Division, TRRL, Contract No 842/539. Crowthorne, U.K.: Transport and Road Research Laboratory; 1983. Weber, D. C. Accident rate potential: An application of multiple regression analysis of a Poisson process. Journal of American Statistical Association 66:285-288; 197 1.
00014575/92 $5.00 + .OO Q1992PnpmonRaLtd.
ESTABLISHING RELATIONSHIPS BETWEEN ACCIDENTS AND FLOWS AT URBAN PRIORITY ROAD JUNCTIONS Department
J. C. GOLIAS of Transportation Planning and Engineering, National Technical University of Athens, 5 Iroon Polytechniou, 15700 Zografou, Athens, Greece (Received 6 August 1990; in revisedfown 6 August 199 1)
Ahs#raet--This papers explores the effects of traffic stream flows on accident potential at urban priority-controlled (i.e. unsignalised), four-arm junctions. Forty-three urban priority junctions were carefully selected so that other than flow parameters expected to influence accident potential have similar values at the junctions considered. Using traffic accident data for five-year time periods and the corresponding 24-hour flows, a new exposure index is proposed consisting of an expression of the flows of the junction’s interacting traffic streams. The regression of this exposure index on the expected number of accidents per year at junctions of the type. examined yields a quite satisfactory correlation coefficient, better than those achieved when other proposed indices are used.
INTRODUCTION
The fact that more than half of all injury urban area accidents occur at road junctions is a well-known result from trafhc accident analyses in various countries (Smeed 1968; United Nations 1985; Department of Transport 1987; International Road Federation 1988). This rather large proportion of accidents concentrated at specific sites in the road network, has caused, as expected, much concern about this extremely important safety problem. It is obvious that the actual number of accidents at a junction in any year depends upon a large number of factors, road features and traffic characteristics being the most important. However, for road junctions at urban areas, where speeds are low, and given the junction type, traffic characteristics are expected to have the dominant significance (Ward et al. 1983). This paper attempts to establish relationships between the expected number of accidents and the flows of the traffic streams passing through the junction. Although the majority of accidents at junctions occur in urban areas, accident analysis in relation to existing traffic flows was initially attempted for rural junctions. In an early paper, Tanner (1953) showed that the number of accidents at three-way rural intersections was related to the square root of the product of the flows on the major and minor roads, a result reinforced later by more thorough research (Colgate and Tanner 1967). McDonald (1953) and Roosmark (1966) deduced similar relationships, the difference being in the power to which major and minor road flows are raised. Although a high proportion of all junctions in urban areas are priority controlled, research on safety at these junctions is rather limited. Grossman (1954) proposed the estimation of accident potential by use of the sum of the corresponding traffic flows only at junction points where these flows cross each other. Breuning and Bone (1959) and Surti (1969) rather than simply adding conflicting stream flows proposed an exposure index that is formed by use of the sum of the products of flows that cross or merge with each other. However, no functional relationship between this index and the expected number of accidents was given. The establishment of such a relationship was attempted in a later study (Hakkert and Mahalel1978), but priority junctions were treated together with those signal&d. The number of accidents at various types of urban intersections was also related (Leong 1973) to the product of the flows of the major and minor road, each one raised to a Rower less than one, but the results were not considered satisfactory as P was always well below 0.50, although the samples of junctions analysed can be considered homo689
690
BriefCommunicationsand ResearchNotes
geneous. Improvements in the way such an exposure can be derived are thoroughly discussed in a later paper (Hodge and Richardson 1978). In a more recent study (Ward et al. 1983) various log-linear models using expressions of the traffic stream flows were used to predict accident potential at three-arm, urban, uncontrolled road junctions. Analysis of the data was carried out using the generalised linear modelling system (Nelder and Wedderburn 1972; McCullagh and Nelder 1983). A log-linear model using as exposure index a function of the sum of the cross products of the flows of the traffic streams that cross, merge, or diverge was found to be the best estimator of the accident potential. However, the relation proposed does not explain more than 32% of the variability of accident numbers at the junctions examined. The use of generalised linear models for the prediction of accidents at junctions has also been adopted in more recent studies. Thus, Frith and Harte (1986) used such models for the assessment of the effects that control changes on urban junction have on junction safety. Maycock and Hall (1984) used the generalised linear modelling system to establish relationships for the prediction of accidents at four-arm roundabouts. They derived through regression analysis log-linear models, which use functions of the flows of the various traffic streams within a four-arm roundabout. A similar approach was followed in a later study for rural T-junctions (Pickering, Hall, and Grimmer 1986), which led to log-linear relations between the total accident frequency at the junction and various functions of the traffic flow through the junction. However, although some functions of flows were found to be highly significant predictors of accident frequency, the percentage of deviance (Baker and Nelder 1978) accounted for by the corresponding models does not exceed 40% in any case. The above review seems to indicate that the problem of the determination of an exposure index to be used as a basis for the prediction of the number of accidents at an urban junction has not been solved yet satisfactorily. The objective of this paper is to contribute towards the determination of a satisfactory exposure index for priority-controlled (i.e. unsignalised) road junctions. Data collection This study considers only four-arm, priority-controlled road junctions. Data on traffic flow and accidents were collected for 43 such urban junctions in the Greater Athens area. As this study aims to research the mechanisms of relationships between accidents and traffic flows of interacting streams, these 43 junctions were carefully selected so that all other parameters expected to have a contribution in accident occurence have similar values. Thus, all junctions have stop signs on the minor road arms and no speed limit signs on any direction. Unfortunately, there are no major road speed measurements for the time period considered at each junction. However, as major road mean speeds were found to be at present similar, ranging from 30 to 40 km/h during morning off-peak period at the 43 junctions, it was assumed that major stream, mean speeds were also of similar range in all 43 junctions for the time periods considered by this investigation. As far as layout is concerned, the effective carriageway width of the major road arms ranges from 4.2 to 5 m per direction, while that of the minor road arms ranges from 3.3 to 3.8 m. Gradients in all arms do not exceed 4%. There are no extra lanes for the left turn manoeuvre and no central or ghost islands at any of these 43 junctions. Visibility along major road arms from minor road arms was also of the same range in all junctions selected, and for a distance of 10 m from the stop line on the minor road arms ranged from 10 to 40. Traffic flow data were collected from existing sources for the above 43 junctions and for the corresponding five-year time periods. The annual average daily flow, expressed in passenger car units (pcu), was finally calculated and used for each traffic stream at each junction. Traffic growth figures of the study area were also used, when necessary, to scale the existing annual average daily flow estimates to represent average daily flows throughout the particular study period for each junction.
Brief Communications and Research Notes
691
The daily flows calculated for the traffic streams of the junctions considered covered, as expected, a very wide range. Thus, the major road traffic stream daily flows range from 3,000 to 25,000 pcus while the minor road traffic stream daily flows range from 1,200 to 3,000 pcus. It should be noted that the number of different traffic streams at the junctions examined is not constant, but ranges from 6 to 12. However, this is not expected to diminish the desired homogeneity of the junction sample, given that the effect of this number can be accounted for indirectly by considering the junction points of conflict, the number of which is directly related to the number of streams. Furthermore, it should be noted that for the five-year period considered at these junctions there were no counts for pedestrian flows, a dominant parameter for the occurence of pedestrian-involved accidents. Thus, it was decided that this analysis deals only with nonpedestrian accidents. However, as it was thought that the intensity of pedestrian activity at a junction may influence driver behaviour and consequently accident occurence, care was taken that it is of the same range at present in the junctions selected, assuming that this ensures that it was also of the same range during the fiveyear time period examined. Pedestrian activity intensity was expressed as the sum of pedestrian flow per hour in the four junction arms, and ranged from 50 to 100 pedestrians per hour for the junctions selected. Data on accident occurence in the 43 junctions finally selected were collected from police records. The number of accidents for the five-year period between 1983 and 1987 was recorded for each junction. Six of the 43 junctions were converted from priority to signalised junctions during this period and hence the five-year time period before the year of signalisation was used for these junctions. The use of a long time-period for the accident investigation in each junction is expected to have rendered negligible the regression to the mean effects (Hauer 1986; Golias 1988). The number of nonpedestrian accidents recorded for the five-year time period at each junction ranged from 5 to 33. More particularly, the above number ranged from 5 to 10 at 14 junctions, from 10 to 15 at 11 junctions, from 15 to 20 at 9 junctions, from 20 to 25 at 5 junctions and from 25 to 30 at 3 junctions, while there was also a junction with 33 accidents in the sample examined. Analysis Taking into account the results of similar research reviewed above, it was decided that for the formation of an exposure index, traffic flows of all streams entering the junction are used instead of total traffic flows per direction. The sum of the products of the flows of traffic streams that cross or merge with each other was initially investigated for the prediction of the accident potential. Therefore, this exposure index I, for a specific junction, is given by the following formula:
I =
2 2 Qi Qj i=l
j=l
(1)
where n: is the number of traffic streams entering the junctions Qi: is the traffic flow of stream i amongst the n traffic streams entering the junction I?z~:is the number of traffic streams of the junction crossing or merging with stream i Qj: is the traffic flow of stream i amongst the mi traffic streams of the junction crossing or merging with stream i. It should be noted that this exposure index is identical to that already used for a mixed sample of signalised and priority junctions (Hakkert and Mahalel 1978) except that the right turning traffic stream out of each arm is considered to merge not only with the straight-going stream of the vertical arm but also with the left-turning stream out of the opposite arm.
692
The regression equation:
Brief Communications and Research Notes
of this index upon the number
of accidents gave the following
Ai = 1.16 + 0.23 X lo-’ Zi
(2)
where Ai: is the mean number of accidents per year in the five-year period examined for junction i Zi: is the exposure index for junction i, given by equation (1). The correlation coefficent was found to be equal to 0.71, i.e. equation (2) explains about 50% of the existing variability, a rather unsatisfactory result. It should be noted that the regression analysis procedure followed in this study uses the weighted instead of the normal least square method so that the fact that accidents in a given period follow a Poisson distribution can be taken into account. (Jorgenson 1961; Weber 1971; Hakkert and Mahalel 1978). When the products used in equation (1) are raised to a power less than 1 and the resulting indices I are regressed upon the number of accidents, better results are achieved, although the improvement can be considered as marginal. The investigation towards this approach revealed that the best exposure index Z to be used, is given by the formula:
z= i
i=l
2 (Qi
Q,)".*
= i [Qp.5;
Qy.51
(3)
i=l
j=l
When this index is regressed upon the number of accidents the following equation derived Ai = 0.78 + 0.50 x 1O-4 Z,
is
(4)
with a correlation coefficient equal to 0.78. The above investigation indicated that if the interactions between the different conflicting traffic streams at a junction were better determined, the correlation coefficient could increase considerably. Thus, a number of different exposure indices, formed on the basis of various interaction assumptions, were regressed upon the number of accidents. The best results were finally obtained by use of an exposure index Z given by the formula:
i=l
L
j=l
_I
which, when regressed upon the average number Ai of accidents per year at junction i, gave the following equation: Ai = 0.37 + 0.60 X 10m3Zi.
(6)
The correlation coefficient was found to be equal to 0.89, i.e. about 78% of the variability of the number of accidents at a junction is explained by equation (6) on the basis of the exposure index proposed by equation (5). The results of the above analysis seem to suggest that the exponent to which traffic flows should be raised when exposure indices are formed should be less than 1 and preferably near 0.5. The most probable explanation for this conclusion, which agrees with results of previous research (Tanner 1953; Ward et al. 1983), is that drivers seem to be more cautious when implementing manoeuvres involved with high traffic flow streams, an explanation in accordance with risk compensation theory (Haight 1986).
Brief Communications
and Research Notes
693
Furthermore, it should be noted that all accident prediction equations established above through thorough regression analysis have constants that are not equal to zero. It is most probable that as drivers are less careful when traffic flows are low and as heavy traffic junctions are expected to have higher design standards, the constant in the prediction equation is required to take these factors into account for the range of values studied. CONCLUSIONS
The relationship between the number of nonpedestrian accidents and traffic flows of the various streams was investigated for 43 urban priority controlled road junctions. The 43 junctions were carefully selected to have similar road features and operational characteristics so that variation of accident number is mainly due to different traffic flows. Exposure indices formed by the sum of functions of cross products of traffic stream flows, which take into account the interaction between traffic streams, were regressed upon the number of accidents per junction and were found to give accident potential predicting equations explaining always more than 50% of the observed accident variability. The exposure index finally proposed after thorough investigation of different relationships among the conflicting streams is the sum of the square root of the product consisting of the flow of each stream entering the junction multiplied by the sum of the flows of the traffic streams crossing or merging with it (equation 5). This result, in combination with those related to the other indices examined, indicates the use of traffic flow exponents that are less than 1 when exposure indices are formed. The percentage of variability in the number of accidents explained by the finally proposed model (equation 6), which was found to be 78%, is considered satisfactory taking into account that the other factors influencing accident potential had values of the same range but not identical at the junctions examined. Furthermore, it should be noted that this percentage is much higher than those of previous similar research. As fas as the remaining variance is concerned for the type of junctions investigated, it is believed that it can be mainly explained by the minor differences in the values of the road feature factors. A model that would incorporate the effect of factors like approaching vehicle speed, visibility from the minor road, level of street lighting for accidents occuring during darkness, gradients would be expected to have greater explanatory power. Whether this improvement will be worth the increase of model complexity is yet to be researched. It is clear from this investigation that the dominant factor influencing the accident potential of an urban junction-at least for the type studied, although it is believed that this would be the case for any urban junction- is an expression of the interacting traffic stream flows. The results of the analysis is believed to have clarified issues concerning the mechanisms that determine this expression. It is obvious that more research is needed to validate these mechanisms in other types of junctions, too, and to establish more general accident prediction equations, applicable in various types of junctions and in different layouts for each type. REFERENCES Baker R. J.; Nelder, J. A. Generalized linear interactive modelling, the GLIM system Release 3, Harpenden, U.K.: Rothamsted Experimental Station; 1978. Breuning, S. M.; Bone, A. J. Interchange accident exposure. Highway Research Board Bulletin 240:44-52; 1959. Colgate, M. G.; Tanner, J. C. Accidents at rural three-way junctions. RRL Report LR87. Crowthorne, U.K.: Transport and Road Research Laboratory; 1967. Department of Transport. Road accidents Great Britain 1986. The Casualty Report. London: H.M.S.O.; 1987. Frith, W. J.; Harte, D. S. The safety implications of some control changes at urban intersections. Accid. Anal. Prev. l&183-192; 1986.
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and Research Notes
Golias, J. C. Techniques for the control of the regression-to-mean effect in before-and-after accident studies. Technika Chronica, Scientific Journal of the Technical Chamber of Greece, Section A, 8(2):7-30; 1988. Grossman, L. Accident exposure index. Highway Research Board Proceedings, 33:129; 1954. Haight, F. A. Risk, especially risk of traffic accident. Accid. Anal. Prev. 18:359-366; 1986. Hakkert, A. S.; Mahalel, D. Estimating the number of accidents at intersections from a knowledge of the traffic flows on the approaches. Accid. Anal. Prev. 10:69-79; 1978. Hauer, E. On the estimation of the expected number of accidents. Accid. Anal. Prev. 18:1-12; 1986. Hodne, G. A.; Richardson, A. J. A study of intersection accident exposure. Proceedings of the Australian goid Research Board 9(5):151-160; 1578. International Road Federation. World road statistics 1983-1987. Washineton. DC: International Road Federation; 1988. Jergenson, D. W. Multiple regression analysis of the Poisson process. Journal of American Statistical Association 56:235-245; 1961. Leong, W. H. J. Relationship between accidents and traffic volumes at urban intersections. Journal of Australian Road Research Board, 5(3):72-90; 1973. Maycock, G.; Hall, R. D. Accidents at 4-arm roundabouts. TRRL Report LR 1120. Crowthorne, U.K.: Transport and Road Research Laboratory; 1984. McCullagh, P.; Nelder, J. A. General&d linear models; Londqn, U.K.: Chapman and Hall Ltd; 1983. McDonald, J. W. Relation between number of accidents and traffic volume at divided-highway intersections. HRR, Bulletin 74:7-17; 1953. Nelder, J. A.; Wedderburn, R. W. M. Generalized linear models. Journal of Royal Statistical Society A 135:370-384; 1972. Pickering, D.; Hall R. D.; Grimmer, M. Accidents at rural T-junctions. TRRL Report RR 65 1986. Roosmark, P. 0. Traffikolyckor trevagskorsningar Statens Vaginstitut Preliminary Report 22. Stockholm, Sweden: 1966. Smeed, R. J. Variations in the pattern of accident rates in different countries and their causes. Traff. Eng. Control 10(7):364-371; 1968. Surti, V. H. Accident exposure and intersection safety for at-grade, unsignalised intersections. Highway Research Record 286:81-94; 1969. Tanner, J. C. Accidents at rural three-way junctions. Journal of the Institution of Highway Engineers II(ll):5667; 1953. United Nations. Statistics of road traffic accidents in Europe 1984. New York: United Nations; 1985. Ward, H.; England, L.; Murphy, R. S. D.; Moore, R. L. Accident occurence, traffic and road features at urban priority type road junctions. Report to Accident Investigation Division, TRRL, Contract No 842/539. Crowthorne, U.K.: Transport and Road Research Laboratory; 1983. Weber, D. C. Accident rate potential: An application of multiple regression analysis of a Poisson process. Journal of American Statistical Association 66:285-288; 197 1.