TRANSPORT and ROAD RESEARCH LABORATORY. Department of the Environment Department of Transport TRRL LABORATORY REPORT 939

Transcription

1 TRANSPORT and ROAD RESEARCH LABORATORY Department of the Environment Department of Transport TRRL LABORATORY REPORT 939 M DAS: A COMPUTER PROGRAM TO ESTMATE DELAYS AT JUNCTONS by J Burrow Any views expressed in this Report are not necessarily those of the Department of the Environment or of the Department of Transport Traffic Systems Division Traffic Engineering Department Transport and Road Research Laboratory Crowthorne, Berkshire 198 SSN

2 CONTENTS Page Abstract 1. ntroduction 2. Program outline 3. Program components 3.1 Capacity calculations Major/mi.n. or junctions Roundabouts Grade-separated junctions 3.2 Queueing delay 3.3 Geometric delay Examples 4.1 Form of output 4.2 Example 1 : small junction. 4.3 Example 2: grade-separated junction Discussion and summary Acknowledgements References Appendix 1 : The flow group structure in MDAS Appendix 2: Setting up an input fide Appendix 3: Definitions of input parameters Appendix 4: Output from example Appendix 5: Output from example Appendix 6: nput for example Appendix 7: nput for example 2 CROWN COPYRGHT 198 Extracts from the text may be reproduced, except for commercial purposes, provided the source is acknowledged 44

3 Ownership of the Transport Research Laboratory was transferred from the Department of Transport to a subsidiary of the Transport Research Foundation on! st April This report has been reproduced by permission of the Controller of HMSO. Extracts from the text may be reproduced, except for commercial purposes, provided the source is acknowledged.

4 MDAS: A COMPUTER PROGRAM TO ESTMATE DELAYS AT JUNCTONS ABSTRACT The assessment of delays is an important step in deciding which type of junction is the most suitable for handling a given traffic problem. A computer program, MDAS: Method for ntersection Delay ASsessment, has been written to predict delays at junctions. A wide range of junction types from small major/minor junctions and mini-roundabouts to large free-flow interchanges are covered. The program incorporates capacity and delay formulae recentlydeveloped at TRRL. Account may be taken of seasonal and hourly variation in flow level and also of the effect of tidal flows during the peak. The program calculates both the traffic dependent queueing delay and also the geometric delay. The output includes details of the performance of the junction as the flow varies through the year, and problems with particular traffic streams may be identified. 1. NTRODUCTON The assessment of delays is an important step in deciding which type of junction is the most suitable for handling a given traffic problem. A computer program, MDAS: a Method for ntersection Delay ASsessment, has been written to enable these delays to be predicted by means of realistic junction capacity and delay formulae. Up to 2 possible junctions may be treated in one run of the program for comparative purposes. MDAS thus enables the performance-in delay terms of a number of junction types to be quickly assessed under arange of traffic conditions. 2. PROGRAM OUTLNE The program will deal with most of thenon-signalised 3-or 4-arm layouts includedin current Design Standards (with the exception of grade-separated 3-arm layouts). The range thus includes small major/ minor junctions and mini-roundabouts at one extreme, and large free-flow interchanges at the other. Detailed input data are required, describing traffic movements and geometry, but certain basic values are built in for use when site-specific values are not provided. Traffic delays and capacities are calculated from the latest available formulae. A flow chart showing the main elements of the program is given in Figure 1. A Fortran listing is given in reference 1. The program uses a system of flow groups similar to those used in COBA 2. n order to model the variation of flow during the day, the hours of the year are divided into a number of 'flow groups', and the flow in each is expressed as a proportion (often called the multiplier) of the annual average hourly flow. When summed over all flow groups the product of multiplier and duration of flow group should equal the total number of hours in a year. Separate multipliers for light and heavy vehicles may be used. J 1

5 n addition to the flow groups the program takes into account the seasonal variation of flow with the time of year by means of scaling factors applied to the demand flows based on the 'site type' categories defined in reference 3 (ie Urban Commuter, Low Flow, Rural Long Distance and Recreational). The difference between the morning and evening peaks can be taken into account by specifying the degree of tidality. The flow group structure is discussed in more detail in Appendix 1. MDAS warns the user of unsatisfactory junction operation. A warning is printed if the flow/ capacity ratio for any stream exceeds.85 (a figure often used as an 'acceptable' design standard), and a further warning is printed if 1. is exceeded. When large delays are experienced at real junctions it is likely that some changes will occur in the pattern of journeys made (for example re-assignment of trips, redistribution within the network, suppression of demand): no attempt is made to model this explicitly. However, it is indirectly taken into account by entering a maximum delay value. f the calculated delay per vehicle in any traffic stream exceeds this value (usually 5 minutes), a warning is printed. The program continues to run, but delays may optionally be restricted to the maximum value, or allowed to grow without a ceiling. The use of time-dependent queueing relationships 4 ensures that calculated delays never become int~mite (as they can do with the steady state theory commonly used in the past). However in these circumstances the junction layout for which the warning was triggered should be carefully reconsidered. Guidance on the setting up of input files is given in Appendix 2. Details of theinput requirements including definitions and ranges of acceptable values are given in Appendix PROGRAM COMPONENTS The program reads in the annual average daily total flow entering the junction on each arm and uses the turning proportions, the flow group details and the percentage of heavy vehicles to produce the necessary demand flows for use in the capacity and delay routines, tn all cases a pcu value of 2 is assumed forheavy vehicles. These flow calculations are carried out in the main program. Appropriate subroutines are used to calculate the capacity of each junction type (see Section 311) and the traffic delay is then calculated using subroutines described in Section 3.2. Finally geometric delay is calculated using subroutines detailed in Section Capacity calculations Major]minor.junctions. A range of major/minor junctions can be considered. On the minor road(s) at a three-way junction or staggered crossroads either one (shared) lane or two lanes (one for each stream) may be specified. At an unstaggered crossroads, two entry lanes are assumed on each of the minor roads. With a two-lane entry at an unstaggered crossroads, traffic following the straight-ahead movement is assumed to divide between the two lanes, according to the ability of the junction to cope with the right-turning demand (more traffic uses the nearside lane if there is a high probability that the offside lane is blocked by waiting right-turners). The capacity of each non-priority flow is calculated using formulae based on those in SR Certain details of the geometry of the junction are required, these are specified in Appendices 2 and 3. The capacity calculations are performed in subroutine PROR Roundabouts. All types of single island roundabout may be considered. The unified capacity formula given in LR 9426 is used and applies to all at-grade roundabouts. t supersedes the previously separate treatment of conventional 7 and offside-priority 8,9 rou n dabouts. These calculations are performed 2

6 in subroutine CRCLE. nformation about the geometry of the junction, as detailed in Appendices 2 and 3 is required. At a roundabout the capacity of an entry is dependent on the circulating flow which is in turn determined by the flow admitted by the other entries. This interactive nature is taken into account by subroutine CAPENT (a simphfied version of the subroutine in program ARCADy1) Grade-separated junctions. Four basic types of four-arm grade-separated junction can be tested, all with dual 2- or 3-lane roads:- i) Simple diamond; ii) Flyover (or flyunder) with conventional large roundabout; iii) Three-level roundabout; iv) Free-flow layout. Figure 2 shows these layouts schematically. The capacity of the merging areas 11 is calculated in Subroutines MERGE (for three-level and free- flow layouts) or MERGE1 (for two-level layouts). n all cases, it is assumed that merges operate with no traffic dependent delay below capacity 12. Above capacity the delay is calculated according to the techniques detailed in Section 3.2. t is also assumed that the diverges cause no traffic dependent delay. For the atgrade components of these junctions subroutines PROR and CRCLE are used as appropriate for the capacity calculations, and the appropriate input data must be provided: for grade-separated roundabouts a slightly modified form of the capacity formula 6 based on recent public road studies 13 is used. 3.2 Queueing delay The capacities available to the various streams at the junction are calculated from the geometric and flow information as detailed in Section 3.1. The queueing delay is calculated by means of time-dependent queueing theory 4. n order to represent realistically the growth and decay of queues and delays over a peak period a'number of factors are taken into account. n addition to the demand flow and the capacity during the peak, the duration of the peak, the nature of the traffic arrival and service pattern, and the flow and capacity before and after the peak are considered. During the peak flow group(s) subroutine FLOWDY is used to calculate the delay. t takes into account the 'length of the peak' and the adjacent-to-peak flo~vs (the relationship between the delay formulae and the flow group structure is more fully explained in Appendix 1). During the other flow groups subroutine FLODEL is used. A full description of the type of formulae used is given in reference 4. The delay to each traffic stream during each flow group is calculated separately, and summed to give the total annual traffic delay. 3.3 Geometric delay Geometric delay is that delay suffered by each vehicle owing just to the presence of the junction, and occurs even in the absence of other vehicles. The program calculates geometric delay by assuming that vehicles approach the junction at a specified speed, decelerate to a lower speed, travel a specified distance 3

7 at the lower speed, and then accelerate to another specified speed. (These 'approach' and 'departure' speeds are the speeds at a sufficient distance from the junction to be beyond its influence.) The program then calculates the position of the 'entry point', where deceleration starts, and the 'exit point', where acceleration is completed, using built in acceleration and deceleration rates, and the total time taken. t then subtracts the time that would be taken to travel from the entry point to the centre of the junction at the approach speed, and from the centre of the junction to the exit point at the departure speed. n order to model geometric delay at this level of detail, subroutine GEOM is used and it is necessary to provide site-specific input (see Appendices 2 and.3). For at-grade junctions if local values are not available, default values of geometric delay are calculated by means of general formulael4,15, using subroutines MCD1 (major/minor) and MCD2 (roundabouts). For grade-separated junctions detailed input must be supplied. A technique using general formulae will be incorporated later 16. Geometric delay can be a significant part of the total delay especially at roundabouts and grade-separated junctions. n these cases particular care should be taken to provide input as accurately as possible. 4.1 Form of output 4. EXAMPLES Examples of the output from the program are shown in Appendices 4 and 5 which illustrate the range of information given by the program. The input Fries used for these examples are shown in Appendices 6 and 7 (for instructions on setting up input Files Appendices 2 and 3 should be consulted). The individual examples are dealt with in detail in Sections 4.2 and 4.3. The details of the demand flow patterns entered are printed first, followed by the details of each junction considered - these include the junction geometry used for Capacity calculations. The capacity and demand flow/capacity ratio of each relevant traffic stream is output, to aid the identification of particular problems. The program also calculates the delay per unit time during each flow group. This is numerically equivalent to the average queue length and is printed out under the heading 'equivalent queue length'. t is important to remember that this is the average of a broad distribution 4. n order to reproduce this figure by sampling real traffic a large numbei of measurements would be needed. n particular, to compare the output with observations of peak hour delay and queues, frequent sampling during many peaks is necessary. Finally for each junction the total delay in thousands of vehicle-hours per year is printed, along with the separate traffic and geometric delay components. The geometric delay suffered by each vehicle making a particular movement is the same for all flow groups. However, the traffic delay varies with flow level, and details of the junction performance are therefore given for each flow group. 4.2 Example 1: small junction The output from a comparison (for a three-way-junction) between a major/minor priority junction and a mini-roundabout is shown in Appendix 4. The junctions are intended to fit into approximately the same outline. There is a total flow into the junction of 14, veh/day (1 per cent heavy vehicles on each arm). Four thousand veh/day enter on the minor road (Bridge Road). Fifty per cent of the minor road traffic turns left (during all flow groups). No seasonal pattern of flows is used but there is a tidal effect between the morning and evening peaks. Forty per cent of the total peak hour traffic entering on the minor road 4

8 occurs during the morning and 6 per cent during the evening. The COBA 2 flow'groups are used (specified by in the 1 lth line of the input fde (Appendix 6) ) but flow group 4, the peak flow group, is split to represent the tidal effect. The program predicts a total delay of thousands of hours per year at the major/minor junction. This is composed of a traffic delay of thousands of hours per year and geometric delay of thousands of hours per year. The total delay predicted for the roundabout is thousands of hours per year and consists of 6.53 thousands of hours per year traffic delay and thousands of hours per year geometric delay. (For both junctions the geometric delay has been calculated using the general formulae provided in the program rather than site-specific data.) These figures show that the mini-roundabout generates more geometric delay, mainly because it inhibits the straight-ahead major road traffic. However, it is the better choice in terms of overall delay. A closer examination of the results for each flow group shows that this is largely due to the excessive delays suffered by vehicles turning out of the minor road'under the major/minor priority system during the evening peak. The difference in delay (caused by the tidal effect) between the morning and evening peaks (flow groups 4 and 5) is clearly shown by the difference in 'equivalent queue length'. The program calls attention to the unsatisfactory operation during the evening peak (flow group 5) and the symbol (*3) is output indicating that the maximum delay value (input as 3 seconds) has been exceeded, and that the delays have been held at that value. (The symbol (* 1) output in the morning peak (flow group 4) shows that demand has exceeded 85 per cent of capacity.) The substitution of a mini-roundabout for a priority junction in these traffic conditions is thus clearly beneficial, bearing in mind the low cost of conversion. 4.3 Example 2: grade-separated junction This example, shown in Appendix 5, illustrates a comparison between a two-level motorway roundabout and a free-flow interchange. The input fde is shown in Appendix 7. The site is stated to be in a recreational area and seasonal variation is thus taken into account. t will be seen that details of operation are given for each season as well as for each flow group. The program has been supplied by the user with specific flow groups which are printed out again in the output; no tidal effect is specified. At each junction the merges are operating below capacity and cause no traffic delay (Section 3.1.3). This means that there is no traffic delay at the free-flow interchange, which suffers only a geometric delay of 15.9 thousands of hours per year. The roundabout shows a geometric delay of thousands of hours per year in addition to a traffic delay of 4.74 thousands of hours per year. t should be noted that the traffic delay varies considerably with season of the year. For both junctions the geometric delay has been calculated using site-specific data, which would need in practice to be carefully measured. n the case modelled the roundabout is preferable in delay terms and would probably have lower cost as well. However future traffic growth may lead to a sharp rise in traffic delay at the roundabout, while the geometric delay will increase more slowly, and at about the same rate for each junction type. This could be tested by running MDAS again with the l~igher (predicted) flows. 5

9 5. DSCUSSON AND SUMMARY A computer program, MDAS, has been developed which can be used as an aid in choosing the most suitable type of junction for a particular situation. t makes a detailed assessment of the likely delays using the most recently developed capacity and flow/delay formulae. There are, of course, other factors to be considered when deciding on the appropriate layout for a junction: for example safety, environmental effects, pedestrian facilities, driver comfort, and compatibility with neighbouring junctions. However, vehicular delay is the major contributor to user cost, and as such remains a prime determinant of choice. t is therefore important that a method is available for realistic delay appraisal. For simplicity no attempt has been made to incorporate the effects of traffic growth or the discounting of benefits over time 2, but repeated runs of the program could enable both to be taken into account. n addition, for investment appraisal, estimates of construction costs have to be considered. This program is one of three recently developed at TRRL 1,17 and is currently available together with a User Manual 18 through Highway Engineering Computer Branch of the Department of Transport. 6. ACKNOWLEDGEMENTS The work described in this Report was carried out in the Traffic Systems Division (Division Head: Mr G Maycock) of the Traffic Engineering Department of TRRL. 7. REFERENCES 1. BURROW, J. MDAS: a computer program to estimate delays at junctions - a FORTRAN listing. TRRL Working Paper TSN67. Crowthorne, 198 (unpublished). (Available on direct personal request.) 2. DEPARTMENT OF TRANSPORT. COBA - a method of economic appraisal of highway schemes. Economics Highways Division, Department of Transport, BELLAMY, Patricia H. Seasonal variation in traffic flow. Department of the Environment Department of Transport, TRRL Report SR 437. Crowthorne, 1979 (Transport and Road Research Laboratory).. KMBER, R M and Erica M HOLLS. Traffic queues and delays at road junctions. Department of the Environment Department of Transport, TRRL Report LR 99. Crowthorne, 1979 (Transport and Road Research Laboratory).. KMBER, R M and R D COOMBE. The traffic capacity of major/minor priority junctions. Department of the Environment Department of Transport, TRRL Report SR 582. Crowthorne, 198 (Transport and Road Research Laboratory).. KMBER, R M. The traffic capacity of roundabouts. Department of the Environment Department of Transport, TRRL Report LR 942. Crowthorne, 198 (Transport and Road Research Laboratory). 6

10 .. PHLBRCK, M J. n search of a new capacity formula for conventional roundabouts. Department of the Environment Department of Transport, TRRL Report LR 773. Crowthorne, 1977 (Transport and Road Research Laboratory). KMBER, R M and Marie C SEMMENS. A track experiment on the entry capacities of offside priority roundabouts. Department of the Environment Department of Transport, TRRL Report SR 334. Crowthorne, 1977 (Transport and Road Research Laboratory).. GLEN, M G M, S L SUMNER and R M KMBER. The capacity of offside priority roundabout entries. Department of the Environment Department of Transport, TRRL Report SR 436. Crowthorne, 1978 (Transport and Road Research Laboratory). 1. HOLLS, Erica M,'Marie C SEMMENS and Sharon L DENNSS. ARCADY: a computer program to model capacities, queues and delays at roundabouts. Department of the Environment Department of Transport, TRRL Report LR 94. Crowthorne, 198 (Transport and Road Research Laboratory). 11. BURROW, J. The capacity of motorway merges. Department of the Environment, TRRL Report LR 679. Crowthorne, 1976 (Transport and Road Research Laboratory) BURROW, J and N C DUNCAN. Journey time studies at motorway merges. TRRL Working Paper TSN42. Crowthorne, 1977 (unpublished). (Available on direct personal request.) SEMMENS, Marie C. The capacity of some grade-separated roundabout entries. TRRL Working Paper TSN68. Crowthorne, 198 (unpublished). (Available on direct personal request.) 14. McDONALD, M and D J ARMTAGE. Geometric delay at priority junctions. Technical Report. Transportation Research Group, Department of Civil Engineering, University of Southampton, McDONALD, M and C NOON. Geometric delay at roundabouts. Technical Report. Transportation Research Group, Department of Civil Engineering, University of Southampton, McDONALD, M and N B HOUNSELL. Geometric delay at motorway junctions. Working Paper. Transportation Research Group, Department of Civil Engineering, University of Southampton, (unpublished). 17. SEMMENS, Marie C. PCADY: a computer program to model capacities, queues and delays at major/minor junctions. Department of the Environment Department of Transport, TRRL Report LR 941. Crowthome, 198 (Transport and Road Research Laboratory). 18. DEPARTMENT OF TRANSPORT. MDAS User Manual. London, 198 (HECB/Department of Transport). 19. DEPARTMENT OF THE ENVRONMENT. Technical Memorandum on the design of major/minor priority junctions. Technical Memorandum H11/76. London, 1976 (Department of the Environment). 7

11 MAN PROGRAM t Enter general traffic data Subroutine PROR ~metric Subroutine MCD1 No l Yes Subroutine GEOM J t 11 ~u~rou~ine Subroutine MCD2 4 Sobro~ne Subroutine ~ i GEOM J =l Subroutine GEOM separated i u~u~-i n? Yes diamond Subroutine PROR Subroutine MERGE1 STOP Roundabou Subroutine CRCLE 2-level 3-level Subroutine CAPENT " [ Subroutine MERGE Free-flow interchange Fig. 1 SCHEMATC FLOW CHART (detailed logic depends on program structure - see text)

12 J, (a) SMPLE DAMOND (b) TWO-LEVEL ROUNDABOUT (C) THREE-LEVEL ROUNDABOUT (d) FREE-FLOW NTERCHANGE Fig. 2 EXAMPLES OF TYPES OF GRADE-SEPARATED JUNCTONS (Not to scale)

13 Arm C Major road Arm A Major road r Arm B Minor road (a) THREE-WAY JUNCTON Arm D Minor road Arm C Major road Arm A Major road Arm B Minor road (b) FOUR-WAY JUNCTON Fig. 3 ARM LABELLNG CONVENTON

14 8. APPENDX 1 THE FLOW GROUP STRUCTURE N MDAS At any junction the level of flow will vary continuously throughout the year. t is clearly impractical to try and model this variation at too fine a level of detail: it is however unsatisfactory simply to take the overall average flow (since flow and delay are not linearly related). MDAS models this variation by splitting the annual flow into (up to 7) groups of hourly flows. (This is the equivalent of producing a frequency histogram of ranges of hourly flow.) During each of these flow groups the hourly flow is assumed to be a constant proportion (the multiplier) of the annual average hourly flow. Low definition time-dependent queueing theory 4 is used in subroutine FLOWDY to estimate peak hour delays. This requires that the adjacent-to-peak flows are taken into account. n all cases in MDAS it is assumed that the adjacent-to-peak flows correspond to those occurring in the flow group with the second-to-highest flow group multiplier. t is thus assumed that peaks are caused by a reasonably steady build-up of traffic rather than a sharp discontinuity. n addition to the basic flow groups outlined above two further sub-divisions may be made. n many cases the level of total flow into a junction may be the same for all peaks, but a marked difference between morning and evening peaks may be observed for particular turning movements. This tidality may be modelled in MDAS by dividing the peak hour flow group into two groups of equal duration and applying a further multiplying factor for each movement. (For each movement, other than U-turns, the user specifies what proportion of the average of morning and evening peak hour flow occurs in the morning peak.) A further division occurs if the user chooses to specify a seasonal variation. n this case each flow group is split into four sub-divisions in order to represent the variation of flow level with season of the year. The same seasonal scaling factors are applied to each flow group and the relationship between peak and adjacent-to-peak flow groups outlined above is retained. 11

15 9. APPENDX 2 SETTNG UP AN NPUT FLE The input may be considered as a series of blocks some of whichmay be repeated as many times as required and others omitted. The blocks, when present, must appear in order as specified here. A more detailed description of the parameters and their ranges of acceptable values is given in Appendix 3. The use of default values is also covered more fully in Appendix 3. t KEY to variable types A - Alphanumeric characters, left justified - ntegers (only), right justified in fields of 1 /R - ntegers or reals, right justified in fields of 1 BLOCK A - General NAME TVPEt First line Next NA lines Title Date Number of arms Names of arms Annual average daily flow into junction for each arm TLE DATE NA NAMES DQ A A A /R Average percentage heavy vehicles in flow for each arm PH /R 'Approach' speed for light vehicles for each arm V /R 'Departure' speed for light vehicles for each arm V /R BLOCK B - Flow group information First line Number of flow groups (if N =, N is reset to 4 and COBA flow groups are used: next input requirements are in block C) Multiplier for light vehicles for each flow group Duration of each flow group YES or NO (if NO then flow group multipliers for heavy vehicles are same as light vehicles and next input is from block C) Multipliers for heavy vehicles for each flow group N GROUPL GROUP JOPT GROUPH /R /R A /R 12

16 BLOCK C - Turning proportions NAME First line Next N-1 lines Next N-1 lines YES or NO (if YES turning proportions for light vehicles are the same in all flow groups, if NO turning proportions are not the same for all flow groups) Turning proportions for light vehicles during flow group 1 (if YES in previous line then next N-1 lines are omitted) Turning proportions for light vehicles during flow groups 2 to N YES or NO (if NO then turning proportions for heavy vehicles are the same as for light vehicles, and next input is from block D) YES or NO (if YES then turning proportions for heavy vehicles are the same for all flow groups,if NO turning proportions are not the same for all flow groups) Turning proportions for heavy vehicles during flow group 1 (if YES in the previous line then next N-1 lines are omitted) Turning proportions for heavy vehicles during flow groups 2 to N JOPT QV QV JOPT JOPT QP QP A /R /R A A /R /R BLOCK D - Seasonal and tidal peaking effects First line Next NA lines Seasonal flow type (see reference 3) YES or NO (if NO, next NA lines are omitted) Tidal peaking factor for each movement (excluding U-turns) Peak length Maximum acceptable delay value YES or NO (if YES delay is used as a cut-off value, otherwise just as a warning) PAT JOPT PK PKL DMAX JOPT A /R A 13

17 BLOCK E - Major/minor junctions NAME TYPE y First line YES or NO (if NO then no (more) major/minor junctions are to be considered - next input from block F. f YES and NA = 3 next line is omitted) nteger to indicate junction type Geometry of major road Geometry for non-priority movements (if NA = 4 then this line is repeated) YES or NO (if YES detailed calculations of geometric delay will be made, next input from block J, if NO then general formulae will be used and next input is from block M) JOPT JTYPE WW WCR W(3) VR(3) VL VR(1) w(1) w(2) JOPT A /R /R /R /R /R /R /R /R A BLOCK F - Roundabouts First line Next NA lines YES or NO (if NO then no (more) roundabouts are to be considered. f NA = 4 next input is from block G, if NA = 3 no further input is required) For each arm the geometric parameters needed for capacity calculations YES or NO (if YES detailed calculations of geometric delay will be made, next input from block K, if NO then general formulae will be used and next input is from the start of this block) JOPT V E ELF R D PH JOPT A /R /R /R /R /R /R A BLOCK G - Grade-separated junctions First line 14 YES or NO (if NO then no (more) grade-separated junctions to be considered. No further input is required) Number of lanes on main carriageway nteger to indicate junction type (if 7 next input from block H if 8 or 9 next input from block if 1 next input from block L) JOPT LANE JTYPE A

18 BLOCK H - Diamond junctions NAME TYPE t First line Next 2 lines Geometry for main carriageway (the 'main' carriageway in this case comprises arms B and D) Geometry for each slip road WW WCR w(3) VR(3) VL VR(1) W(1) W(2) /R /R ir /R /R /R /R /R (next input from block L) BLOCK - Grade-separated roundabouts NA lines For each entry the geometric parameters (next input from block L) V E ELF R D PH /R /R /R /R /R /R BLOCK J - Detailed geometric delay at major/minor junctions First line Next NA-1 lines Next NA-1 lines Next NA-1 lines Speed through the junction for light vehicles for each movement from arm A As in previous line for remaining arms Distance travelled through the junction for each movement from arm A As in previous line for remaining arms Excess distance travelled due to the presence of the junction for each movement from arm A As in previous line for remaining arms (next input from block E) VJ VJ D D E E /R /R /R /R /R /R BLOCK K - Detailed geometric delay for roundabouts As for block J but return to block F for next input BLOCK L- Detailed geometric delay at grade-separated junctions As for block J but return to block G for next input BLOCK M - Geometric delay at major/minor junctions by general formulae First line YES or NO JOPT (if YES junction meets visibility standards of H11/7619) (next input from block E) A, 15

19 1. APPENDX3 DEFNTONS OF NPUT PARAMETERS The input is arranged in a series of blocks as described in Appendix 2. The input variables are defined here in the order they appear in Appendix 2 and any restrictions on acceptable values are noted. The variable JOPT is used on a number of occasions to allow the user to specify a choice between available options. These choices are indicated as they occur in Appendix 2 and are thus omitted here. The only acceptable values for JOPT are YES or NO. A diagram showing the arm labelling conventions is shown in Figure 3 ; the program treats the arms in alphabetical order. n all cases characteristics such as turning movements must be specified in clockwise order (ie left-turn, straight, right-turn, U-turn) for each arm. BLOCK A - General RESTRCTONS TLE DATE NA NAMES Array containing title for run Array containing date Number of arms Array containing a distinguishing name for each arm (in order as in Figure 3) Up to 6 characters Up to 2 characters 3 or 4 only DQ Array containing annual average daily flows in Non-negative veh/day into the junction for each arm PH V Array containing the average percentage heavy vehicles on each arm Array containing 'approach' and 'departure' speed for each arm in km/h (see Section 3.3) Up to 6 characters for each arm Non-negative Not greater than 1 Non-negative BLOCK B - Flow group information N The number of flow groups nteger to 7 (if N = then N is reset to 4 and COBA flow groups are used) GROUPL Array containing flow group multipliers for light vehicles. These specify the proportion of the average hourly flow of light vehicles occurring during each flow group Non-negative in ascending order see also note* GROUP Array containing duration of each flow group Non-negative in hours see also note* GROUPH Array containing flow group multipliers for Non-negative heavy vehicles in ascending order (see GROUPL above) see also note* * Note - The sum over all flow groups of the product of multiplier and duration should equal the number of hours in a year. The sum of the durations should also equal the number of hours in a year. This is normally taken as 876 but to allow for the use of 8766 hours ( days) a tolerance of hours is allowed. BLOCK C - Turning proportions QV QP 16 Array containing turning proportions for light vehicles Array containing turning proportions for heavy vehicles Non-negative for each arm the sum over all movements must be 1. As for QV above

20 BLOCK D - Seasonal and tidal peaking effects PAT ndicates seasonal flow type 3 - no seasonal effect 1 - Urbad commuter 2 - Low flow non-recreational rural 3 - Rural long distance 4 - Recreational PK PKL' DMAX Array containing the tidal peaking factors. These specify for each movement (excluding U-turns). the percentage of the average peakhour flow which occurs during the am peak ndicates the length of the peak 1 - short peak (half-hour) 2 - average peak (one hour) 3 - long peak (two hours) This is used in queueing formulae Maximum acceptable delay value in seconds. A technique to indirectly allow for the effects of re-assignment etc (see Section 2) RESTRCTONS nteger to 4 Non-negative Not greater than 1 nteger 1,2 or 3 if integer outside this range is used, then it is reset to 2 Non-negative BLOCK E - Major/minor junctions JTYPE WW WCR W(3) VR(3) VL VR(1) W(1) W(2) ndicates junction type at 4-way 2 - crossroads 3 - right-left staggered 4 - left-right staggered The full major road width in metres excluding any central reserve either by kerbed or ghost islands The width in metres of any central reserve by kerbed islands The avaiiable lane width in metres for right-turning major road traffic The visibility in metres for right-turning major road traffic The visibility to the left for minor road traffic in metres The visibility to the right for minor road traffic. in metres The available lane width in metres for left-turning traffic from minor road The available lane width in metres for right-turning traffic from the minor road (if W(2) is omitted (ie put equal to ) then all traffic is assumed to use the 'left' lane, W(1)) nteger 2, 3 or 4 Not less than 6.5 Not greater than 2 Non-negative Not greater than 1 Not less than 2.2 Not greater than 5. Non-negative Not greater than 25 Non-negative Not greater than 25 Non-negative Not greater than 25 Not less than 2.2 Not greater than 5. Not less than 2.2 Not greater than 5. n this case is acceptable A more detailed definition of these terms is given in reference 5. f the geometric parameters entered are outside the specified range they are reset to the nearest value within the range and an appropriate message given in the output. \ 17

21 BLOCK F - Roundabouts RESTRCTONS V E ELF R D PH The-approach half width in metres The entry width in metres The length over which the flare is developed in metres The entry radius in metres The local value of the inscribed circle diameter in metres A representation of the angle of conflict between entry and circulating flow in degrees. Not less than 2. Not more than 12 Not less than 3. Not more than 16 Also E must not be less than V Not less than 1. f V = E, then ELF is irrelevant Not less than 3. Not less than 13. Non-negative Not more than 8 A more detailed deffmition of these terms is given in reference 6. f the geometric parameters are outside the specified range they are reset to the nearest value within the range and an appropriate message given in the output. BLOCK G - Grade-separated junctions LANE Number of lanes on the major road 2 or 3 only JTYPE ndicates junction type nteger 7, 8, 9, simple diamond 8 - two-level roundabout 9 - three-level roundabout 1 - free-flow interchange BLOCK H -Diamond junctions For each major/minor junction at the end of the slip.roads the geometric parameters are as defined in block E. t should be noted that in this case arms B and D have priority and are considered as the 'major' road. BLOCK - Grade-separated roundabouts For each arm the geometric parameters are as defined in block F. Where appropriate the straight-ahead traffic is assumed to pass through the junction without using the roundabout. BLOCKS J, K, L - Detailed geometric delay (see also Section 3..3) VJ D E Array containing speed in km/h of light vehicles as they negotiate the junction for each movement Array containing the distance travelled at speed VJ in metres Array containing the 'extra' distance travelled due to the junction in metres. This represents the difference in distance between travelling through the junction and travelling to the mid-point of the junction and out again Non-negative Non-negative f VJ = then the corresponding D must also be Can take any value including negative BLOCK M - Geometric delay at major/minor junctions by general formulae The only input is a value for JOPT to state whether or not the junction meets the Department visibility standards as laid out in H 11/

22 11. APPENDX 4 OUTPUT FROM EXAMPLE 1 -- = M~ ' ~ N ~ ~2 o $~ggg LD g % c ~ C ' ~.<: ;~gggg~ C, M ~ ~x C ~, l-- ~ C -- C~ ~" e~ gt D ~ _ O O C L"d M'~ ~f*,,m F- w ~ C O ~.~(D-- C ~ -.- u.j ~ C~C; gx~ =&g& ~D i l l ~J u.11 O l " -- l ~ D w ~ O Q O O ~ 19

23 , U g c- ~o c? t~3 i-- c c. * g ~,< ill l- M ~ c c < tg~. cu~,o ~ O o c, < -OU%C~ <~K W = C C < > :r~ < - ~ O U % ~ < (n UC. C O,OU%C < :r -4" C -4" ,, '-* ~ O < ~ o :> ~ o o o.< %- < &u -*~l o :~ -4"-4" :r< < C C O OU%,O Q~: O < ~-*c o o -4) *% < :r -4"-4-.,-:,~ o~ o < OU%,O < U C C C D U'. _-.r ~ C ; O C < > -.T C> -~ '<~- m ~ -J C~ C l-- ~n.,w Q. n- t9 n- t9, ~ m u Q. -.~ ~9 tv t~- i'~,' i~: )C: 2

24 ! ~-.,-- ~-*, g O~ l-- t~ )- ~. C. un F- <~F-- C ~C' C'C' J ~ ~ C ~ ~ O ~ o e l ~ o ~g~g ~ e e a -2 u. q.~ C.,O~DO < -- ~ 4 C f%l (.9_~- ~ -J<. ~ C ~ C < ~ ' :r ~c --,-* D ~ l o O >,lj < ", ~,< ~ X O Q 5- ~- -r 21

25 !! C " >'- u'~ g g '-'";%% :E-. '~ i'~. of* i.u :> o,,,, (/) '=~ ::,P- ~ T- :> LL/ :~: l--- ~.-- :: ~:.,=- ~ C' 3 ~r- _~.. O ~. ~ ~-.- r,.. ~ c ~ N <E~ T- %.- s p.- F.- C. --- '- _J O. e~ U4 L~ w :C ndi r~.,;, ~ ~ou "~" -~'~-~ ~ i~ ~Y Jv 22

26 !! ~"* *" ~ o~, ~, g o,. F.- " -- >- o C J, o ~O :~ D:: ~, ".- r" O O.../ ~.i..!-- ee, tm ~ N ~.~ ~- r..- o r,.. ~.~,- ~. ~K e.. M-, O O O M. o F-.,.t O --s O u. O O..P :E O ::E" '~" =E~ t~. ~,,C t 23

27 o! ~ ~ 7 u ~ g O ---- m m o o O _-,r c~: i~: ~- o ~.% H a~ -- l- ~ ct~ H i.- v- l i o n.-4~ n~ "~4~ 4~ w M-J Y e~.l( u. ~ ct~ H ~ P..q t,~.,j 4~ ~,.4 ~.,e x n,'u) O w ua4~ ::.1~.-4~! w t u ~ i _ae., X.- 4K 24

28 m Q~ C. O" U, -- e a,..~_ ~ u,.i t,~',~ O- --m t.,u ~ c > r,.u u,j~ e.j o o ~l~ C~ - O u OC ~ O.J O C u F-- l,-- g < t,.m.l ~ < ~, h- ~ U U v C) J- ~ v (y) > O ~ C A _= g.,~p %1 qr- v LJ ",- ~_ " T f~ 25

29 ~2!,'..- ",,-,,,-,,,-,, ~, M o g ~ ~ Q C v % o ~ > ~- Ow ~ ~ g~ ~ O. C'> J J C r, o u ~ u v ~ ~ ~ v 26

30 !! ~ w LJ )-.-.,i. >- u'~..) pj vh ~ ~ T- f*u C to.- L.~,c~ v u.~ --._l ~ Lu -- u ~ -- O, l- O -- 27

31 =[ r, ~C C) t5 l '~,,,",,-,,-,, ~, ~,~.7 O, ~ p ~ t',. t t ~ O O C --J U'~ C" L ~. L~ -J O U~ ~ v ~ ~,!! >-.. iv~, Q~ -- U 11- uj uj --.~ o. n.~ uj <:O- O~:ul F-.l~ :~ 't "~ ",*..! ~'~ c,..-,! u) s.~ O - Q~ ~3 := ~ r,-,o ~- ~=. J..f x.m ~.~.--.1~.-. '~ o.-. - ". "~- o. ~ uj tu uj 28

32 t ~ o:, ~ W o r,~ ~..~ ~ (~ l~-.j Lu,,~.,..i"(~ ~[~._. c --b C e e o ~ -- >- (.) 1d < (~4 ',- ~3 U ~,"),,:"(',J..J C..f OCC~ "~. r%j..4r- N O ~ o c m--lf 14. Cb o. l'-- (.b g --,.i.. O.- u. u v ~g O O.J 1,1. (,.~p v i~1.o ~ r ~ C ~ O A < g ~ v ~ v w U ~.'P l'-').<',,~o..u F--"F-- LU.U, A 29

33 Q~! l t Qc o ~ >... > i i m ~ m ~ a - = &&&.L.J. g --, = _~ -- ~ ~. ~ * < _~ ~ O A x W ~.3

34 o F.- o,1 c, L ~,o" r ~,~. v-- 3 F- ~OW'- o F- v U w ~_ ~ o m N Q 31

35 12. APPENDX 5 OUTPUT FROM EXAMPLE 2 t,el: l,~ O~-,M ~-.*,-.,~-,t-eo J ~L~ ~" G') ~ -- l-i g ~r L~ t.u ~.4T-eO,r.-eO... ~.-- qrcn C u ~ ~;JgJg u. F- -'~.~-O o C >- u n "t cn.t U ~ 4~ -J 4~ -~.t C).1~ U.~ t~ '~d.~ ~"~ ~ C: >- - v J _-9 4~,,,,it - -~ J4~ L~ -2 l-- C> ~'- t 'l M~! -J.t ~.~.t ). 4~.t C~4c 4~,..~ UJ~-- M -- 3 O l~... ~t l.rl...t ~g--& ~ '~ m ~- m P.- ' 9 LJ..~2~ --3 M!! -.J ~ t,.j ~.J F-- G9 v M3 a. ~.J..f._ M. U.,~ ~ J ~L JJ" "t 32

36 O,.,. ~ O m ~-.,-~*-* ~ *-.*-* ~t C> -- C':.~,...t ~D ~- C G. ~ ~ ~ ~ J * e < F- ~ C ' C O O O C O ~ e m e O ~ m l O ~ ~ l o l l t~.)c~ < - ~ ~ l-- mm M ~ m...~e l e o e UO :: ~E < ~ O Q O ~ ~2 " <! o. ~ a l l a ~ -- ~ m i o ~ O C O < -- N r.- < o * * D F--! t~ Q. --!

37 ~K n. o o iv o,n : r e-e ~-e e-e n~ "-',-" '-' t u C) C < C C ~-, -f-.~,-* 25 m. ~ O C O C ~ e e l e ~.. _-2 < f~.u ~, LU --!-- -'- "~" ~"" ~"" ~ e:( -s- O W ~ -"r",~ < e~,r- ~" ~ C~ ~ i,l,j X ~ UU,~ n. n. n, C) n,,. < ~ ~- t~ tv n~ 34

38 7 u e,,- w -- -t-.. ~,- U u a o D e ~ ~, ~ l e o e C, m s e m g!' f~ :::) /) :~:..1-.u v -- e e o c ~. ~ ~ o e m,ec,,. ir~ i.l~ t%t Ln. "'! C) X l/~ (,,~ (/) i..e -t i-~.,.e,~ ~t,~ u ~, >- oo r r~ ::~ -J u. C C! ~ u ~ u.i r. 35

39 ~T e ~ i C.7. C o e e e ~. ~ "~ O(~ 'T- O "'- ~ CO, g 2~ G C. ~;.-m o e o e ~-o ~ ~O C OO T- ~=gggg LUcY,~=.. v'- ~l e e e e J U.l ~ m v -- O -- ~ ~ x ~, r,- l,u.9 e~.- ~ m u ~ ~ 36

40 :E r, Xggg a~ ~2 t,-,,-,,-,! cc o: L~ ~ m ~ m m C~ o ~ ~Ngggg ~2 ~ o o ~ u ~ o o o O.q )- 9 O (D CD '-- m..,o -.g i.-, >- -- r-, -- e,, e~ o 142, u~ d~.. ~ G') ~.9 A~.. %1 ~. ~ ~ ~ O~ w - Lu! cn "-" tu t~ ~ ~ o o o o O ~... ~. '-4 X um i o,-,! -- l ---l--- J41&t l~ J4 37

41 "".., C L~,- ~ ) f i l l ~.~ U-t C.. ~ > -,..~ogj,- --..,&&jg ~ ) i l l UJ C: F- ".~ ~ v ~" >- C.~ C,-O-, o J&&& t C::- c, c> c~ c~ o ggg& o J &J&& (:D u ~ C ~ A t.m ~.,~,, (/) ~- C.J ~ v v,~. u v -q ', e,~ j O A,'~.,h O=,_t*,* A,'T" ~'~" _.1 e,- la. "P" ~ r,.,} T- ~'--.~ ~'- ~-- L.J,.,~a. X ~ ~ O.l U~.U >=- :1,- ).- >- t.v- X ~.- 1~.- l= J.&ll Ji. Wj

42 . =3 r~ +e.,, l e+,, n.,, l ~.~ ~C C3 - ~,~ D~ 2+ C r. ----, ~ --. C~,~- O T=- ~ ~ ~ ) l -t J LU,="- ~,-- ~ -.., P.= C C. ~ C ~ C" C.- W3 "7- v uj tu "' Cr O ~ (/3 D,.,~,O,r- ~O eo ~.~,W~ V3, N ~,.=. u r'-('~~-~ -- -J -..t o J &&&& r. r~ DC ~. ~..,,~r~. ~a,;.uo J &.~ U ~ ~ v ~ v n,+" l, nj,o ~ +"+"~" ll =+ gr) f ') Orb(l) "~ Ll ~'~..",+ C ~ C ~ U~.-~ ~ v ~ ~ O ~ u ~,M W,Ll ~ ~ 39

43 ~ ~ i f.~ E ~" " t r. --'- ~ ---- 't,,~ uu~ -.t ~.,..t ~ ~t o.i ~g~gg s l e u.~ O ~ O ~ >-. - "-~ o &~g& o o e l O C U o.,- N N "' O ~ CO ~r~ &g&,g U ~ o gggg '- 12. Jr-,," --!-- /) ~,,. ~.UO J U v ~ U ~ ~ v ~ v M tl'~,/) i...e. ~ ~ ~ ~ ~ O A O ~ X ~ ~ U N ~ N ~ ~ O ~ ~'~ v- r-!~ v U ~ O" ~. ~ ~ 4 ~ ~ " 14W &ll ~l,~

44 ~ ~r E r~ u i ~! C Q c e(:, r. c -- ~: -, )- C - o." "' c.. c,~ ~" C. ~"! C. c, O- C" ".-. ~ C. u,,!" c L ~, l- '~,~C -J g ~!-.---l--,al: w C~ '~, ~ ", r/) ~#'~ ii/) f,o :: ['- v :,- f uc.. uj "" --J,cC,,~ uj --.u -- la.. uj i,~! X --! -- 41

45 e~ --, :E e,.. e,- n-" ~.,,,..,,,-.,,,"', C, l,y C: i-" c" c~ Ua ~-~ C ~.- "" "--,! 1 C C ~ C ~ C~ G " l C! ~ eo '~. ~ --.J X ~ F- F- -- ~D U r'~ w~ r...~.k u,.l~ ~ M~ uj.l~ U "-- --.U 11 u. :C F- 1 m: -- "" >- --a "' l C:~ '~C [ --l '- 1 '- >- )-.-.- ~ E. l.u l.- n,. tl ~ U, -~" m ~F U.l l.j 42

46 13. APPENDX 6 NPUT FOR EXAMPLE C>C~O,O,O ~-- ~'% 12"~ 12", M% ~- ~--,r- C C" Lr'. C~ C~ C: C' J 222 r- w- C C. C~ C_ C" C'- "~ C C' C: C C C C~ C'~ U'.,., f~j w'- &f', w'- f', w-- C -- < ~ C C C - l.r~ -.. C.C ~ - ~. C" ~":, C: C~ <T C~(t. L".<t,O f'g %..- C.,/3 C JJ~ cn -- t.~ ooc. ~ U.,Y (r fj) C' CC, CCC,Ll (~C ~, ~D~ OCC(%JC ll$% L%,,C~,.,,~"."- C:" a.,,o C D o m ~-...} O,--~ ( ~ --,-' ~D (,9 X ~ {#'~ ~ :t ~ O till )- ~ >- C ~ O ~ O ~ ~ C ~ O C O ~ O ~ C O ~ C, C C ~ O ~ C O C C O ~ O C ' ~ C ' ~ O ~ O O C ~ C O O ~ C C - C ~ O O O O O O O C O C ~ C C C C ~ C O C ~ O O O COC. O C O ~ C O O C C O ~ O C C O O C C O C ' C C C ' C O O O O O O O O ~ O O ~ O O O O O O O ~ O O O O O O O O C ' O ~ O ~ O O O O C O O O O O O O ~ O O O O O O O O C O O O O C O O O O O ~ O O ~ C O O 43

47 14. APPENDX 7 NPUT FOR EXAMPLE 2 o c o c, ~ Ù o c. C C C, C'~d~. ~', &r, u",o OC OOC~-C 7 U CC. O ~ C'O L,% t ~ t.~ ~-, OOC. C C. O ~-- -.t -4" -4" -.t -.t ~t -4' -4" ~-- l~'3 ~- ~3 C. tr' 1.3 ~, i..3 i~3.d f~ ~ %1 ~ -,o o,o o.,~o w,c.,~o u~o c o o o oc. c " " * - - ~- -4".'- -4" 12% ~ l"% ~ O ~ C O "" ~ ~ o o o o ~! xo O O k~ O O Lu uu )=" ~ :)" :,- O O C O O C O C ' O O O O O O O C C, C C C O C. C~ C- O O C. O C, C~O C O O O O C. O O O C O O C-O (D ~--. O C, O OC, C. C~ O O O goooogocggoogoo~ oo~oooogooc oog, ooooooooo=o o= ooooocoo2ggoc ooooo ~ O C O CC, O C O C O C O C ' O C OCC, CO O C C' C' C C.C. C C' C, C" C, C ~ C-O,O C.O 44 (737) Dd ,5 5/8 HPLtdSo'ton G191S PRNTED N ENGLAND

48 ABST R ACT MDAS: a computer program to estimate delays at junctions: J BURROW: Department of the Environment Department of Transport, TRRL Laboratory Report 939: Crowthorne, 198 (Transport and Road Research Laboratory). The assessment of delays is an important step in deciding which type of junction is the most suitable for handling a given traffic problem. A computer program, MDAS: Method for ntersection Delay ASsessment, has been written to predict delays at junctions. A wide range of junction types from small major/minor junctions and mini-roundabouts to large free-flow interchanges are covered. The program incorporates capacity and delay formulae recently developed at TRRL. Account may be taken of seasonal and hourly variation in flow level and also of the effect of tidal flows during the peak. The program calculates both the traffic dependent queueing delay and also the geometric delay. The output includes details of the performance of the junction as the flow varies through the year, and problems with particular traffic streams may be identified. SSN ABSTRACT MDAS: a computer program to estimate delays at junctions: J BURROW: Department of the Environment Department of Transport, TRRL Laboratory Report 939: Crowthorne, 198 (Transport and Road Research Laboratory). The assessment of delays is an important step in deciding which type of junction is the most suitable for handling a given traffic problem. A computer program, MDAS: Method for ntersection Delay ASsessment, has been written to predict delays at junctions. A wide range of junction types from small major/minor junctions and mini-roundabouts to large free-flow interchanges are covered. The program incorporates capacity and delay formulae recently developed at TRRL. Account may be taken of seasonal and hourly variation in flow level an.d also of the effect of tidal flows during the peak. The program calculates both the traffic dependent queueing delay and also the geometric delay. The output includes details of the performance of the junction as the flow varies through the year, and problems with particular traffic streams may be identified. SSN