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C TRANSPORT RESEARCH LABORATORY TITLE by Analysis of the effect of bus size on route performance S Vijayakurnar and G Jacobs Overseas Centre Transport Research Laboratory Crowthorne Berkshire Uni~ted Kingdom PA 1244/90 VIJAYAKUMAR, S AND G D JACOBS (1 990). Analysis of the effect of bus size on route performance. In: Traffic Engineering and Control, 31 (12), 644-648, 653 DRIVE and DRIVE 2 A joint 1 EG/ILE mceting was, field in Lon- don early last month to discuss the benefits of U.K. involvcment in the EC's DRIVE re- search programmc, now a full two ycars into its thrce-year coursc, and the opportunities for participation iniits successor, DRIVE 2. Kcit h Keen from the programme's Brus- scls officc first described thc structure and aims of DRIVE, to be achicvcd by the devel- opmcnt of a common Europcan environment of better-informed drivers who interact with the road infrasiructure. The 71 projects in the programme are divided into four groups - general approach and modelling; be- havioural aspects and traffic safety, traffic control, and services, communications and databases- each carried out by an interna- tional consortium made up of universities, consultancies, industrial companies and gov- ernment agencies. The consortia meet four timecs a year, with SECFO, the System Engi- ncering and Consensus Formation Office, having the r6le of bringing together all the technical outputs and producing a consensus onl the promotion of such technologies to out- side organisations (users, industry and stan- dards bodies). Ian Calling then highlighted the level of U.K. participation in DRIVE, with 41 U.K. organisations involved -- bettered only by Germany, with 43 - and the U.K. being prime contractor (consortium leader) in 19 of the 71 projects, more than any other member state. 1 hese latter projects cover areas sueh as aceident analysis and prevention; incident deteetion and congestion management; tech- nological developments such as cellular radio, digital maps and that required for road pricing; the human response; urban mod- elling, and pollution. Breaking down the U.K. involvement by type of organisation, it was seen that the major contri butors were universities (13) anidconsultancies (10), withi only eight from industry. This was contrasted with Germany and France, with a similar total number of contributors but an industrial involvement Which was nearly twice as hich as that of the U.K. In particular, neither the automotive industry, nor the electronics and supply industry have any U.K. representa- tion in DRIVE. Looking to the advantages and costs of in- volvenient in DRIVE, Mr Cathing identified two key issues. Firstly, the potential for coni- miercial exploitation of the research work, to- wards which many, of the projects haive been wvorking. There are, however, a number of projects- particularly in the general mod- elling and behavioural safety groups where the commercial gain is less easy to identify, and( these tend to be projects where university participation i's the greatest. Sec- ondly, financin gdepends on the type of insti- tution, with aeademic research institutes re- ceiving 100 per cent of their marginal costs (that is, the full cost of recruiting staff specif- ically for DRIVE, but not the cost of any per- manent staff), whereas industrial participants receive 50 per cent of total costs. This may have been a major reason for the reluctance of the larger British companies to get in- volved - although the initial signs are that a number of new industrial partners are emerg- ing across Europe for DRIVE 2. It was seen as a major advantage that partners own the intellectual property rights for their researeh, but two speakers commented on the diffi- culty of obtaining participation from U.K. in- dustry in DRIZVE projects. Confinued on page 660 Analysis of the effect of bus size on route performance by S. Vijayakumar * and by G. Jacobs, Transport and Road Research Laboratory I. INTRODUCTION The Bus Route Simulation Model was devel- oped by Vijayakumnar tat Imperial College, London, atid the Overseas Unit of the Trans- port and Road Research Laboratory. The model can replicate a complete day's opera- tions of a specified bus route. Using informa- tion which describes the characteristics of the route, the buses onl the route and the pas- senlgers using the route, the model can be used to determine various performance char- acteristies of that bus route system, as well as the eosts of operating the route. This paper outlines the structure of the model, its data needs and its capabilities, and also describes some examples of its use to examine the performance of a bus route and the implications of changes in hiis operating policies whcn the route is serviced by 'ehi- cles of varying size. This analysis is partly extended to two other routes to see to what extent specific conclusions for one route can be applied to others. The sensitivities of sonic of the model assumptions are also criti- cally examined. The purpose of this paper is not to provide definitive guidelines onl route operations, but to denionstrate the capability of the model and areas for future applica- tions. Route information from the Delhi T1ransport Corporation has been used to test and validate the model. The simulation model is structured such that movement of every bus from stop to stop along a route can be represented. The impor- tant model components (such as passenger boardings and alightings, bus running times, etc.) can only be defined at bus-stop level, and thus monitoring of bus performance is most easily undertaken at the same level. The primary objective of the model is to describe the level of service provided by a 'h fits pa per describes some of t he work undertak- en bv Dr Vijayakumar for his doctoral dissertation at Imperial Collcege, London- specified vehicle fleet of giveii operational characteristics running over a single route subject to a fixed travel demaitd, albeit vary- ing over the timec of the day. Inl order to (Ic scribe the level of serx'ice and thc associated cost of providing it, the main outputs from the simulation model are: -total route operating costs, -total travel times of passengers using the route: and -total wait timies of passengers using the route. lo provide these outputs the niodel therefore needs to accumulate information onl wait time, in-vehlicle time and total operated bus kilometrage. In order to accuntulate the niec- essary information the model scans the ,ictiv- ities of both passengers and boses et ach bius-stop during each second (or other sjieci lied time unit) of the simulation. Thie niodel therefore has to be capable of- representing both the arrival of passengers and of- buses at stops, as well as the subsequent departure iif those passengers whether they hoard the tnext bus or one of those following. A passeig~er is in the system from the tinie of' fits arri, dl it bus-stop until the tinic of alighting at hisl. cho- senl destination. Thus each passenger hi,is to he monitored throughout this time period and the wxait' and 'ride' times for every pissen- ger are cumulated to give total travel ill the system. 2. MODEL INPUT The data which need to be input to the model consist of three broad types: -characteristics of the route and its op- eration;-characteristics of the bus fleet, and -characteristics of the passengers. Much of the data is based on survey inforilna- tion and is contained in an input file, although souiic data are contained within the model in the form of functional relationships. Sonic of the input date are time-dependent in that they vary between different specified periods of the day. 644 ~~~~~~~~~~~~~~~~~~~TRAFFIC ENGINEERING + CONTROL This paper describes a Bus Route Simulation Model which can be use~d to as^ sess the performance of a bus route when operated by vehicles of different sizes. The model is used to examine various operating policies on a candidate route. The analysis is extended to other types of route to see whether specific conclusions for one route can be applied to others. The analysis is not exhaus- tive, but serves simply to show the capability of the model. 644 The model contains a number of function- al relationships which enable inter-stop tray- el times, time lost by buses at stops, passen- ger generation at stops, passenger destination, operating costs for buses and trip revenues to be calculated from the input data. 2. 1. Inter-stop running function Running time between bus-stops can he ex- pressed as a probability distribution, e.g. a shifted gamma distribution, which eaters for unpredictable delays and congestion. H-ow- ever, for the routes surveyed in Delhi it was found that the variation in running timecs was small for each time period and the values were symmetrical around the mean. Con- sequently a normal distribution was used to generate the running timecs between stops for each different time period- This distribution is determined by its mean value and standard deviation, which were observed in survey work. 2. 2. Lost time function Many studies, e.g. P~retty and Russell 2, have shown that lost time at stops tends to vary lin- early with the number of boarding and alight- ing passengers. If no passengers either board or alight at a stop then the lost time is zero. Relevant lost-time equations were estimated from survey data. Specifying the type of bus (minibus, single- or double-deck) controls the appropriate boarding arid alighting time relationship used in thie simulation. 2. 3. Passenger arrival at stops P~assenger arrivals are essentially dependent onl the frequency of service. However, it is normally assumed and supported by obser- vation (Danas 3) that when bus frequency is iclatively high, arrivals form a Poisson pro- cells. b,11 the variable overhead cost of the DTC as a w~.hole.The daily cost C' of an individual vehicle, exclusive oft any fixed-overhead component, is given by the following equation, where K is the daily output per vehicle. C=bK+b,(V= I) This equation was used in applications of the cost model since only incremental changes in output level were being considered, which would be unlikely to have any effect on the fixed cost component. On this basis the daily cost (in paise, where lO0paise = 1 Rupee and 15 Rupees = £1I) to the DTC of operating a single-deck, double-deck or minibus was found to be: -single-deckCS = 22 400 ± 93 K5 - double-deck CD =31 10(1+ 133KD -minibusCM = 17 40(0 + 93Kk,, where Ks, K D and KM are the daily kilome- trages run by each vehicle type (single, dou- ble, mini). These equations represent condi- tions where a vehicle is used throughout the day (on two shifts). They can be modified to represent the case where vehicles are used only in the peak (one split shift) as follows: -single-deck (peak only) C"-= 17 400 +93 K" - double-deck (peak only) C = 26 1(1(1+ 123 K" -minibus (peak only) C"-= 15 000 +91K" All these equations enable specification of the type of bus, and whether it is a peak vehi- dcl or all-day vehicle, to control the selection of the appropriate cost equation. 3. MODEL OUTPUT The output from the model canl be classified into three basic groups: -output relating to bus perfoirmaince. output relating to the service received by passengers; and output relating to the overall pcrf or- mance of the route. As wsith the input data, sonic of the output data can be produced for individual time pe- niods or for thie complete day's operations. Some output data are also produced for in- dividual buses and for individual bus trips. Table I presents the full output data from the model. 4. VERIFICATION AND VALIDATION The process of verification andl validation of' the model is described inl Vijaiyakutiiari vhere it was concluded that 'the model per- formed well onl all the tests on the two sets of (trial) input data. The reasonable assump- tions and the flexibility in representing var- ied conditions give further confidence that the model is valid for a broad range ofeon- tent- 5. OPERATING COST ANALYSIS 5. 1. Current conditions The first runs of the model were with existing demand data for Route SO of the Delhi Trans- port Corporation', varying the number and size of buses in use- 2. 4. Passenger destination The number of passetigers alighting at any stop can be modelled in a variety of ways de- pending on the quality of the data that are available. Ideally full information on board- ing and alighting patterns should be avail- able, but from the Delhi surveys inforniation was availableconlyvon the numbers offpassen- gers boarding and alighting at each bus-stop. Coiisequently a multiple linear regression model was developed so that the conditional probabilities of passengers alighting at a stop j, given that they had hoarded at stop i, could be estimated. Thus the numbers (if passen- gers alighting at any stop could be allocated to boarding points on thie basis of these con- dlitional probabilities. 2. 5. Cost functions The measures of output used for formulating a simple cost model for the Delhi Transport Corporation (DTC) were restricted to num- bers of buses used and kilomectrage run. The model can be expressed very simply as: TC =FC +bK+ ,V Table 1. Data output from the simulation Output type Bus performance Service level Route performance Where TC is the total daily operating cost, FC is the fixed-overhead cost per day, K is the daily kilomectrage output of the fleet, V is the number of vehicles in use per day, bl is the cost per km and b, the cost per vehicle employed. Thus bK is1 the direct cost and Description Bus journey times for each irip (mmii. Total bus-km for each bus Passengers carried by each bus on each trip Number of trips by each bus Load factor for each bus trip Average load factor for each bus over whole day, by direction of travel Average journey time for buses Revenues collected in each period by bus Total revenue for whole day by bus Total operating costs for whole day by bus Average wait times at each stop by period (min.) Total passengers travel and wait times for each direction (mmin Overall average wait time and ride time of passengers (min.) Total passengers demand at each stop for each period Total alighting passenger at each stop for each period Total daily demand in each direction Average passenger journey length (km) Average travel time (min.) Average wait time (min.) Revenues collected Running costs Profit December 199064 645 io Sc, o -Oout~le deck .0- Sngle dleCk Z 50 ~E 40 WD 30 00 AAA9 A A X 20 10 ii1 1 5 1 9 0 X o OoAbIe deck An Se~gie deck X ,K . 0 In 0Al0 X K n 0 6 0 XA Al X 3 , ii s15 9 23 NUMBER OF BUSES Fig IS yst'emn cost againet number of buses (current demnand level, Route 80). NUMBER OF BUSES Fig 2. Ateta eKWaitinng tuine against number of bus es (current demand level, Route_ ko). The three curves in Fig 1 have a character- istic and similar 'U' shape. Thus, costs are high for small numbers of vehicles, reflect- ing both the high walling times that travellers will experience with a low frequency of oper- ation as well as the high probability of being unable to hoard one or more buses. Overall ride timeis will also be enhanced because of the additional delays at bus-stops caused by large lumbers of passengers boarding and alightinig from each bus. However, as the numbers of vehicles is increased, so waiting times and, to a lesser extent, ride times are re- duced and the cost curves decline. Waiting- time savings are generally substantially larg- er than the additional costs of the extra buses. (N.B. In this first example, waiting times andl riding times have been valued at the samec rate.) Figure 1 shows that a minimum point is reached, beyond which costs begin to in- crease. This point occurs when additional buses cost more to run than the benefits of re- duced waiting times. Thus the rate of improvement in waiting times diminishes as more vehicles are deployed; passengers have a very low probability of having to wait for more than one bus and waiting times are a simple function of bus headways. F-igurc 1 also shows that the minimum sys- tem cost for each bus type is related to bus size: generally the smaller the vehicle, the more of them are required to achieve a mini- mum total system cost. Thus, using double- deck buses on Route 80, something like 10 vehicles would be needed to meet current de- miand levels at minimum system cost for that vehicle type. Similarly 12 single-deck buses or 14 minibuses would be needed to achieve a minimum system cost, if these vehicle types were to be used to fulfil current demand levels on Route 80. Comparison between ye- hicle types shown in Fig 1 indicates that the single-deck buses can achieve a marginally lower total system cost than other bus types. By comparison, double-deck buses perform relatively badly on this route. 5.2. Cost sensitivities The model was re-run, varying some of the input data for Route 80 to assess bow sensi- tive the system costs are to s'arious assump- tions.Table II contains a summary of this sensi- tivity analysis. It shows bow system costs vary (measured from the minimum system cost under current conditions) w~ith changes in some key variables. Perhaps not surpris- ingly, system costs are most sensitive to de- miand. Increasing demand has a greater effect on system costs than does decreasing de- mand. Furthermore, the effect is pronounced for both double-deck buses and ininibuses. It would appear that under these conditions double-deck huses are adversely affected by long headways, and hence high wait times for passengers unable to board the first arriv- ing bus; minibuses are adversely affected by a limit on available space for passengers wanting to board along the route. Once filled at the terminals, there is no room for any fur- ther boardings along the route. Table II. A summary of the main results from the sensitivity analysis undertaken for Route 80 Variable Range of Resultant range of variation in system cost- variations' (percent) (per cent) Double-deck Single-deck Minibus Demand level + 50 + 86 + 53 + 87 -50 -44 -43 -36 Travel time weight + 100 41 28 22 Value of time + 50 + 42 + 30 + 20 -50 -42 -30 -20 Speed of buses + 10 18 -12 -7.0 -10 ± 31 + 8 + 7.5 Bus operating costs + 10 + 1.5 + 2 ± 4 10 1.5 -2 -4 Measured about current operating conditions "Measures asa deviation from the minimum system cost under current conditions (Section 5.1) 646 ~~~~~~~~~~~~~~~~~~~TRAFFIC ENGINEERING + CONTROL sol 0 0 40 0 0Z U7 30 0 20 10 ,20 00,c A X L 3 646 FREOUEN~CY Gi~SES P5p -Os-p 470- 370- 9: 270- 170- 70 1 2000 0 0 6 Buses n -6 Buses x -10 Buses 0 11500r ~~1000 A 0 0 XA2 L,1 Os 0 XA1 500 In XA 07-10 090 1 10 1 30 50s DEMAND RATE Fig 3. Av'erage waiting times agail st demand rate/or different nun bets of single-deck. bus (Route 80). A AtA 2n A1 /1I I = 11 6 0 1 0' a 0 10 0 200 360 6.00 5 00 600 700 tOO0 PASSE NG ERS PER HOUR I PEAK PERIO D I PEAK CDIRE CTiON) Fig 4. Average waiting times a/passengers against the ,iumber ofpas sengers using the system (minibus). Changes in travel-time weights and value of time are somewhat more critical for the larger buses, bccause operating costs are a larger component of system costs. Changing the weight ratio from 1: 1 (wait:ride) to 2:1 in- creases double-deck system costs by 41 per cent compared with 22 per cent for minibuses. Similarly, increasing the value of time by 50 per cent pushes up double-deck system costs by 42 per cent as against a 20 per cent increase for minibus system costs. For the same reason, changes in the unit operat- ing costs of buses have a greater effect on minibuses than larger buses. Changes in the speed of buses have a greater effect on double-deck buses than on single-deck and minibuses. For a l0 per cent increase in speeds total system costs are reduced by 18 per cent for double-decks as against 12 per cent and 7 per cent for the latter two respectively.The model can also be used to show how the components of travel time vary with changed specification. As an example, Fig 2 shows how the average waiting times for pas- sengers vary with the numbers of buses in use for Route 80 with the current demand level. The graph is similar to the system cost graph of Fig 1, as expected, since a large proportion of system costs are attributable to wait times. As argued in Section 5. 1, wait times will de- cline with increasing numbers of vehicles. However, the rate of decline decreases and wait times become essentially constant after a certain number of vehicles are in use. (This is because doubling the number of buses in use would be required before the already low wait times are halved.) Figure 3 shows how the average wait time varies with the demand rate for different numbers of single-deck. buses. As might be expected, the average wait time increases with increasing demand. With the current number of buses (eight) on Route 80, a 50 per cent increase in demand generates a 60 per cent increase in wait times. Furthermore, the fewer the number of buses in use, the more sensitive is average wait time to demand level, over the range indicated. At the current demand level a 25 per cent reduction in the number of buses (from eight to six) presently used leads to a 40 per cent increase in wait times. With a 5O percent increase in demand, the same reduction (25 per cent) in the nunm- ber of buses presently used leads to an in- crease in wait times in excess of 1 00 per cent. Clearly a point is reached where the number of vehicles in use is inadequate to service the demand. 6. ROUTE CAPACITY Output from the model has been used to es- tablish the capacity of Route 8O for different vehicle types operated at different headways. For any 'run' of the model a steady state is reached during the two peak periods, when all buses are in use. The system is most likely to be working at, or near, capacity (in the sense of carrying most passengers) in one di- rection only - the peak direction of travel. Data are recorded of the numbers of passen- gers being handled by the system (i.e. the numbers able to board), their waiting times during the peak periods and in the peak direc- tion. It is these data which have been used to determine the route capacity. Figure 4 presents the way in which aver- age wait times of passengers respond to changes in the numbers using the system dur- ing the peak, and in the peak direction, for minibuses. Each curve is for a different fre- quency of operation expressed as number of buses per hour. For any vehicle type (the analysis has also been done for double- and single-decks) curves representing a higher frequency lie to the right of curves represent- ing a lowv-frequency operation. The curves have been drawn to pass through those points on the Y axis where w,,ait time would be exactly equivalent to half the headway. If buses maintained strict head- ways and passengers arrive randomly, thien this would be the expected wait time. In prac- tice, bus headways are not constant, and thus passengers are not always able to board the first arriving bus, particularly' as demand level increases. Consequently, there is quite a variation in the average waiting times. For the most part the curves show comnmon characteristics. Wait times are relatively in- sensitive to passenger throughput, up to a critical threshold in demand; beyond this level wait times become unstable and uncer- tamn. The threshold of passenger throughput at which this transformation takes place may, be regarded as the limit in the capacity of the route, beyond which wait times for passen- gers become unacceptably high and/or unre- liable. This point is reached when the proba- bility of being able to board the first arriving bus becomes small. If passengers are forced to wait for two or more buses before being able to board, large queues build up and the system quickly becomes overloaded. December 199064 f 60 11 // / 647 Table lit. Route 80 capacity data Vehicle type Vehicle Frequency limit of Associated passenger (veh/h) passenger limiting capacity throughput' wait (crush/normal) (passengers/h) times-(m i .) Double-deck 140/100 5.1 650-800 13-23 Single-deck 99/60 4.7 450 525 15-17 5.1 550 650 15-25 6.2 600-700 13-20 Minibus 48/30 7.3 300-400 8-23 11.6 500-600 7-15 16.0 800-900 10-20 In peak period and peak direction These are the wait times which can be expected up to the limit of the passenger throughput; beyond this threshold, wait times become unstable demand levels the minibuses could equally well becused on long routes with long average leads. This proposition has not yet been test- ed.Another point concerning Table IV is that the comparison is simply between vehicle types of equivalent capacity (i.e. the capacity of 16 minibuses, eight single-deckers and five double-deckers is approximately same). An operator may be more interestcd in know- ing what is the best option (in the sense of providing a service at minimum system cost) given the constraint of an operating cost bud- get, i.e. it might be better to compare options in terms of those with equal operating cost. If the performance of the buses was compared on operating costs alone, it seems probable that minibuses would provide a much more expensive service in comparison with the other two types. Table III summarises the capacity data for a number of different operating policies. A range is given for the limit of capacity (pas- seniger throughput) because the threshold which is derived from graphs is not precise. The associated wait times are also given, which indicate the level of service which can be expected by users when the route is work- ing at its limiting capacity. Clearly, the data presented in Table Ill provide capacity information for a relatively small number of the many possible system options (combinations of vehicle type and frequency of operation on Route 80). It does show, however, how capacity and level of service could be tailored to meet the specific needs of a route. If the level of service (i.e. acceptable wait time) is fixed, and the peak demand level (in the peak direction) is known, then it should be possible to select a fleet option which meets this required speci- fication. Indeed, it should be possible to ex- tend Table Ill to cover many more options, and thus to provide a set nf operating guide- lines for bus operators. Whether or not such guidelines would be universal for all routes would need further examination. Route length may have some influence on capacity., particularly if passenger 'lead' (i e. average passenger trip length) increases with route length. If this is the case, then capacity guide- lines would have to be prepared for different route length and/or average passenger lead. type. Minibuses provide the cheapest system cost (per passenger and per passenger-kin) for the shortest lead (on Route 80), while sin- gle-deck buses provide the cheapest system costs for the longer leads found on Route 89 and 521. The rate of increase in system costs with increasing lead is fastest for minibuses: the 90 per cent increase in journey lead be- tween Route 80 and Route 521 is associated with 79 per cent increase in system costs per passenger-km. The corresponding increase in system costs for double-decks is 41 per cent, though they do start at a higher level (RsO.44 per passenger-kin) than minibuses (RsO.33 per passenger-kin). There is some evidence here, then, that the longer the average lead, the larger the vehicle should be. This analysis is far from exhaus- tive, however. In particular, demand level is likely to be a key component in such an anal- ysis. Table IV represents the situation for an overall demand of about 8- 10 000 passengers per day. Using the same capacity to meet a much lower demand is likely to be reflected in much less sensitivity in costs because user costs will not be so dominant. For a demand rate of half the current level on Route 80 there is very little difference in system cost for a wide range of numbers of any vehicle type. If the same holds true for longerjourney leads (and this seems likely) then for lower 8. SUMMIARY The main criteria for comparison of route performance using the model is 'total system cost' which is made up of total bus operating costs plus total travel time costs. (The latter excludes walking costs which arc deemed to be independent of the characteristics of a single route.) Whatever the specification of the route and the vehicle in use, there is evidently a trade-off between increasing operating costs (of using more vehicles) and decreasing time costs (from the improved service level). For small numbers of vehicles the reduction in travel times outweighs increased operating costs, but a point is reached where additional vehicles add more to total system costs than is 'saved' in reduced travel times. Thus there is a minimum total system cost. Using the Route 80 input data, and comparing three ve- hicles sizes, minimum total system cost is achieved when employing 12 single-decks. This option gives a slightly lower total sys- tem cost than employing 14 minibuses with 30 seats, and asubstantial sav'ing over the use of 10 double-decks (these being the optimum numbers of vehicles of each type for the specified conditions). It is apparent fromt the analysis that the value of time adopted is critical to the dcci- sion-making process. The larger the vehicles, the more important is the tinie component in 7. MODELLING 0OTHER ROUTES Two other DTC routes (89 and 521) have been modelled, partly to check that the simu- lation is sufficiently robust to handle other conditions and partly to see whether results from one route are readily transferable to an- other. The performance of the three routes was compared, using the simulation model, by imposing on each, in turn, the same bus capacity, provided three different ways: using five double-decks, eight single-decks or 16 minibuses. Table IV shows the compar- ative performance of each hbus type for the three routes. Taking each vehicle type in turn, it is evident that system costs increase broad- ly in line with average passenger lead (jour- ney distance). This is true for each vehicle Table 1V. Comparative performance of three bus types (of equivalent capacity) on three routes 16 Minibuses 8 Single-deckers 5 Double-deckers 80 89 521 80 89 521 80 89 521 Average wait time (min.) 6.5 33.7 61.6 Average ride time (min.) 13.2 24.4 25.3 Average passenger lead (kin) 5.4 8.5 10.3 System cost -per passenger (Rs) 1.78 4.18 6.04 11.5 30.3 59.9 14.7 31.3 28.3 5.3 10.0 10.5 1.88 4.16 5.67 18.5 64.3 71.2 15.6 29.6 25.7 3.5 9.9 10.0 2.32 5.48 6.17 - per passenger-km (Rs) 0.33 0.49 0.59 0.35 0.42 0.54 0.44 0.56 0.62 Operating cost -per passenger (Rs) 0.60 0.69 0.83 0.31 0.46 0.38 -per passenger-km (Rs) 0.11 0.08 0.08 0.06 0.05 0.04 0~28 0.35 0.36 0.05 0.04 0.04 648 ~~~~~~~~~~~~~~~~~~TRAFFIC ENGINEERING + CONTROL 648 total system costs. Thus the value of time and the travel-time weighting factor (the ratio of wait times to in-vehicle times) criticall aft feet tile total system cost; the higher these values, the less likely that larger buses would be favoured over small buses. The sensitivity analysis demonstrates this relationship. Total system costs are much less sensitive to changes in unit operating costs of buses. because operating costs make up a relatively small proportion of the total. As might be expected, the level of demand is also a critical factor in route performance. Total system costs rapidly escalate when the same number of vehicles is used to meet an increase in demand level. The sensitivity analysis of Route 80 suggested that this cost- escalation is much greater for the smaller and larger vehicles, in comparison with the sin- gle-deck buses. Using the model, an attempt has been made to establish the capacity of Route 8O for different vehicle types at different headwavs. This is based on the level of passenger throughput (passenger per hour in the peak period and peak direction of travel) beyond which average passenger waiting times be- come unreliable and unstable. Only a rela- tively small number of possible options have been examined, but it is demonstrated that capacity and level of service could be tai- lored to meet any particular service needs. When comparing the performance of dif- ferent-size vehicles on different routes there is evidence that the longer the average lead (passenger journey distance). the larger the vehicle should be. A CKNO WLEDGMENTS We ackniowledge tire assistanice provided by. P R. Fowuriac.- Overseas Uniit, Tran %port and RoadRe- sea rei Laboraitori., D. Gilber t, ninperiail Collegi'. aiid L. H1 Na vegon, independent coniputer co/i- sudtanit, in thie prepaiation oft/ics paper. Tire kt'ork described in /ifis paper faorted part of i/ie pro^ grammne of i/ie TRRL atid is published by permission oft/ice Director REFERENCES VIJAYAKUMAR, S. Optimal vehicle size for road- based urban public transport in developing countries. Thesis submitted for the degree of Doctor of Philosophy in the Facultyof Engi- neering, Imperial College, University of London. t987. 2PRritT-y. R. L. and D. J. RUSSELL. Bus boarding raies- Aust. Road Res. 18(3), September 1988, t45-52. 'DANAS, A. 1980J. Arrivat of passengers and buses at two London bus-stops. Traiff Engng Coti irol. 21(t0) tO, October t980,472-47S. 'FoUJRACRE, P. R., D. A. C. MAUNDER, M. G. PAMiAK and C. H. RAO. Studies of bus opera- tions in Delhi, India. TRRL-- Supplementary Report SR 710. Transport and Road Re- search Laboratory, Crowthorne, 1981. The address of Dr Vijayakumar.. 54 Be/gra via H-ouse, 30 Clarenice Avenue, London SWY4 8/IY, and of Dr Jacobs: Overseas Uniti, Tratisport utid Road Researc/i Laboratory. Crowt/orn,ie Bet-k s/ure RG 1 6A U. The TRICS Consortium of South-East County Councils has released version 2.2 of its Trip Rate Data Base Sys- tem. The new database contains some I 340 days of travel data from 390 different sites, an increase of some 30 per cent on the pre- vious version and largely due to the inclusion of data from Manchester and Lancashire, an increase of industrial estate data and the in- clusion of a number of superstores in central London. According to Col in Eastman, an As- sociate of JIMP Consultants who manage the system on behalf of the County Councils, 'al- though the size of the database is expanding rapidly we can still identify significant gaps in its coverage - we are particularly keen to hear from anyone who has access to data on BI developments and data within London'. There are now 57 registered users of the TRICS System. * JMP? Consultants are to carry out for TRICS a two-month 'study to identify maximum parking demands for a wide range of land uses. Their research will examine the data currently held within the TRICS database and supplement these with data from extensive automatic traffic count data for a series of retail stores. This is the third re- search project to be commissioned by the TRICS Consortium. The first project on the tenmp oral stability, of trip rates has been con- clu ded wvhile the second project, which is a series of before-and-after studies of the intro- duction of retail stores, will be ongoing throughout 1991. Editorial Index: Volume 31. 1990 Readers and Librarians are reminded that the Editorial Index to Volume 3], 1990. appears on pages 678 and 679 of this issue.