EXPLORING THE NATURE OF URBAN TRAFFIC CONGESTION: …

EXPLORING THE NATURE OF URBAN TRAFFIC CONGESTION: CONCEPTS, PARAMETERS, THEORIES AND MODELS

M.A.P. Taylor B.Eng.(Hons), M.Eng.Sc., Ph.D., FIEAust., MITE, MAITPM, MCIT

Professor and Head of Civil Engineering, University of South Australia

SUMMARY

Contemporary transport planning is focussing on issues of travel demand management (TDM) for environmental, social and economic reasons. A central part ofTDM is concerned with the use of congestion management techniques. This paper considers the nature of traffic congestion and develops parametric descriptions of the levels of congestion in an urban road network. It suggests that there are a variety of manifestations of congestion, which may be grouped into two basic classes: point congestion and network congestion. The use of congestion as a TDM control mechanism is examined, including congestion pricing. The input-storage-output routing equation for interrupted traffic flows is taken as the starting point in the development of a theory of traffic congestion, and for mathematical models that examine the effects of congestion. The paper comprises a review of established theories of the build up of congestion, including Rahmann's storage-output system, the Wardtop-Jewell models of traffic assignment, from which a TDM-modelling strategy can be defined. It considers a set of parametric measures of traffic congestion, involving capacity, travel time and delay at the node, link and network levels.

PROCEEDINGS 16th ARRB CONFERENCE, PART 5 83

84

Mike Taylor is Professor and Head of Civil Engineering, and Director of the Transport Systems Centre, at the University of South Australia in Adelaide, Australia. His expertise is in the areas of transportation, engineering systems and engineering management. He received his B.Eng, M.Eng.Sc. and Ph.D. degrees at Monash U ni versity, where he was an academic on two separate occasions (mid 1970s and mid 1980s).

His work experience includes time as a traffic engineer in the Country Roads Board of Victoria, as a consultant with the Road Transport Research Program of OECD, and as a research scientist in the Division of Building Research of the Australian scientific research organisation CSIRO. His main research interests lie in the development of computer models for transportation systems, methods for the collection, storage and analysis of traffic and transport data, and the general application of information technology in transportation.

His current interests include modelling the environmental, energy and social impacts of road traffic, central city traffic and car parking, planning and design of metropolitan transport networks, and performance assessment for public transport systems. Mike Taylor is a Fellow of the Institution of Engineers, Australia, and is a Member of the Institute of Transportation Engineers, the Australian Institute of Traffic Planning and Management, the Chartered Institute of Transport, and the Australasian Association for Engineering Education.

PROCEEDINGS 16th ARRB CONFERENCE, PART 5

INTRODUCTION

1. At the Sixth ARRB Conference held in Canberra in August 1972, W M Rahmann presented a seminal paper (Rahmann 1972) that sought to change the then conventional wisdom about road planning and traffic congestion. Rahmann' s thesis was that traffic operations at or near capacity were a natural phenomenon that would always be found during peak hours on principal urban roads, irrespective of the level of investment in the road network. The previous design philosophy had been that the emergence of congestion was in some sense a symptom of system failure. Rahmann argued that traffic congestion was a necessary equilibrium or pricing mechanism. Its existence was permanent; the transport planner and traffic engineer needed to recognise this fact, and then to use the congestion mechanism in transport systems planning and design. In subsequent work Rahmann (1973) went on to demonstrate how an urban road network could be designed to cater for and use the congestion mechanism, by considering the road network as a storage-output system.

2. Twenty years on, contemporary transport planning is focussing on issues of Travel Demand Management (TOM), for environmental, social and economic reasons. A central part of TOM is concerned with the use of congestion management techniques as one means for achieving some of its goals. Rahmann's thesis is an integral part of the TOM process, yet there are still indications that the community (and indeed some transport professionals) still desires to see congestion eradicated: the old beliefs die hard?

WHAT IS CONGESTION?

3. Congestion is widely discussed in the transport literature, but seldom is a definition attempted. The common lay view is that congested traffic conditions mean the blockage of traffic routes by queued vehicles. The traffic engineer sees congestion in terms of the occurrence of delays and queuing, or perhaps as a poor level of service for a traffic stream, or perhaps in the existence of over-saturated flow conditions. The planner often sees congestion as a symptom of an imbalance of travel demand and the supply of transport infrastructure (or as the misuse of the available infrastructure). The economist sees congestion in terms of additional travel costs imposed on other travellers by a given individual traveller. Now, all of these views share some common bases, and it is likely that individuals holding different perspectives would, on viewing a given traffic situation, make much the same judgement as to whether congestion existed or not.

4. The difficulties with these different perspectives will arise when we wish to quantify the extent of congestion, or compare and rate different traffic situations. This circumstance will, however, arise frequently in the transport planning and decision-making process. Can we find formal definitions of congestion? How can we measure the level of congestion? What phenomena are associated with congestion? How can we analyse congestion phenomena? How can we predict the likely level, extent and duration of given levels of congestion in a transport network? Solutions to these questions, amongst others, provide the goals for this paper.

A list of symbols is presented at the back of this paper.

PROCEEDINGS 16th ARRB CONFERENCE. PART 5 85

SOME DEFINITIONS

5. The perspectives on congestion offered above provide a start towards the definition of traffic congestion. A number of researchers and commentators have attempted to provide formal definitions. Some of these effons are described below.

6. A basic and perhaps general definition of congestion, perhaps representing the wide community view, can be sought from the dictionary. The Concise Oxford Dictionary (Sixth Edition) defines congestion as the 'abnormal accumulation (of blood in a part of the body; of population, traffic, etc.), On the other hand, the Second Edition of the Macquarie Dictionary defines congestion as '1. filled to excess, overcrowding. 2. unnatural accumulation of blood in the vessels of (an organ or part) '. Is it possible to see the analogy of traffic with blood, as representing the life fluid of the city, compared to that of the body? Pragmatically, however, these definitions fail because they maintain that congestion is abnormal or unnatural. Can a phenomenon that occurs regularly, cyclically and universally be abnormal or unnatural? A more limited but technically consistent definition is required.

7. The disciplinary perspective of the commentator often provides the basic perspective for a technical definition of traffic congestion. The following disciplines, amongst others, can each attempt a definition: (a) economics; (b) transport planning; (c) urban planning, and (d) traffic engineering.

Economic perspective

8. The economic perspective is to see congestion as the imposition of additional costs (such costs being manifest as delays and queuing) by one traveller on other travellers. For example, Bruzelius (1979, p. 29 and pp. 33-34) defined traffic congestion in the following terms:

The reason why the latter two market failures, congestion and public goods, occur in the transport market is basically related to the condition that travelling takes time ... Thus road congestion may be viewed as an external effect which arises when many motorists use the same road at the same time, so that the time required to complete a journey increases.

9. Agnew (1977) saw congestion as an observable phenomenon, and sought to couch his definition in this vein:

86

Congestion occurs whenever the users of a facility interfere with one another and mutually suffer from their interference. Highways are typical and important examples of a congestion-prone facility . They are subject to costly and disagreeable ovedoading during peak hours due to the delays to drivers caused by the behaviour of those who prel:t:dt:d them on the road.


Transport planning perspective

10. The transport planning perspective focuses on the interaction between urban activity, travel demand and the supply of transport facilities. Meyer and Miller (1984) saw congestion as part of the cyclical pattern of activity in an urban area. They provided the following definition (see pp. 24-25):

The peaking of travel demand in specific time periods results in congested highway facilities and transit services. Congestion is simply a condition of any transportation facility in which use of the facility is so great that there are delays for the users of that facility . Usually this happens when traffic approaches or exceeds facility capacity.

11. Hartgen (1991) simply stated that 'traffic congestion is caused by the mismatch between traffic and road space available' .

Urban planning perspective

12. The urban planner sees congestion in similar but wider vein to the transport planner. According to Helly (1975, p. 103):

Congestion is perhaps the most prevalent and vexing problem of urban life. Some people view it as the urban disease. Patently, congestion is the result of excessive demand by customers for services by overtaxed facilities. Wherever there is congestion, some or all of the customers will be denied service or will queue up to wait until service is provided.

13. Wetzel (1977) considered congestion in respect to the demand to travel to and use particular land use facilities (his basic interest was in recreational facilities). He proposed the following definition of congestion (Wetzel 1977, p.243) :

The role of congestion with regard to recreation has been commonly ignored or assumed away in most economics of recreation studies. Congestion may be defined as attendance levels divided by some physical attribute of the resource site, such as acreage. It will be assumed that individuals regard congestion as ' bad ' and are congestion avoiders rather than congestion seekers.

Wetzel's definition, though not strictly related to traffic systems, is of interest because it adds an explicit value judgement about congestion (that individuals do not like it and may seek to avoid it) and because it requires the level of congestion to be related to some parameter representing the capacity of the facility in question.

Traffic engineering perspective

14. A common view in traffic engineering practice is that presented by Rosenbloom (1978), that ' peak-period traffic congestion occurs when travel demand exceeds the existing road system capacity'. This definition was further developed by an OECD (1981) Road


Research Group concerned with traffic systems control under saturated conditions, which defined congestion in the following way:

The very aim of traffic control is to provide the best traffic conditions for the users of the network. It is usual to rate these condltIOns In terms ot 'qUalIty ot service' and assess them on the basis of the results of a series of measurement. 'Congestion', or more technically 'saturation', is a state of these conditions. It is intuitively understood that congestion constitutes a poor quality of service and that it is associated with the existence of queues which increase over time, whether at a signalised intersection or at a bottleneck. The key point of interest in traffic control operation is clear: to identify when congestion starts, i.e. the saturation point, since the task of the traffic engineer is to avoid such a traffic state which is both below standard and inconvenient to road users.

This definition restricts congested conditions to occur only when the capacity of a network element has been reached, and the traffic demand exceeds that capacity. Such a definition has the attractions of precision and specificity, but does not include many situations that would be regarded as congested. For instance, the build up of significant queues may occur at flow levels well below capacity, even if such queues may be regarded as being in equilibrium.

15. A more generally applicable definition was provided by Wright and Huddart (1989), as follows:

There are several distinct forms of traffic congestion, each of which tends to occur within a specific road environment. Most drivers are familiar with the slow crawl along busy shopping streets, the long queues that form when accidents occur on rural roads, and the rapid; unpredictable slowing down and speeding up of traffic on overloaded motorways (often without any obvious physical cause) ... One of the most acute forms of traffic congestion, however, is the area-wide 'jam', in which vehicles can become embedded for long periods of time. It is usually triggered off by the interaction between two or more queues. Consequently, to understand traffic jams, it is useful to begin by considering the queuing mechanism itself.

Thus, for Wright and Huddart, traffic congestion exists when large-scale or multiple queuing occurs. The queuing may be generated around or within a single traffic stream (i.e. uninterrupted flow conditions), or from the interaction between two or more traffic streams (interrupted flow).

A UNIFIED DEFINITION OF CONGESTION?

16. There are a number of recurrent ideas in the above definitions, that perhaps form the basis of a generalised, technical definition of congestion. Three recurrent ideas are: (a) congestion involves the imposition of additional travel costs on all users of a

transport facility by each user of that facility; (b) transport facilities (e.g. road links, intersections, lanes and turning movements) have

finite capacities to handle traffic, and congestion occurs when the demand to use a facility approaches or exceeds the capacity, and

88 PROCEEDINGS 16th ARRB CONFERENCE, PART 5

(c) congestion occurs on a regular, cyclic basis, reflecting the levels and scheduling of social and economic activities in a given area.

Thus a useful definition for transport systems planning and engineering purposes could be that traffic congestion is the phenomenon of increased disruption of traffic movement on an element of the transport system, observed in terms of delays and queuing, that is generated by the interactions amongst the flow units in a traffic stream or in intersecting traffic streams. The phenomenon is most visible when the level of demand for movement approaches or exceeds the capacity of the element.

17. It follows that congestion may always be present in any part of a transport system, but that the level of congestion may have to exceed some threshold value to be recognised. The threshold may be context-specific. Peak periods are recognised as prone to congestion, but this is not to say that congestion does not occur at other times.

MANIFESTATIONS OF CONGESTION

18. There are many manifestations of congestion, which may be grouped into two basic classes: point congestion and network congestion. Point congestion is concerned with bottlenecks, i.e. site-specific constrictions on traffic capacity. Bottlenecks may be permanent, or temporary (e.g. at accidents or breakdowns). The effects of bottlenecks are localised, although removal of an individual bottleneck may have important and sometimes severe repercussions across a surrounding network. Network congestion is an area-wide phenomenon, characterised by unstable flow conditions that may erupt at a variety of sites in an area, either at the link level or at the node level. Network congestion is indicative of a general lack of road capacity in a region, another term for this phenomenon is gridlock.

THEORIES ON CONGESTION

19. Given that traffic congestion is an identifiable and observable phenomenon, the next task is to propose hypotheses that can be used to explain the occurrence of congestion. In this way theories can be formulated that may be used to answer questions, and to predict the consequences of policies and decisions aimed at alleviating congestion, or to use congestion as a travel demand management tool. The identification of queuing as an important part of the congestion mechanism (Wright and Huddart 1989) provides a starting point, as reflected in the unified definition of traffic congestion given in para. 16.

20. Queuing processes are made up of three components: (a) the input (the rate and pattern of arrivals) to the queue; (b) the queue discipline (such as the order in which customers will be served, such as

'first-in first-out', or priority customers who gain preference on arrival at the queue, etc), and

(c) the form of service offered (this includes the number of servers - or the number of customers who can be served at the same time - and the time taken and manner in which service is dispensed).

Queuing will occur whenever the rate at which customers arrive exceeds the capacity of the servers to deal with them. If arrival and service rates are regular and fixed (i.e.


detenninistic), then queues will only be observed when the arrival rate exceeds the service rate. Under these circumstances the queue will continue to grow until the arrival rate drops below the service capacity. Such queues are rare, more commonly there are variations in arrival and service times so that queues can form for short periods of time and then dissipate. An equilibrium can c "1st ill this l:ase, where the equilibrium condition means that the probability of finding a given number of customers waiting in the queue is constant over time. A detailed account of queuing theory and its applications in traffic analysis is given in Young, Taylor and Gipps (1989). A conceptual equation that encompasses all of these ideas is Rahmann ' s storage-routing equation for a time interval L1t (Rahmann 1973)

This equation has found wide application in traffic capacity and control analysis (e.g. Gazis 1973; Taylor 1976; Stephanopoulos et al. 1979; Akcelik 1981; Daganzo 1983).

21. A further influence on the development of congestion (and on the finite capacity of any element of a traffic system) is the type of feedback mechanism by which flow takes place. This is particularly important for road traffic flows, which consist of many vehicles being operated by individual decision makers (drivers) who have to respond to the behaviour of the vehicles around them. When the vehicles are in close proximity to each other the mechanism is one of car-following (Gipps 1981; Young, Taylor and Gipps 1989). Car-following theory hypothesises that a driver reacts (accelerates or brakes) at a given time in response to the acceleration or braking behaviour of the vehicle in front and the separation between the two vehicles at a slightly earlier time (a 'reaction time' before). The more severe the behaviour of the leading vehicle, the more severe the reaction; the closer together the two vehicles, the more severe the reaction. Further, different drivers (and their vehicles) will have different personal characteristics that also affect the response.

22. The earlier discussion leading to the unified definition of congestion also provides some important requirements of any theory of congestion for transport systems. These include: (a) the need for the inclusion of a measure of the capacity of the system in any

quantification of the level of congestion; (b) the existence of a base cost (e.g. 'free-flow' travel time) incurred for use of that

system element, regardless of the actual level of use. Congestion will be seen in additional costs imposed on the use of the element because of the level of demand to use it, and

(c) the ability to relate the extent and level of congestion to the underlying activities that cause the travel demand to exist.

23. Traffic flow theory and queuing theory can be used to present suitable conceptual and analytical models that represent congestion. The distinction between uninterrupted flow and interrupted flow (see para. 15) is important because it provides a dichotomy between the model types needed to describe flows (e.g. freeway traffic) in which the congestion is generated by the internal interactions in the traffic stream, and congestion generated by the interaction between intersecting traffic streams (e.g. a signalised intersection). The freeway traffic represents uninterrupted flow, the signalised intersection is an example of interrupted flows. Figure 1 shows stereotype speed-volume and travel time -volume curves.


24. For purposes of network analysis it is recommended that unit travel time (u) (time per unit distance, e.g. rnin/km) be used in preference to speed (v). For example, this measure can be directly applied to calculate delays and travel costs, and is compatible with applications in areas of travel demand modelling such as modal choice and destination choice - see Taylor (1984), Taylor and Anderson (1984) and Rose, Taylor and Tisato (1989). Figure 1 indicates one significant difference between uninterrupted and interrupted flows: for uninterrupted flows there can exist more than one travel time or speed value for a given traffic volume (q). This is not the case for interrupted flow. See Fehon and Moore (1982) for more details.

Fig. 1 - Travel time-flow and speed-flow curves for uninterrupted and interrupted flows

(al Uninterrupted Flou

uO

U T n r 1 a t u

e T I

n S e p

e u8 e

d

B Uolune (ql S Il Uolwne (q) S

(b) Interrupted Floll

U T n r i a t u

e T 1

n S e p

e uB e

d

B Uolune (q) S Il Uolume (q) S


CONGESTION IN UNINTERRUPTED FLOWS

25. Congestion in uninterrupted flows occurs because of the interactions of vehicles within a single traffic stream. The clearest examples are found in freeway traffic, most noticeably when a capacity restriction is applied. For pure freeway operations this will occur with an incident such as an accident, breakdown, or some special event (e.g. a sudden deceleration of one or more vehicles) that restricts flow in one or more lanes. The resulting congestion may linger long after the initial incident has been resolved, because of the queues that may have formed. There are a number of models that represent flows in such cases (e.g. Gazis 1973; Heidemann 1990), but the car-following models such as those described by Gipps (1981) (see also Young, Taylor and Gipps 1989) provide useful behavioural interpretations, because they are based on physical and psychological premises that can be directly related to the driving task.

CONGESTION IN INTERRUPTED FLOWS

26. Interference between two or more traffic streams, usually but not always at intersections, and the resulting queues that form are the typical basis of congestion in urban road networks. The effects of such queues can remain localised around a single junction or bottleneck, or may spread through a network when the extent of queuing starts to affect traffic movement at neighbouring intersections. Queued vehicles take up finite amounts of longitudinal road space! The underlying theories required for studies of congestion in interrupted flow situations (e.g. urban surface street networks) are drawn from the study of flows in networks (e.g. Potts and Oliver 1972; Young, Taylor and Gipps 1989). The Wardrop-Jewell theory of network equilibrium, especially with the consideration of elastic travel demand (Evans, 1976), is one useful development that is explored in a later section of this paper.

ROLE OF CONGESTION IN TDM

27. Modern transportation systems planning and management has come to embrace TOM (AUSTROADS, 1991). TOM may be seen as a means to achieve a balance between the construction, operation and management of the scarce resources 'roads in urban areas' and 'funds required to maintain, manage, extend and reconstruct them', whilst providing economically, socially and environmentally responsible (sustainable) levels of mobility and accessibility for (urban) populations. There has been a steady shift in public attitudes to road-based transport, associated with growing levels of congestion, heightened environmental, social and quality-of-life concerns, a greater willingness to constrain traffic and travel access and movement for gains in safety and lifestyle, and global issues such as the role of transport in society and greenhouse gas emissions. TOM combines the established methods of transportation systems management with new policies and objectives aimed at influencing the travel behaviour of individuals and groups, primarily in space and over time of day. Important elements of travel behaviour include route, mode and destination choice, and the timing of trip making (Wigan 1990). Discussion of alternative strategies for use in TOM are available, for example in Hitchcock (1973), Wigan et al. (1973), Rosenbloom (1978), Howie (1989), Orski (1989, 1991), Hensher (1991), May (1991), and Wayte (1991).


28. Following from Rahmann (1972,1973) [and building on earlier studies such as Roth (1963) and Tanner (1963)], congestion provides a partial but natural restraining mechanism on travel demand. The additional costs (delays, queuing and inconvenience) resulting from congested conditions can act as a form of deterrent to the generation of further travel demand (see AUSTROADS 1991). However, there is widespread belief (based on direct observations) amongst transport professionals that the congestion 'price' of itself is inefficient as a demand management tool. Individual drivers may not be fully aware of the true costs that they impose on other travellers and the transport system on the basis of congestion delays alone. Some other pricing signal is required to this end. Assuming that travellers will respond to a composite generalised cost (i.e. a total travel cost containing components from travel time, travel distance, out-of-pocket expenses, fuel cost, wear and tear, etc.) by trading-off the different cost components in their travel decision making, the further step is to impose a congestion tax, toll or road pricing charge on travellers in an intelligent, selective fashion (e.g. for travel on some parts of a network at some times of day) (Agnew 1977; Small 1983). There has been a resurgence of interest in this topic, largely as a result of the new technological capabilities for vehicle identification and modelling (Hensher 1991; Jones and Hervik 1992).

29. The economist's conceptual model for a congestion tax or price is that shown in Figure 2. This shows the average travel cost curve, which may be equated to the travel time curve for interrupted traffic flow shown in Figure 1. The marginal cost curve is also shown in Figure 2; this curve indicates the additional travel cost imposed by each new driver using the facility. Figure 2 shows that average cost and marginal cost are similar for small traffic volumes, and that marginal cost increases more quickly than average cost. The unified definition of traffic congestion says that congestion is any additional travel cost above the minimum cost to traverse the system element. Figure 2 indicates that the congestion will not be perceived or observed at small flows, but that a threshold value will have to be reached first. The growing disparity between marginal cost and average cost might be used to indicate the threshold. Figure 2 also shows an economic demand curve, which provides the relationship between the travel demand to use the facility and the cost of doing so. The intersection of the demand curve and the average cost curve (at (ql' CI» may be taken as the actual level of flow on the facility. Now the average cost (C I ) is less than the marginal cost, so the motorists are not meeting their full marginal cost. A congestion charge could be imposed on motorists to this end, this would see a decrease in traffic volume to Ch with the cost of travel at ~ (including a congestion charge of ilC).

30. Now, the relationships between the curves of Figure 2 indicate that the actual congestion charge to be imposed is not easily determined. It requires detailed knowledge of the characteristics of the facility and its average and marginal cost curves, and the level of traffic flow. There is a need for considerable data, some of which has to be monitored continuously over the time that the congestion charge is being imposed - a significant task. The technological capability to perform this task does now exist (e.g. Hensher 1991). The further result of new technology may be the ability to provide drivers with information that will assist them in making their travel choices (e.g. Ploss et al. 1990), and this might be the factor that wins community acceptance of a congestion pricing scheme? However, as is indicated in a later section of this paper, the available information may not be of as much value to the individual as it might be to the community.


Fig. 2 - The economic price of congestion and travel demand

Marginal Demand

T r .. u e I

C 0

s C2 t .. c:

C1

CB

B q2 q1 s

Volume (q)

MEASURING THE LEVEL OF CONGESTION

31. A crucial part any transport planning or traffic control strategy for TOM requires determination and subsequent monitoring of the level of congestion. Thus there is a need to collect and analyse data on congestion. Several measures can be used, and although the definition of traffic congestion would suggest that delay time is an essential parameter, it is almost certainly not a sufficient measure. The set of factors reflecting the level of congestion includes: (a) delay, possibly disaggregated to consider delays to different road users (e.g. private

vehicles, public transport, pedestrians, etc) or delays on different roads (major arterial roads, local roads and streets, etc);

(b) the equitable distribution of delays between competing traffic streams; (c) the reliability of travel times and travel costs. Delays reflect an overall (or average)

level of congestion experienced by travellers. Under congested conditions individual travellers may experience considerable variation in travel times which have significant effects on travel choices (e.g. how reliably one can determine an arrival time at a given destination may have a strong influence on the choice of mode or route for the journey to work);

(d) queue management, which is of importance in urban traffic network control, in the attempt to prevent queuing and congestion at one point in a network from moving upstream to block other intersections. Queue management is necessary in congested road networks to maintain the overall capacity of the network;


(e) incident detection, which is important for traffic flow control on limited access facilities such as freeways;

(f) excess energy consumption caused by delays and queuing; (g) additional emissions of gaseous and noise pollution caused by delays and queuing,

and (h) the possible increase in accident potential due to reduction in manoeuvring space

and increased frustration and anxiety of driving in congested conditions.

DELAY TIMES

32. The above factors are those that are commonly used as general measures of perfonnance of a traffic system. This reinforces the central role of congestion in affecting systems perfonnance. The basic variable used to indicate the level of congestion is travel time, either the individual travel times for all drivers on a route (then represented as a frequency distribution), or an average travel time, taken to represent the state of traffic flow on the network element (for example in comparisons between elements of a network, between times of day, or between networks). Taylor and Young (1988, pp. 157-173) discussed the collection, analysis and application of travel time data. Travel time of itself is not sufficient, and some datum is needed to assist in the assessment of the extent and level of congestion. Delay (d) provides a derivative of travel time that is a direct indicator of congestion, being defined as an excess travel time above the minimum travel time needed to traverse a facility . For the present circumstances delay is given by

d C - Co

This result is for system delay which is the most appropriate measure of delay for use in congestion studies, as it is a direct measure of the additional time costs imposed by one motorist on others Sometimes alternative definitions of delay (e.g. stopped time) are used, as discussed in Taylor and Young (1988). There are differences between these alternatives and care is needed to ensure compatibility between definitions and computational procedures when assessing the level of delay and making comparisons between different studies.

33. The cause of delay may also be of concern. For example, Lindley (1987, 1989) provided assessments of congestion levels on urban freeways in the USA in tenns of vehicle delays, with the delay times being divided into two classes: recurrent delays due to cyclic variations in travel demand, and delays due to special incidents (such as breakdowns or accidents).

CONGESTION INDEX

34. The level of congestion, as defined by the system delay, may be expressed in tenns of a congestion index (el), which is a dimensionless quantity greater than or equal to zero. A congestion index of one means that the actual travel time is twice the free-flow travel time. Such an index is a useful parameter for comparisons because it is independent of route length, road geometry or intersection control and capacity factors that could mask actual differences between two sites. The index is given by


CI-

Alternative dimensionless parameters that may be of use in congestion analysis include the ratio of actual speed to free speed (vivo) or the degree of saturation (Akcelik 1981). Possible applications of the Congestion Index were described by Richardson and Taylor (1978) and Taylor (1982), with special emphasis on variability in travel time.

VARIABILITY OF TRAVEL TIMES

35. Travel time variability can become most important for individuals caught in congested flows, as it confounds the ability to predict arrival times. From the work of Herman and Lam (1974) and Richardson and Taylor (1978) it is known that travel time variability increases as the level of congestion increases. Further, it is possible to deduce a relationship between average travel time and the variability in individual travel times. The standard deviation (s) and the mean travel time (c) may be related in terms of a routespecific constant (the travel time variability factor, y) as follows

Thus prior knowledge of y and direct observation of c can provide a means for assessing the likely level of variability in travel times.

ACCELERATION NOISE

36. Underwood (1968) described two measures of congestion that appear to have fallen from present day use, but which are worthy of revival because they can be applied for purposes of evaluation and comparison. Part of the explanation for their demise might have been the previous difficulty in obtaining the required data for their application, but the modem availability of instrumented vehicles (e.g. ARRB's TTDAS system) that permit logging of speed-time profiles (and fuel consumption) in detail gives cause to revisit these measures. Acceleration noise (cr) is given by

where Ll~ is the time interval taken for a speed change Llv j • Underwood found that acceleration noise provided a useful parametric measure of the level of congestion when overall average unit travel time was less than 2 min/km (i.e. an average travel speed of greater than 30 km/h).

37. A second parameter, the mean velocity gradient (p) , defined as

p

96

ou o v


was suggested as a measure of congestion that could be applied over a wider range of unit travel times. There is scope for renewed research interest in these parameters to determine their usefulness in describing congestion levels.

STOPPED FRACTION

38. Herman and Prigogine (1979) developed a macro-level model of traffic flow on links and routes (the 'two-fluid' model) was subsequently shown to provide reasonable representations of arterial road traffic flows in many cities around the world (Ardekani and Herman 1985; Herman et al. 1988). An important variable in this model, as seen later in this paper, is the stopped fraction (Fs)' the proportion of the total traffic flow that is stationary at any time. The stopped fraction can be observed directly (e.g. from video records), or it can be estimated from stopped time and total travel time. Herman and Prigogine (1979, p.150) showed that the simple relationship

c

was acceptable 'as a type of ergodic condition relating ensemble averages to time averages' and was supported by available observations.

QUEUE LENGTH

39. Queue management is an important measure in controlling the spread of congestion in urban road networks. If queues can be prevented from backing up to block neighbouring intersections, then severe congestion can be localised, avoiding gridlock. Monitoring of queues needs to be an integral part of an urban traffic control system, and queue lengths can be calculateci from traffic flow data and signal settings of the previous cycle in an online system. Luk (1992) provided details on how this can be done.

MEAN SPEED

40. Mean travel speed may also be used as a measure of congestion, given a datum for comparison. Duncan et al. (1980) compared mean travel speeds in 1976 in towns and cities throughout the UK with those found in an earlier (1963) study. They also produced regression models that related mean speed to traffic network characteristics such as intersection density, percentage of network length with direct frontage development, and peak period traffic flow factors.

FUEL AND EMISSIONS

41. Estimates of fuel consumption and emissions in different traffic conditions are also useful in congestion analysis. The fuel consumption models reported by Biggs and Akcelik (1986) provide the starting point for such investigations. These models as reported are strictly for the fuel consumption of pre-1985 motor vehicles, with a subsequent addition by Akcelik (1990) to include emissions for carbon monoxide, hydrocarbons and nitrogen oxides. This addition has been included in recent versions of SIDRA. Current research at the University of South Australia (with funding support from ARRB, ARC and SENRAC)


is extending the scope of the Biggs-Akcelik models for fuel and emissions analysis for post-1985 cars and for trucks.

OTHER MEASURES

42. There other many other measurements that can be used in the assessment and monitoring of congestion levels and in the evaluation of TDM programs. Orski (1991) suggested that vehicle occupancy and the proportion of single-occupant vehicles should be observed to help gauge the effectiveness of TDM programs. Lindley (1991) also proposed use of this measure. Luk and Sin (1992) described the use of the ratio of flows from successive observation points along a freeway for the detection of congestion-inducing incidents. Zahavi (1972) defined the a-parameter,

qv

as equivalent to the 'kinetic energy' of traffic flow. This parameter represented the interaction of flow and speed combined, and could be used to characterise the quality and performance of traffic flow on a road section or network. He applied this parameter to six world cities, including London.

MODELLING CONGESTION

43. The complexity of urban traffic systems points to the necessity to use mathematical and computer based models to help the analyst in understanding the nature, causes and effects of congestion. Modelling may be considered at the following levels: (a) the intersection; (b) the link or route, and (c) the network (at the strategic or local area levels).

INTERSECTION MODELS

44. The SIDRA (Akcelik 1984) and INTANAL (SIMS 1991) software packages for the design and analysis of signalised intersections provide excellent examples of a model of traffic flows at intersections that provide useful information on the development of congestion for the whole intersection, and individual legs, phases, turning movements and lanes.

LINK MODELS

45. A useful functional representation of congestion on a road section (or link) is the Davidson function, which in its original form is

c co[ 1 + S J_q q ]


where J is an environmental factor that accounts for road type, physical geometry, and abutting land uses. The revived interest in this function for use in estimating congestion levels in urban road networks is clearly demonstrated by the recent interpretations, revisions and modifications proposed for it by Tisato (1991) and Akcelik (1991). There is a need for substantial empirical work to estimate values for the Davidson function parameters for a wide range of road types and road environments. A detailed discussion of these needs is available in Rose, Taylor and Tisato (1989), whilst Taylor (1977) derived the numerical procedures required for parameter estimation and testing.

NETWORK MODELS

46. Transport planners have long made use of transport network models that provide information on travel in an urban area. However, much of this modelling has been at a broad level (e.g. consideration of 24 hour flows) that provides only limited information on congestion and the variation of congestion levels over the hours of a day. There are some model developments in this genre that can be usefully applied to congestion analysis. These include the equilibrium assignment models (for fixed demand and for elastic demand) based on the Wardrop-Jewell criteria.

The Wardrop-Jewell Criteria

47. Two objectives used to formulate theoretical models of traffic assignment that are responsive to congestion levels were given by Wardrop (1952) in a seminal paper on transport research. Wardrop's principles are: (1) drivers could select routes that minimise their own individual travel times, on the

basis that all other drivers are making their own individual decisions and that these decisions are made independently. Under the resulting flow patterns, all of the alternative routes used for a specified journey will have equal travel times, and these travel times will be less than those on any other possible route for that trip. The resulting flow pattern is stable, for no one driver can change route and gain any advantage by doing so. The resulting model is the 'individual travel time minimisation model' . This model provides a realistic simulation of present-day driver route choice behaviour. Alternatively,

(2) drivers could select routes so that the overall amount of travel (vehicle-hours of travel) in the network is minimised. This principle requires complete cooperation and sharing of information between drivers. It leads to a 'system travel time minimisation model' flow pattern with the minimum amount of total travel for the supplied (fixed) travel demand, but this flow pattern is unstable as individual drivers may find alternative routes that offer them quicker individual travel times. However, by taking this individual advantage, they will distort the flow pattern away from the theoretical solution, causing longer travel times for other drivers, who will then change routes - eventually the equilibrium solution of Principle (1) will be achieved! Thus an overall control on individual behaviour is required to maintain the minimum total travel time solution, which implies some social and political restrictions on travel.

48. The Wardrop principles may be treated as meeting different economic objectives for network travel, if travel time is taken as one possible alternative measure of travel cost.


Jewell (1967) expanded this argument by suggesting a third principle for traffic assignment: that the ultimate pattern of flow in a network will satisfy some explicit economic objective, for instance minimum generalised travel cost or minimum fuel consumption (both either individual or system-wide). Taylor and Anderson (1984) provided alternative solutions for a range of such objectives, including individual travel time minimisation, system widetravel time minimisation, individual fuel consumption and system-wide pollution emissions. An important consequence of the Wardrop-Jewell principles, clearly demonstrated by Taylor and Anderson (1984), is that the resulting flow patterns for the different objectives are quite different. Here is a dilemma for transport planning. The supply of travel information (such as travel conditions on different parts of the network) has been proposed as one future method to regulate congestion and improve overall travel conditions. This is likely to result in an attempt to generate flow patterns of the system-minimisation type. Yet these are unstable, and there is evidence that seeking such patterns may actually exacerbate congestion (e.g. Smith and Ghali 1990; Arnott et al. 1991).

Equilibrium Assignment Model (Fixed Demand)

49. The equilibrium assignment model is an expression of Wardrop's first principle (individual travel time minimisation). This model formulation provides a useful macroscopic simulation of travel on a metropolitan network. It may be written as the following non-linear optimisation problem, for which a convergent solution may be found (as indicated, for example, in Taylor (1984»:

q(.)

Z - min {E f ce(x)th} e 0

subject to the continuity of flow constraints

and

where

1 o

q(e) E ~etJr Xrij tjr

Vi, j

Vi, j

if and only if e is in path r from i to j, otherwise,

and the function ce(q) is. the travel time function for link e. The equivalent system-wide travel time minimisation problem may be written as a similar optimisation problem, with objective function


Z - min cE q(e) c.(q(e»} •

with the same conservation of flow constraints.

Elastic Demand Models

50. The fixed demand assignment models assume that the origin-destination trip matrix (Tjj ) is static, i.e. the pattern of trip movements from origins to destinations does not change. Now increased congestion increases the cost of travel between origin-destination pairs, and so the propensity for travel between different pairs may alter. This effect is seen in the formulation of the trip distribution models used to model the trip matrix. For example, consider the family of 'gravity ' models for trip distribution (destination choice) defined by Wilson (1967). For the case of the 'doubly-constrained' trip distribution model (one in which the row and column sums of the matrix are known a priori), this model is

This model includes two sets of constants (1\ and bj ), which have to be found in the calibration of the model. The models were combined by Evans (1976) to yield a joint model of destination and route choice that is responsive to differences in congestion levels. This combined model allows the number of trips Tjj to vary as congestion levels vary. Horowitz (1989) described an efficient solution algorithm for the combined assignmentdistribution problem.

The CENCIMM Model

51 . The network models described above are for application at the strategic level, where the network represents the main skeleton of the road system. Modelling applications more closely related to traffic management and control require the consideration of dense network models. The need for a dense network model is apparent in cases where, for instance, there is interest in what happens at specific intersections (e.g. turning movements flows and delays). Young, Taylor and Gipps (1989) described the characteristics of dense networks. The recently-developed CENCIMM dense network model is of particular interest. CENCIMM is a model of the central city traffic and parking systems, that allows study of the interaction between traffic flow and car parking and the build-up and dissipation of congestion. Taylor, Chambers and Young (1991) provided an introduction to CENCIMM and its applications.

CONCLUSIONS

52. Contemporary transport planning is focussing on issues of TDM, for environmental, social and economic reasons. A central part of TDM is concerned with the use of congestion management techniques as one means for achieving some of its goals. This paper considered the nature of traffic congestion and defined a set of parametric measures of the level of congestion in an urban road network. It suggested that there are a variety


of manifestations of congestion, which may be grouped into two basic classes: point congestion and network congestion. Point congestion is concerned with bottlenecks, i.e. site-specific constrictions on traffic capacity. The effects of bottlenecks are localised, although removal of an individual bottleneck may have important and sometimes severe repercussions across a surrounding network. Network congestion is an area-wide phenomenon, characterised by unstable flow conditions that may erupt at a variety of sites in an area, either at the link level or at the node level.

53. The use of natural or artificial congestion as a TOM control mechanism was examined, including congestion pricing. Rahmann's input-storage-output routing equation for interrupted traffic flows was used as the starting point in the theoretical consideration of traffic congestion. This led to a set of mathematical models that examine the effects of congestion. The paper thus provided a review of established theories of the build up and dissipation of congestion, including the Wardrop-Jewell models of traffic assignment in congested road networks and Evans' combined model of trip distribution and traffic assignment, and dense network models, which may be used as the basis of a TOM modelling strategy.

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LIST OF SYMBOLS

~ an origin-specific constant, found in Wilson's gravity models of trip distribution,

Aj the total number of trips finishing at destination j,

bj a destination-specific constant, found in Wilson's doubly-constrained gravity model,

c travel time (i.e. the time to traverse a network element),

cr running time, the component of travel time that a vehicle spends in motion,

Cs stopped time, the component of travel time for which a vehicle is stationary,

Co free-flow travel time (i.e. the minimum travel time on a network element),

C generalised travel cost (usually expressed in units of money),

CI congestion index (a dimensionless parameter),

d delay time,

f(Cij) an impedance function based on the travel cost from origin i to destination j,

Fs stopped fraction (the proportion of stationary vehicles in a traffic stream),

ill the number of arrivals to a queue in the time interval ilt,

J environmental factor in Davidson's travel time function,

k traffic density (vehicles per unit distance),

ilN the change in the size of the queue over the time interval ilt,

Pi the total number of trips originating at an origin i,

ilQ the number of departures from a queue in the time interval ilt,

q traffic volume (vehicles per unit time),

s standard deviation of travel time distribution,

S absolute capacity, the instantaneous maximum flow rate on a network element,

ilt a time interval,

Tij the number of trips from origin i to destination j,

u unit travel time (time per unit distance),

v overall travel speed (distance per unit time),

vr running speed (distance travelled divided by running tim\.!),

Vo free-flow travel speed (the average maximum speed),

Xnj the number of trips using path r between i and j,

a Zahavi's parametric measure of the kinetic energy of traffic flow,

y travel time variability ratio,

p mean velocity gradient,

o Dirac delta function

cr acceleration noise.


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