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8 Dynamics and Replacement of U.S. Transport Infrastructures NEBOJSA NAKICENOVIC This chapter uses several indicative examples to assess the time needed to build new and replace old transport infrastructures and energy transport systems. As the examples will show, both the growth and senescence of transport infrastructures evolve as regular processes, which are describable by S-shaped logistic curves. Not all growth and senescence phenomena can be described by simple logistic functions, however. Sometimes more complex patterns are observed, which are often described by envelopes that can be decomposed into a number of S-shaped growth or senescence phases. Two typical cases are (1) successive growth pulses with inter- vening saturation and a period of change, and (2) simultaneous substitution of m-ore than two competing technologies. In the first case, successive S- shaped pulses usually represent successive improvements in perfor- mance for example, aircraft speed records in which the first pulse is associated with the old technology, the piston engine, and the second with the new technology, the jet engine. In the second case, simultaneous substitution of competing technologies is usually described by increasing market shares of new technologies and decreasing market shares of old technologies. This chapter will demonstrate that the evolution of transport infrastructure can be described both by the performance or productivity of competing technologies and by their market share (see also chapter 71. For both of the cases just mentioned, it will be shown that the devel- opment of transport networks is subject to regular patterns of change, which can in principle be used for forecasting future trends. Most of the examples are taken from the United States because it is one of the few 175
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176 NEBOJSA NAKICENOVIC countries to have well-documented experience of most of the technological changes that have occurred over the last 200 years. Because most of these changes subsequently diffused throughout the world, the examples also indicate the dynamics of these processes elsewhere. In this chapter, the use of the term infrastructure is rather narrow, referring only to transportation and energy grids and networks, and other components of these two systems. These systems are interesting because they have played a crucial role in the economic and technological devel- opment process, are very capital intensive, and, in general, have long lifetimes. Analysis of the historical development of these two systems will include a quantitative description of performance improvement, the gen- eral evolution of a particular infrastructure, and the replacement of old technologies and infrastructures by new ones in terms of their relative market shares. The term performance is used as a multidimensional con- cept (i.e. as a vector rather than a scalar indicator), and, where appropriate, the size of an infrastructure is measured as a function of time. The first section of this chapter describes the evolution of transport systems and their related infrastructures. The analysis starts, somewhat unconventionally, with the youngest technologies, aircraft and airways, and ends with the oldest transport networks, canals and waterways. The second section describes the evolution of energy consumption and pipe- lines as an example of dedicated transport infrastructures; The appendix briefly describes the methods and statistical tests used for this analysis. TRANSPORTATION Aircraft Aircraft are the most successful of today's advanced modes of trans- portation. Other concepts of rapid transport such as high-speed trains have shown limited success, but they are not used as universally as aircraft. In fact, the rapid expansion of air travel during recent decades has its roots in the developments achieved in aerodynamics and other sciences many decades ago and especially in the engineering achievements made between the two world wars. The DC-3 airliner is often given as the example of the first "modern" passenger transport because in many ways its use denotes the beginning of the aircraft age. The use of aircraft for transportation has increased ever since, and their performance has improved by about two orders of magnitude (about a hundred times). Figure 8-1 shows the increase in air transport worldwide measured in billions of passenger-kilometers per year (pass-km/year). It includes all carrier operations, including those of the planned economies.
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U.S. TRANSPORT INFRASTRUCTURES 1 800 1 600 1400 1200 - _ - y a.' 1 000 - cn Q) u, (A cow ~800 o 600 400 l i/ At= 29yr 1940 1950 1960 1970 1980 1990 2000 Year FIGURE 8-1 Air transport worldwide, all operations. 177 The logistic function has been fitted to the actual data, and it indicates that the inflection point in the growth of air carrier operations occurred about 10 years ago (around 1977~. Thus, after a period of rapid exponential growth, less than one doubling is left until the estimated saturation level is achieved after the year 2000. The growth rate has been declining for about 10 years. If the projection here is correct, it will continue to do so until the total volume of all operations levels off after the year 2000 at about a 40 percent higher level than that experienced at present. Figure 8-2 shows the same data and fitted logistic curve transformed as X/(K -X), where x denotes the actual volume of all operations in a given year (from Figure 8-1, given in millions of passenger-kilometers per hour [pass-km/in]) and K iS the estimated saturation level. The data and the estimated logistic trend line are plotted in Figure 8-2 as fractional
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178 1n2 ~ Year FIGURE 8-2 World air transport, logistic plot. NEBOJSA NAKICENOVIC ~ - / / (K=200) ~ iB747 /\B707 ~ t = 29yr ~-B377 1 1 '1 1 1 1 1 1 1 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020 - 0.99 - - - _ _ 0.90 _ _ _ _ 0.70 0 IL 0.30 0.10 0.01 shares of the saturation level,f = X/K, which simplifies the transformation to/1 - A. Transformed in this way, the data appear to be on a straight line, which is the estimated logistic function.] Perhaps the most interesting result is that it took about 30 years for world air transport to reach the inflection point (about half of the estimated saturation levelly and that within two decades the saturation level will be reached. This raises a crucial question: What will happen after such a saturation? Can we expect another growth pulse, a decline, or the insta- bility of changing periods of growth and decline? Most likely a new period of growth associated with new technologies will follow the projected saturation. To understand the implications of a possible saturation in world air transport operations and future developments, one must look at the trans- port system in general, comparing aviation with other modes of transport, and analyze the various components of the air transport system itself. Aircraft, airports, and ground services are the most important components of the air transport infrastructure. The commercial aviation infrastructure differs, however, from the infrastructures of other competing transport systems such as roads or railways in that airports are not continuously connected physically as are pipelines, roads, and railroad stations.
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U.S. TRANSPORTINFRASTRUCTURES 179 The global fleet of commercial aircraft and how it developed can be described in a number of ways. An obvious descriptor of the fleet is the number of aircraft in operation worldwide. This number increased from about 3,000 in the l950s to almost 10,000 in the 1980s. During the same time, however, the performance or carrying capacity and speed of aircraft increased by about two orders of magnitude. Thus, the size of the fleet is not the most important descriptor, because much of the traffic is allocated to the most productive aircraft operating among the large hub airports while other aircraft constitute the feeder and distribution system for des- tinations with a lower traffic volume. The analogy between air transport systems and electrical grids or road systems is very close: large aircraft correspond to high-voltage transmission lines or primary roads. Figure 8-3 shows the improvement over time of one important perfor- mance indicator for commercial passenger aircraft: carrying capacity and speed (often called productivity) measured in passenger-kilometers per hour. Each point on the graph indicates the performance of a given aircraft when used in commercial operations for the first time. For example, the :, - 1o-1 // ( K= 1200} B747/, / / TU-144 B707 / . DCA130O 1011 DC-8' ·. Concorde TU-114~ ~ B527 DC 7 ·CV880 DC-7C- .;Caravelle L649,4 / DC-4/ · ·. CV340 DC-3 ~ / ~/ ·:/ 1o-3- / i/ 1 1 1920 1930 1940 1950 1960 1970 1980 1990 2000 2010 2020 At = 30.8 yr Lag = 9 yr Year / / _ 0.99 _ 0.90 _ 0.70 . - 0.10 0.01 . _ 0.001 0.50 O 0.30 ce 11 FIGURE 8-3 Passenger aircraft performance. Source of data: Angelucci and Ma- tricardi (1977), Grey (1969~.
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180 NEBOJSA NAKICENOVIC DC-3 was introduced in 1935 with a performance of about 7,400 pass- km/h (21 passengers at 350 km/h); the B-747 was introduced in 1969 with a performance of about 50O,000 pass-km/in (500 passengers at 1,000 km/ hi. The largest planned B-747s can carry almost 700 passengers. They are therefore about a hundred times as productive as the DC-3 50 years ago. The upper curve in Figure 8-3 represents a kind of performance fea- sibility frontier for passenger aircraft because the performance of all other commercial air transports at the time they were introduced was either on or below the curve. Long-range aircraft on the performance feasibility curve were commercially successful; all other planes, whether they were successful or not, are below the curve. Thus, at any given time there appears to be only one appropriate (best) productivity specification for long-range passenger planes. Because the more recent jet transports all fly at about the same speed, the appropriate design for a new long-range transport should allow for a capacity of more than 700 passengers. Ac- cording to the estimated curve, the asymptotic capacity for the largest aircraft is about 1,200 passengers at subsonic speed (1.2 million pass-km/ h or 10 billion pass-krn/yr). This implies that the next pulse in aircraft performance, if it occurs, would take place after the saturation phase. It would start at about 1.2 million pass-km/in and grow to much higher levels by at least one if not two orders of magnitude. Thus, after the year 2000, long-range aircraft might be larger and faster. Another interesting feature of Figure 8-3 is that the productivity of all passenger aircraft is confined to a rather narrow band between the performance feasibility curve and a "parallel" logistic curve with a lag of about nine years. This logistic curve represents the growth of world air transport from Figure 8-2. It took about 30 years for the performance of the most productive aircraft to increase from about 1 percent of the estimated asymptotic performance to about half that performance (for example, the DC-3 represents the 1 percent achievement level and the B-747 roughly the 50 percent mark). In many ways the achievement of the 50 percent level represents a struc- tural change in the development of the entire passenger aircraft industry and airlines. With S-shaped growth (that is, a logistic curve) the growth process is exponential until the inflection point or the 50 percent level is achieved. Thus, at the beginning, the productivity of aircraft is doubled many times within periods of only a few years. Once the inflection point is reached, however, only one doubling is left until the saturation level is reached. In Figure 8-3, for example, this development phase occurred in 1969 with the introduction of the B-747. Because the B-747 can, in principle, be stretched by about a factor of two, it could remain the largest
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U.S. TRANSPORTINFRASTRUCTURES 181 long-range aircraft over the next two decades. Thereafter, a new growth phase with either larger or faster long-range aircraft is conceivable; the more distant future may possibly see both. Before the inflection point, stretching does not help for more than a few years, given the rather frequent doublings in productivity. Conse- quently, new solutions are necessary. The necessity for new solutions also means that having a model that performs poorly on the market can be a crucial but nevertheless reversible mistake, provided the manufacturer is able to launch a new, improved performance model after a few years. After the inflection point, however, this strategy is no longer possible because those aircraft that are successful can be stretched to meet market demand through the saturation phase. Thus, in the late 1960s the introduction of new, long-range aircraft suddenly became riskier because it was no longer possible to launch a new model after a few years. The B-747, for example, had the appropriate productivity, whereas two other competitors, the DC- 10 and L- 101 1, were too small. The introduction of a 700- to 800-passenger aircraft in the near future would be risky because a stretched B-747 can do the same job; the introduction of a smaller long-range aircraft would probably fail because it would fall short of the primary market requirements. The only routes open to smaller, longer range transport such as the MD11 or Airbus 340 are those for which the B-747 is too large. In the long run, most of the long-range traffic will be between large hubs and will be less in the form of direct traffic between smaller airports. The market niche for long-range aircraft with fewer than 500 passengers will therefore be very limited. A feasible alternative might be to redesign the MD11 and the Airbus 340 as wide-body, shorter range transports suitable for frequent cycles. The design of a cruise supersonic aircraft able to carry 300 to 400 passengers, or a hypersonic transport able to handle 200 to 300 passengers, may therefore be a better strategy for the first years of the next century. To some extent, these principles also explain why the Concorde cannot be a commercial success: with a capacity of 100 passengers, it is 150 passengers short of being a serious competitor for the B-747. How probable is the development of a large cruise supersonic or hy- personic transport? S-pulses do not occur alone but usually in pairs. Thus, at saturation, structural change will occur, leading to a new growth pulse (probably S-shaped) and in turn to new productivity requirements and therefore to supersonic or hypersonic transport. The alternative is that air transport will saturate pe~anently over the next few decades, and the wide-bodied families of subsonic transports will actually constitute the
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182 1ol 10° 10 1_ 10 - 2 NEBOJSA NAKICENOVIC 1o2 ·/ :, - Jets Pistons (hp.) Max Thrust (kg)~ ( ~ = 3800) ( K = 29,000) - ~- 1936 / ~k. . ~ -~9 = · ~ . . 1966 ·/ I/ 30 yr-/ i hit= 30yr . , , , , , , , 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 Year . - 0-99 0.90 - y 0.70 ~ - 0.50 0 0.30 0.10 - 0.01 FIGURE 8-4 Performance of aircraft engines. Source of data: Angelucci and Ma~icardi (1977), Grey (19691. asymptotic technology achievement. This alternative is unlikely, however, because air transport may become the dominant mode of passenger (long- distance) travel in the next century. Figure 8-4 shows the improvement in the performance of civil aircraft engines since the beginning of aviation. The first piston engine visible on the plot is the French Antoinette engine, rated at 50 horsepower (hp.) in 1906, and the last is the American Wright Turbo Compound, rated at 3,400 hp in 1950. These engines represent an improvement in power of almost two orders of magnitude over 44 years and about 90 percent of the estimated saturation level for piston engines (about 3,800 hp.). A parallel development in the maximal thrust of jet engines follows with a lag of about 30 years, starting in 1944 with the German Junkers Juno 004 (rated at 900 kg) and ending with the American Pratt and Whitney JT9D in the early 1980s with 90 percent of the estimated thrust saturation level at about 29,000 kg. Both pulses in the improvement of aircraft engines are characterized by a time constant (fit) equal to about 30 years. The midpoints (inflection points) of the two pulses, which occurred in 1936 and 1967, respectively, coincided with the introduction of the DC-3 and
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U.S. TRANSPORTINFRASTRUCTURES 183 the B-747. In fact, the Pratt and Whitney Twin Wasp, introduced in 1930, became the power plant for the DC-3. This engine also served as the basis for subsequent and more powerful derivatives such as the Wasp Major introduced in 1945 toward the end of the aircraft piston engine era. Thus, certain parallels are evident in the dynamics of passenger aircraft development beyond the obvious similarity in the time constant (/\t = 30 years). Those engines introduced slightly before the inflection point, such as the Twin Wasp, are "stretched" by doubling the cylinder rows to increase the power. In the Wright Turbo Compound, representing the last refinement in aircraft piston engines, turbocharging was used to derive shaft power. Otherwise, the engine was a direct derivative of the Wright Cyclone series introduced in the early 1930s with Cyclone 9 (which orig- inally powered the DC-24. The time constant for the development of passenger aircraft is therefore about 30 years. Thirty years after the standard industry design emerged during the 1930s, the B-747, the first wide-body jet to enter service, became one of the most significant improvements in commercial transport, and its productivity represents half of the estimated industry saturation level that may be approached toward the end of this century. Thus, within a period of 60 years the life cycle will be completed: from standardization and subsequent rapid growth characterized by numerous improvements through the inflection point, when the emphasis changes to competition characterized by cost reductions and rationalization. These characteristics of the industry, including steady improvement in performance, are well illustrated by the development of the B-747 family. The emergence of a new aircraft engine at the beginning of a new phase of growth is very likely toward the end of the century after the projected saturation has been reached. Furthermore, the characteristics of the long- range aircraft in this hypothetical growth pulse are implicit in this analysis. The saturation in the thrust of turbojet and turbofan engines indicates that a new generation of engines will emerge over the next few decades, a generation having much higher thrust ratings and growth potential. The only realistic candidates are the ramjet or scram engines with efficient off-design flight engine characteristics, or perhaps the HOTOL-type air- breathing rocket engines. Thus, a new pulse in the improvements of aircraft engines will most likely be associated with some variant of the variable- cycle air-breathing engine with a high Mach number and perhaps even ballistic flight potential. This trend would single out methane as the fuel of choice between Mach 3.5 and Mach 6, with a small overlap of hydrogen starting at Mach 5. Thus, cryogenic methane-powered cruise supersonic aircraft may become the mode of transport with the highest productivity after the year 2000.
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184 NEBOJSA NAKICENOVIC The Automobile At the beginning of this century, few proponents of the automobile envisaged that its use would spread as rapidly as it did throughout the world. As a commercial and recreational vehicle the motor car offered many advantages over other modes of transportation? especially animal- drawn vehicles. Perhaps the most important advantage was the possibility of increasing the radius of business and leisure transport. At first the railroads were not challenged by the automobile. Rather, railroads helped the spread of the automobile by offering efficient long- distance transport that combined well with the use of motor vehicles for local urban and rural road transport. Within a few decades, however, the automobile had become an important form of transport for both local and long-distance passenger travel in the United States. Since the 1930s the total mileage traveled by motor vehicles in general has been divided almost equally between rural and urban travel. The automobile had a relatively late start in the United States in relation to European countries (for example, France, Germany, and the United Kingdom). According to the records, four motor vehicles were in use in the United States in 1894. This was followed, however, with an impressive expansion of the automobile fleet: 16 vehicles in 1896; 90 in 1897; 8,000 in 1900; almost 500,000 10 years later; and more than 1 million after another 2 years. Thus, the United States quickly surpassed the European countries both in production and in the number of vehicles in use. Figure 8-5 shows the rapid increase in the number of cars used in the United States. The automobile fleet is characterized by two distinct secular trends, with an inflection in the 1930s followed by less rapid growth rates. Because the two secular trends of the curve appear to be roughly linear on the logarithmic scale in Figure 8-5, the automobile fleet evolved through two exponential pulses. Thus, in this example the growth of the automobile fleet did not follow a simple, single S-shaped growth pulse. The working hypothesis in this case is that the two trends indicate two different phases of the dissemination of motor vehicles in the United States. The first characterizes the substitution of motor vehicles for horse-drawn road vehicles, and the second the actual growth of road transport after animal-drawn vehicles essentially disappeared from American roads (see Nakicenovic, 19861. Only after the completion of this substitution process did the automobile emerge as an important competitor of the railroads for the long-distance movement of people and goods and perhaps as a com- petitor of urban transportation modes such as the tram, subway, or local train. Thus, the first expansion phase was more rapid because it represents a "market takeover" or expansion in a special niche; the second represents
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U.S. TRANSPORTINFRASTRUCTURES 105 _% cn ° 4 _' in .~ o 3 a) 10 Q 1o2 1o1 1 850 ~, /' Cars - Horses _~: - - 185 - / 1 900 1950 2000 Year FIGURE 8-5 Number of road horses and mules and automobiles in the United States. the actual growth of the road vehicle fleets and their associated infra- structures. The lack of historical records of the exact number of horse-drawn vehicles in the United States soon after the introduction of the automobile in 1895 makes it difficult to describe accurately the assumed substitution of the motor car for the horse during the first, more rapid expansion phase of the motor vehicle fleets. The number of draft animals (road horses and mules) and automobiles given in Figure 8-5 therefore are a rough ap- proximation of this substitution process. Horse and saddle were sometimes used as a "road vehicle," but often more than one horse was used to pull buggies and wagons. City omnibuses used about 15 horses in a single day, and a stagecoach probably used even more because the horses were replaced at each station. Figure 8-5 therefore may exaggerate the number of horse-drawn vehicles if the number of draft animals is used as a proxy for the number of vehicles actually in use. On the other hand, farm work animals are not included in Figure 8-5, although certainly they were also used for transport, especially in rural areas. Although estimates of nonfarm horses and mules are not very accurate and are unevenly spaced in time, Figure 8-6 indicates that the automobile replaced horse- and mule-drawn road vehicles during a relatively short period and that the substitution process proceeded along a logistic path.3
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U.S. TRANSPORT INFRASTRUCTURES 211 () 1 +exp(-~t-~) (1) where t is the independent variable usually representing some unit of time, and a, is, and K are the unknown parameters. Alternatively, the logistic growth curve can be expressed as a linear function of time by moving the (usually) unknown parameter K to the left side of the equation and taking logarithms of both sides: in ~ (r) ~ ~ = cat + (2, This is a convenient form for showing the logistic growth process on semilogarithmic paper because the historical data indicate a linear secular trend (assuming that K can be estimated from the data or that it is a priori known). The three parameters are interpreted as follows in terms of the under- lying growth process: ~ denotes the rate of growth; ~ is the location parameter (it shifts the function in time, but it does not affect the function's shape); and ~ is the asymptote that bounds the function and therefore specifies the level at which the growth process saturates (as t tends to infinity, x(t) approaches K). Thus, all three parameters have clear physical interpretations, although the values of ~ and ~ are not necessarily clear intuitively. The logistic function is a symmetrical S-shaped growth function, with an inflection point, to, at which the growth rate reaches a maximum, x~to) -CX K/4. Symmetry implies that the value of the function is half the asymptote at the point of inflection, ditto) = K/2. Thus, the location parameter of the function can be defined as the point of inflection, to = -Q/c~, or, alternatively, as the time when 50 percent of the saturation level K is reached. The growth rate of the function can be defined alter- natively as the length of the time interval needed to grow from 10 to 90 percent of the saturation level a. The length of this interval is At = (ln 81~/~. This second set of parameters K, /\t, and to also specifies the logistic growth curve (in the same way that K, CX, and ~ do), but these alternative parameters have, in addition, clear intuitive interpreta- tions. A nonlinear least-squares regression method was used to estimate the three unknown parameters of the logistic function from the empirical observations. Alternative estimation algorithms were then used to test the sensitivity of the estimated parameter values to different assumptions about the errors and weighing of observations.6 The estimation methods used in the analysis are reported in Grubler et al. (19871. The values of the estimated parameters for the logistic growth processes, =
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312 NEBOJSA IVAKICENOVIC as well as the correlation coefficient R2 and uncertainty ranges for the parameters, are given in Table 8-1. Estimation of the uncertainty ranges is based on a Monte Carlo simulation approach by Debecker and Modis (1986) for the three-parameter logistic function. A total of 33,693 different S-curves were generated and subsequently fitted by the logistic function providing values for K, At, and to, with known and varying distributions of statistical fluctuations. Debecker and Modis concluded that the value of the estimated asymptote K is the most sensitive (it varies the most), depending on the amount and accuracy of the data available. Their results indicated that as a rule of thumb the uncertainty of parameter K will be less than 20 percent within a 95 percent confidence level, provided that at least half of the data are available (at least up to the point of inflection) and that they are at least 10 percent accurate. A more comprehensive treatment of uncertainty ranges and estimation methods is given in Grubler et al. (19871. In all cases, except Figure 8-18, the values of the estimated parameters were within the specified uncertainty ranges. Even alternative algorithms used to estimate the parameters provided values within the specified ranges. The Technological Substitution Models and Parameter Estimates In general, the examples of technological substitution are inherently more complex than the determination of single logistic growth pulses. From a statistical point of view, however, the estimation of substitution processes is much simpler. By setting K = 1, a three-parameter logistic function x~t) can be normalized by setting fats = X(t)/K. For given values of K, it then reduces to a function with two unknown parameters. In the examples of technological substitution, this known asymptote specifies the size of the "market" in which old technologies are replaced by new ones. In the simplest case, there are only two technologies. The market shares are fate for the new technology and 1 - fats for the old technology (Fisher and Pry, 19711. Thus, only the values of to and At must be determined from the observations. Fisher and Pry used the two-parameter logistic function to describe a large number of technological substitution processes. They assumed that once substitution of the new for the old had progressed as far as a few percent, it would proceed to completion along a logistic substitution curve fats At ~ = at + ~ (3) Ordinary least squares were used to estimate parameters At and to in
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213 o ._ C) . ~ Cal ._ o so an en a' An: Cal Cal U) a a ~0 1 y y ._ ~4 .= 00 ~ ~ 00 ~ - O of ~ AN ~ ~ Cal ~ cry ~ cut ~ as . . . . . . . . . . . . . O O O O O O O O O O O O O t~ ,~ _ ~ ~ ~ 00 0 - ~ ~ ~ ~ C~ ~ C~ ~ ~ 0 ~ ~ ~ ~o cr~ ~ c~ ~ a~ ~ ~ oo 0 oo o~ ~_______4~____ 00 00 0 ~ ~ ~ ~ ~ 00 \0 . . . . . . . . . . O O ~ O O ~ - ~ ~ O +1 +~ +1 +1 +~ tl t~ tl +I tl _~ ~ oo ~ . . o -_ _ Z +1 +1 O O oo ~ ~D ~ ~ O oo cr c~ r~ ~ . . . . . . . . . . . . . 0 0 0 ~ ~ ~ 00 ~ r~ oo a~ oo O ~N _ 1 ~ U~ U~ ~ o ~ . . . . . . ~ o ~ ~ o ~ a~ - ~\ ~ - t- tl tl +1 +1 +I tl oo ~ - ~ a~ . ~_ . ~_ . . _ o ~ oo ~ oo _ _ st ~ C: - t l z - Z t l ~ ~ o oo oo ~ ~ C~ oo ~ oo . . . . . . . . . . . oo o oo ~ C~ ~ C~ oo ~o oo oo ', oo _ - o ~ oo ~ ~ ~ ~ ~ o ~ ~ ~ _ - , oo ~'t - CN ;^ =: ~ ~ ~ ~ ~ ~.> o o o ~ ~ o o o ~o ~ o _ _ _ =( _, _ _ _ `_ ~ ~ ~ _ o - ~ ~ oo oo - ~ ~ ~ d" ~ - _ _ _ _ _ _ 1 1 1 1 1 1 ~ 1 1 1 1 1 1 oo oo oo X ao oo oo oo oo oo oo oo oo .= . ~ .= .° o o Ct Ct ~ ·_ - ;> - oo ._._ C~ s~ C~Ct C~U: ._ ~ ~ . _ C =4 · - 3 ~ ~: Co4 .C .° C~ e~ - O ~ ~ U - ;> C)
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214 NEBOJSA lVAKICElVOVIC all cases in which one old technology is replaced by a new. Table 8-2 gives the estimated parameter values, the estimation period, and the cor- relation coefficients for the three examples given in this chapter. In dealing with more than two competing technologies, a generalized version of the Fisher-Pry model was used because logistic substitution cannot be preserved in all phases of the substitution process. Every given technology undergoes three distinct substitution phases: growth, satura- tion, and decline. The growth phase is similar to the Fisher-Pry substi- tution, but it usually ends before complete market takeover is reached. It is followed by the saturation phase, which is not logistic but which en- compasses the slowing of growth and the beginning of decline. After the saturation phase of a technology, its market share declines logistically (for example, see the path of railway and road substitution in Figure 8-14 and coal substitution in Figure 8-171. It is assumed that only one technology saturates the market at any given time, that declining technologies fade away steadily at logistic rates "uninfluenced" by competition from new technologies, and that new technologies enter the market and grow at logistic rates. The current saturating technology is then left with the residual market share and is forced to follow a nonlogistic path that curves from growth to decline and connects its period of logistic growth to its subsequent period of logistic decline. After the current saturating technology has reached a logistic rate of decline, the next oldest technology enters its saturation phase, and the process is repeated until all technologies but the most recent are in decline. For example, n competing technologies are ordered chronologically according to their appearance in the market, technology 1 being the oldest and technology n the youngest (i.e., i = 1, 2, . . ., n). Thus, all technologies with indices k, where k < j, will saturate before the tech- nology with index j, and technologies 1, where I > j, will saturate after technology j. The historical time series is denoted by aft), where the indices i = 1, 2, . . ., n represent the competing technologies and t the time points (year, month, etc.) of the historical period for which data are available. The fractional market shares of competing technologies, fi (t), are obtained by normalizing the sum of the absolute shares to one: x;(t) jets (4) By applying the linear transform of the logistic function to the fractional market shares,
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215 l o ._ ~_ C~ ._ U: ._ C~ o OCR for page 216
216 NEBOJSA l!lAKICENOVIC (I) l [ f (') ] (s) a transformed time series with piecewise linear secular trends can be obtained. In fact, only three distinct possibilities exist: a decreasing or an increasing linear trend or a phase of linear increase that is connected by a nonlinear saturation phase to a phase of linear decline. The oldest tech- nology (i = 1) always displays a declining linear trend, and the youngest technology (i = n) an increasing linear trend (see Figure 8-17). These linear trends can be estimated, including the increasing linear trends of technologies that enter the saturation phase during the historical period. Ordinary least squares were used to estimate the linear trends for each competing technology. Table 8-2 gave the estimated parameter values for the three multiple substitution processes used here, as well as the esti- mation period (historical time interval for which the parameters were estimated) and the correlation coefficient. Parameter values were not given for cars in Figure 8-15 because they have been saturating during the entire historical period. Consequently, their substitution path is specified by the model. Each estimated linear equation with estimated parameters At and to can be transported into a logistic function with coefficients ~ and ¢: 1 + exp(-ait- Pi) (6) where f(t) is now the estimated fractional market shares of technology i. Because such a logistic function does not capture the saturation phases and represents only growing or declining logistic trends, n Ifi(t) i=1 may exceed 1 for some value of t, although it must be equal to 1 for all t. Thus, the n- 1 estimated logistic equations were left in their original form (6) that is, as specified by coefficients Hi and Pi and one of the n equations was defined as a residual 1 Aft) = 1 ~j 1 + exp (-cxit-Qi) (7) that is, as the difference between 1 and the sum of the n- 1 estimated market shares f(t). The latter equation represents the oldest still growing technology, j, such that of ' 0 where off_ ~ 1. The selected technology cannot, however, be the oldest technology (i.e., j ~ 1), be- cause the oldest technology is replaced by the newer technologies and,
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U.S. TRANSPORT INFRASTRUCTURES 217 consequently, its market shares decline logistically from the start (i.e., ox < 01. Thus, initially, there are n- 1 technologies denoted by indices i ~ j that follow logistic substitution paths, and one technology, j, that reflects the residual of the market that is, the complement of the sum of other technologies and 1. Based on the point in time, tj, at which technology j is defined as a residual, application of the linear transform of the logistic function to the market shares of technology j, defined above, produces a nonlinear function that can be written in the form of equation (59. This function has a negative curvature. It increases, then passes through a maximum at which technology j has its greatest market penetration, and finally decreases. After the slope becomes negative the curvature dimin- ishes for a time, indicating thatfj~t) is approaching the logistic form. But then, unless technology j is shifted into its period of logistic decline, the curvature will begin to increase as newer technologies acquire larger mar- ket shares. Phenomenological evidence from a number of substitutions suggests that the end of the saturation phase should be identified with the point at which the curvature of yet), relative to its slope, reaches its minimum value. This criterion is taken as the final constraint in this generalization of the substitution model, and from it the coefficients for the jth technology in its logistic decline are determined. Thus, the point in time at which the rate of decrease of yet) approximates a constant is determined. From this point on, the rate of change is set equal to this constant, thereby defining a new logistic function. This point of constant slope is approximated by requiring that the relative change of slope is minimal, y (t) .~( ~ = minimum (8) for tj ' t < te' yet) < 0, and yet) < 0. If this condition is satisfied (the point in time at which this occurs is tj~ ~ > tj), the new coefficients for technology j can be determined as ~j=yj~tj+l, and (9) A = yj~tj+~)-yj~tj+~)tj+~. (10) After time point tj, technology j + 1 enters its residual phase. The process is then repeated until either the last technology n enters the sat- uration phase or the end of the time interval (te) is encountered. These expressions, which have been developed in algorithmic form, determine the temporal relationships between competing technologies.
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218 NEBOJSA A7AKICENOVIC | PENE (fj(t), c;, Bj, iYo, no) | t, -1901 +iyo+no | t: - 1900 + iyo J I t:-t+1 1 i , NO ~ ~ YES tr ~) Y | f`(t)-1/(1+exp( ~;'t-§j)) | NO /: YES fj(t) $~: ~t)] 2 _ y "(t) ~ y (t) aj ~ y'(t) ,Bj ~ y(t) - y'(t) · t _ \/ ~ (t)~1 - :: f`(t) L: l°g [fj(t)/(1 - fj(t))] FIGURE 8-20 Flowchart of the logistic substitution algorithm. Figure 8-20 is a flowchart of the algorithm that describes the logistic substitution process. A more detailed description of this procedure and the software package for the generalized logistic substitution model is given in Nakicenovic (1979, 1984~.
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U.S. TRANSPORTINFRASTRUCTURES 219 NOTES 1. One general finding of a large number of studies is that many growth processes follow characteristic S-shaped curves. A logistic function is one of the most widely applied S-shaped growth curves and is denoted by X/(K - X) = exp(cxt + Q), where t is the independent variable usually representing some unit of time; a, if, and K are constants; x is the actual level of growth achieved; and K - X iS the amount of growth still to be achieved before the (usually unknown) saturation level K is reached. Taking logarithms of both sides results in the left-hand side of the equation being expressed as a linear function of time so that the secular trend of a logistic growth process appears as a straight line when plotted in this way. Substituting f = X/K in the equation expresses the growth process in terms of fractional share f of the asymptotic level K reached- that is, the equation becomes[(1 - f) = exp(at + B). 2. This period of elapsed time we call At, and we define it as the time elapsed between the achievement of 1 and 50 percent of the saturation level K (in this example At = 30.0 yr). Given the symmetry of the logistic function the same time is required for the increase from 50 to 99 percent of the saturation level. An alternative definition of At is the time elapsed between the achievement of the 10 and 90 percent level. This definition of At differs slightly from its first definition, but for all practical applications both definitions can be used interchangeably. 3. A large number of studies have found that the substitution of a new technology for an old one, expressed in fractional terms, follows characteristic S-shaped curves. Fisher and Pry (1971) formulated a simple but powerful model of technological substitution by postulating that the replacement of an old technology by a new one proceeds along the logistic growth curvef/(1 -f) = exp(cxt + p) where t is the independent variable usually representing some unit of time, ~ and ~ are constants, f is the fractional market share of the new competitor, and 1 - f is that of the old one. 4. The fractional shares (f) are not plotted directly but as the linear transformation of the logistic curve that is, p( 1 - f ) (in this more general cases if is the fractional market share taken by a given energy and (1 - f) is the sum of the market shares of all other competing transport infrastructures). This form of presentation reveals the logistic sub- stitution path to be an almost linear secular trend with small annual perturbations. Thus, the presence of some linear trends in Figure 8-14 indicates where the fractional substi- tution of transport infrastructures follows a logistic curve. In dealing with more than two competing technologies, the Fisher-Pry model must be generalized because in such cases logistic substitution cannot be preserved in all phases of the substitution process. Every competitor undergoes three distinct substitution phases: growth, saturation, and decline. This process is illustrated by the substitution path of railway tracks, which curves through a maximum from increasing to declining market shares (see Figure 8-14). In the model of the substitution process, it is assumed that only one competitor is in the saturation phase at any given time, that declining technologies fade away steadily at logistic rates, and that new competitors enter the market and grow at logistic rates. As a result the saturating technology is left with the residual market shares (i.e., the difference between one and the sum of fractional market shares of all other competitors) and is forced to follow a nonlogistic path that joins its period of growth to its subsequent period of decline. After the current saturating com- petitor has reached a logistic rate of decline, the next oldest competitor enters its saturation phase, and the process is repeated until all but the most recent competitor are in decline. A more comprehensive description of the model and assumptions is given in Nakicenovic (1979).
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220 NEBOJSA NAKICENOVIC 5. As in Figure 8-14, the fractional shares f are not plotted directly but as the linear transformation of the logistic curve that is, f/(1 - f ) (as the ratio of the market share taken by a given energy source over the sum of the market shares of all other competing energy sources). The form of presentation in Figure 8-17 reveals the logistic substitution path as an almost linear secular trend with small annual perturbations. Thus, the presence of some linear trends in Figure 8-17 indicates where the fractional substitution of energy sources follows a logistic curve. 6. In this particular application the difference was in the assumptions about weighing of the observations in the estimation procedure for example, whether unit- or data- dependent weights are used. BIBLIOGRAPHY Angelucci, E., and P. Matricardi. 1977. Practical Guide to World Airplanes, vols. 1-4. Milan: Mondatori (in Italian). Debecker, A., and T. Modis (Digital Equipment Corporation, Geneva, Switzerland). 1986. Determination of the uncertainties in S-curve logistic fits. Paper submitted to the Sixth International Symposium on Forecasting, Paris, June 15-18, 1986. Epstein, R. C. 1928. The Automobile Industry, Its Economic and Commercial Develop- ment. Chicago: A. W. Shaw Co. Fisher, J. C., and R. H. Pry. 1971. A simple substitution model of technological change. Technological Forecasting and Social Change 3:75-88. Grey, C. G., ed. 1969. Jane's All the World's Aircraft. London: David and Charles Publishers. Grubler, A., and N. Nakicenovic. 1987. The Dynamic Evolution of Methane Technologies. WP-87-2. Laxenburg? Austria: International Institute for Applied Systems Analysis. Grubler, A., N. Nakicenovic, and M. Posch. 1987. Algorithms and Software Package for Estimating S-shaped curves. Laxenburg, Austria: International Institute for Applied Sys- tems Analysis. Marchetti, C. 1979. Energy systems the broader context. Technological Forecasting and Social Change 14:191-203. Marchetti, C. 1983. The automobile in a system context, the past 80 years and the next 20 years. Technological Forecasting and Social Change 23:3-23. Marchetti, C. 1986. Fifty-year pulsation in human affairs, analysis of some physical in- dicators. Futures (June):376-388. Marchetti, C., and N. Nakicenovic. 1979. The Dynamics of Energy Systems and the Logistic Substitution Model. RR-79-13. Laxenburg, Austria: International Institute for Applied Systems Analysis. Martino, J. P. 1983. Technological Forecasting for Decision Making;. 2d ed. New York: North-Holland. Nakicenovic, N. 1979. Software Package for the Logistic Substitution Model. RR-79-12. Laxenburg, Austria: International Institute for Applied Systems Analysis. Nakicenovic, N. 1984. Growth to Limits, Long Waves and the Dynamics of Technology. Ph.d. dissertation. University of Vienna. Nakicenovic, N. 1986. The automobile road to technological change, diffusion of the automobile as a process of technological substitution. Technological Forecasting and Social Change 29:309-340. Reynolds, R., and A. Pierson. 1942. Fuel Wood Used in the United States, 1630-1930. U.S. Department of Agriculture, Forest Service Circular No. 641.
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U.S. TRANSPORTINFRASTRUCTURES Schumpeter, J. A. 1935. The analysis of economi 7:2-10. Schurr, S., and B. Netschert. 1960. Energy in the American Economy, 1850-1975: An Economic Study of its History and Prospects. Baltimore, Md.: Johns Hopkins University Press (for Resources for the Future, Inc.). Taylor, G. R. 1962. The Transportation Revolution, 1815-1860. Vol. 4, The Economic History of the United States. New York: Holt, Rinehart and Winston. U.S. Department of Energy. 1982. Monthly Energy Review, August 1982. DOE/EIA- 0035(82/08). Washington, D.C.: Energy Information Administration. U.S. Forest Service. 1946. A Reappraisal of the Forest Situation, Potential Requirements for Timber Products in the United States. Forest Service Report No. 2. 221 c change. Review of Economic Statistics
Representative terms from entire chapter: