Scientific Proceedings of RTU. Series 7. Telecommunications and Electronics, 2002
TRANSPORT INTELLIGENT SYSTEMS COST/PERFORMANCE
RESEARCH IN RELATIONSHIP WITH HARDWARE PARAMETERS
V. Bistrov, E. Peterson
Keywords: PC, performance, cost, clock frequency of processor, volume of RAM
The infrastructure of transport intelligent systems contains a large number of computers
incorporated in telecommunication networks. Minimizing expenses is necessary to update and
create a given infrastructure. This work offers an approach to minimize computers costs in these
networks through the optimization of computers parameters. The optimization of such systems is
a process for achieving maximum performance of the systems with minimal costs.
The well-known Grosch law was formulated in 1953 when specialists tried to find the
relationship between cost and performance. According to this law, performance of computer
systems is proportional to cost to the second power .
Later, a new law was formulated . It IS ASSOCIATED WITH computer system costs and its
parameters. A modified form of this is:
B0 – permanent part of cost, V - volume of RAM, D – volume of HD, Ei – other influenced
factors, B1, B2, βi – coefficients.
Personal computers (PCs) are nowadays widely used in transport intelligent systems. The authors
of this paper decided to research this class of computer systems in order to find the relationship
between a PC’s performance and its cost. To achieve this goal we analyzed, PC test data given
by D. Belaev . These PCs are built on Intel Pentium processors.
Performance characteristic of computer systems
Each system in  is described by four parameters. These parameters include the clock
frequency of the processor, the volume of RAM, the overall computer performance and costs.
The system performance as indicated by the function of clock frequency, the processor and the
volume of RAM are represented by surface in three-dimensional space, shown in Figure 1. The
surface is formed by a number of points. Each point characterizes a system state. A system state
is defined by two independent parameters: the clock frequency of the processor, the volume of
RAM and the computer system (CS) performance that is the third parameter. The method of
Delaunay triangulation of data is chosen for surface interpolation. This method is applied to
functions with irregular distributed argument approximation. Three-dimensional interpolation
dependence is shown in Fig. 1.
The points on the surface, which are marked by circles, characterize the systems that are actually
tested. The other points are obtained with the help of interpolation. The shape of the surface
describes possible performance change. Figure 1 illustrates known performance dependence on
clock frequency of the processor and volume of RAM. The greatest performance increase is
observed from the point that describes the system with minimal values of parameters, to the
point that describes the system with maximal values of parameters. However, this path is not
Fig. 1. The Relationship between performance of CS, clock frequency and volume of RAM.
We found that a decrease in performance is observed during increasing values of parameters.
The decrease in performance is caused by non-optimal selection of parameter values. These
systems are non-effective. For this reason, it is necessary to know the functional relations
between the parameters of CS and its performance and cost.
The Relation between parameters of computer systems of equal cost and performance
These relations are found with the help of additional number of points that are obtained as a
result of data interpolation. CSs that participate in testing are marked with circles
(Fig. 2-3). Curves are shown in pairs. The one curve in pair leads to a rough approximation; the
other curve, a precise approximation. The difference between them is the different number of
points used during interpolation.
The following abbreviations are used in this paper. C- CSs’[CS] cost, P- CSs’ performance, F-
clock frequency of processor, V- volume of RAM.
The functional dependencies between system parameters are not monotonous, as shown in Fig.
2 (see the functional curve P=75). The relations between clock frequency and volume of RAM
are hyperbolic for larger values of performance.
Analytic description of curves for systems of equal performance is:
V = +V0 (1)
F − Fo
where G – permanent coefficient;
Fo – minimal value of clock frequency defined for equal performance systems
Vo – minimal volume of RAM defined for equal performance systems
In addition, functional curves for systems of equal cost are represented. The most convenient
expression for description of these curves is:
where A and B – permanent coefficients defined for equal cost systems.
Unknown coefficients in expression 1 and 2 may be defined. For example, the unknown
coefficients of expression 1, calculated for systems with equal performance P=85, are:
G = 341 MB / MHz; Fo = 853 MHz; Vo= 82 MB.
Fig. 2. Relationship between parameters of equal performance systems
Fig. 3. Relaationship between parameters of equal cost systems
The analytical curves (shown in Fig. 4) are built in accordance with expression (1) and
calculated coefficients. The experimental curve also is represented in Fig. 4.
Unknown coefficients in expression 2 for systems with equal cost C=250 are:
A=1.3 MB/MHz; B=1396.6 MB.
Summarizing the result obtained at this stage, we can state that:
- relationships between volume of RAM and clock frequency of processor are hyperbolic for
equal performance systems;
- relationships between volume of RAM and clock frequency of processor are quasi linear for
equal cost systems.
Fig. 4. Relationship between clock frequency and volume of RAM for equal performance
The purpose of additional research is obtaining the relation between performance and cost of CS.
Relations between performance and cost for systems with equal clock frequencies
Interpolation dependencies for several systems with fixed equal clock frequencies, but with
different RAM values are shown in Fig. from 5th to 8th.
Systems with clock frequency F=866 MHz and F=933 MHz have analogous to other shapes of
functional dependencies. There are two curves shown in each figure (see Fig. 5-8): the first is
obtained with the help of experimental data  (broken line); the second is the result of
interpolation. The second line crosses the broken line in the points of changing volume of RAM.
The shape of functional relationships (Fig. 5-8) is the same. The saturation of functions is
characteristic for these relationships. The points, where curves achieve saturation characterize
systems with optimal configuration. Actually, it is not reasonable to increase the volume of
RAM and hence waste money if performance will not increase. For such systems these
functional dependencies may be expressed with standard functions:
P ( F ) = −(a − ( C −C0 ) ) + P0( F ) , (3)
where a=1.0 ÷1.4.
The upper index of argument C and P (in expression 3) means the fixed clock frequency of the
processor for which this expression is obtained.
P0 – the function P saturation value defined for fixed clock frequency,
C0 – cost value of system with optimal configuration.
Fig. 9. Relations between system performance and cost for systems with fixed clock
frequency of processor.
We will define values of parameters a, C0, P0 for several systems with fixed clock frequency.
If F=733 MHz, then a =1.15, P0=80, C0=164;if F=800 MHz, then a =1.11, P0=79, C0=192;
if F=933 MHz, then a =1.2, P0=94, C0=248.
Analytical (functional) curves are built in accordance with expression (3) and calculated
unknown coefficients. The result is shown in Fig. 9. The analytical expressions for these curves
P 850 = −(1.16 − ( C − 218) ) + 82
P 750 = −(1.15 − ( C −163) ) + 76
Summarizing the result obtained at this stage, we can state that if volume of RAM continuously
increases, CSs’ performance will approach to the threshold value.
Relations between performance and cost for systems with optimal configuration
From the analysis presented, it follows that the optimal volume of RAM is defined for each
system with a fixed clock frequency. In such systems performance of CSs will not increase,
while the volume of RAM will increase. This system configuration (fixed clock frequency,
optimal volume of RAM) is optimal. We may thus define the relation between performance and
cost for these systems. Relations both experimental and analytic are shown in Fig.10.
Clock frequency of processor (MHz) / volume of RAM (Mb) are shown in brackets in Fig. 10.
For example, the value of clock frequency is 800 MHz and the volume of RAM is 128 Mb for
the fourth system. Thick lines are approximation curves describing the relation between P and C.
Dashes describe the consequences of the system’s transition from one configuration to an other:
Dependence P(C) is approximated with polynomial to the first, second and third power. The best
approximation of experimental data is obtained with polynomial to the second power. The error
of approximation of this polynomial was the smallest among other approximation errors of
polynomials to the first and third power:
P(C) = 0.0000231510C3 -0.0122436227C2 +2.2789670597C -70.99011, ERR =2.39;
P(С)= 0.00199789C2 - 0.60110232C + 120.24428666, ERR =2.33;
P(C) =0.1958570587C+ 42.8918122913, ERR =2.83.
From this analysis follows that dependence between system performance and cost is described
Fig. 10. Relations between performance and cost for computer systems with optimal
with polynomial to the second power for PCs with optimal configuration. This statement is very
close to what has long been known as Grosch’s law.
The class of optimal CSs is revealed. It is found that dependence between system performance
and cost is approximately quadratic for optimal systems.
It is found that relation between the volume of RAM and clock frequency for equal performance
systems is hyperbolic.
It is clear as well that relation between volume of RAM and clock frequency for equal cost
systems is quasi linear.
1. Cale E., G. Cremelion , Mc. Kenney I. // Price/Performance Patterns of US Computer
Systems - Comm. ACM, 1979, p.225-232.
2. Grosch, H.R.J. High speed arithmetic: The digital computer as a research tool. J. Opt. Sot.
Am. 43 (Apr. 1953), p. 306-310.
3. Д. Беляев," Эффективная производительность" [D. Belaev, “Efficient performance”] //
RIGA: "Digital Times" №13, 03.04.2001., p. 6-7
Vadim Bistrov, RTU student for Master Degree [M.S. student at RTU]
Riga Technical University,
Institute of Transport Machine Technologies
Address: Lomonosova iela 1, LV 1042 Riga Latvia
Ernests Pētersons, RTU professor, Dc. hab. sc. ing.
Riga Technical University,
Institute of Transport Machine Technologies
Address: Lomonosova iela 1, LV 1042 Riga Latvia
Phone: +371 7089980
Bistrovs V., Pētersons E. Intelektuālo transporta sistēmu veiktspējas un vērtības pētīšana atkarībā no sistēmu
Dotajā darbā tiek analizētas sakarības starp datoru veiktspēju un to vērtību. Ir novērtētas likumsakarības starp
cenu un galveniem datoru parametriem – procesora takta frekvenci un galvenās atmiņas apjomu.
Ir izpētīts arī šo parametru ietekme uz skaitļošanas sistēmu veiktspēju un vērtību , rezultātā bija atrasts optimālo
Bistrov V., Peterson E. Transport intelligent systems cost/performance research in dependence on hardware.
Transport intelligent systems cost/performance research in dependence on hardware In this paper dependence
between performance and cost of personal computers is discussed. The interrelation between volume of RAM and
clock frequency of processor is established.
Influence of the specified parameters on performance and cost of computers is investigated. Moreover, the results
reveal a class of optimal computing systems.
also that in result, has enabled to reveal a class of optimal computing systems.
Быстров B., Петерсон Э. Исследование зависимости производительности и стоимости
интеллектуальных транспортных систем от их параметров.
В данной статье рассмотрена зависимость стоимости и производительности персональных
компьютеров. Представлена взаимосвязь объема оперативной памяти и тактовой частоты процессора.
Было исследовано также влияние определенных параметров, в результате чего был найден класс
оптимальных компьютерных систем.