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SYSTEM SIMULATION AND MODELING
1- Draw and explain about automobile suspension problem.
Ans. Suspension is the term given to the system ofsprings, shock absorbers and linkages that connects
a vehicle to its wheels. Suspension systems serve a dual purpose — contributing to the car's
roadholding/handling and braking for good active safety and driving pleasure, and keeping vehicle
occupants comfortable and reasonably well isolated from road noise, bumps, and vibrations,etc. These
goals are generally at odds, so the tuning of suspensions involves finding the right compromise. It is
important for the suspension to keep the road wheel in contact with the road surface as much as possible,
because all the forces acting on the vehicle do so through the contact patches of the tires. The
suspension also protects the vehicle itself and any cargo or luggage from damage and wear. The design
of front and rear suspension of a car may be differentAutomobiles were initially developed as selfpropelled versions of horse drawn vehicles. However, horse drawn vehicles had been designed for
relatively slow speeds and their suspension was not well suited to the higher speeds permitted by the
internal combustion engine.In 1901 Mors of Germany first fitted an automobile withshock absorbers. With
the advantage of a dampened suspension system on his 'Mors Machine', Henri Fournier won the
prestigious Paris-to-Berlin race on the 20th of June 1901. Fournier's superior time was 11 hrs 46 min 10
sec, while the best competitor was Léonce Girardot in a Panhard with a time of 12 hrs 15 min 40 sec. [2]
In 1920, Leyland used torsion bars in a suspension system. In 1922, independent front suspension was
pioneered on the Lancia Lambda and became more common in mass market cars from 1932
2- Discuss about modified Exponential Growth models
Ans.- A production unit, which is planning to launch a new product, first problem faced by it is, how
muchquantity of a product can be sold in a given period. A market model should be able to predict,
rateof selling of a product, which obviously cannot be proportional to itself. There are several
other parameters to be considered while modeling such a situation. In practice, there is a limit to
whichone can sell the product. It depends on how many other brands are available in market, and
whatis the probable number of customers. The exponential growth model can not give correct results
asit shows unlimited growth. Thus we have to modify this model.Exponential growth model can be
modified if we assume that rate of growth is proportional tonumber of people who have yet not
purchased the product. Suppose the market is limited to somemaximum value X , where X is the number
of expected buyers. Let xbe the number of people whohave already bought this product or some other
brand of same product. The numbers of people whohave yet to buy are ( X – x).
3-
What is logistic function?
Ans.- A logistic function or logistic curve is a common sigmoid curve, given its name in 1844 or 1845
by Pierre François Verhulstwho studied it in relation to population growth. It can model the "S-shaped"
curve (abbreviated S-curve) of growth of some population P. The initial stage of growth is
approximately exponential; then, as saturation begins, the growth slows, and at maturity, growth stops.
A simple logistic function may be defined by the formula
where the variable P might be considered to denote a population, where e is Euler's number and the
variable t might be thought of as time.[1] For values of t in the range of real numbers from −∞ to +∞,
the S-curve shown is obtained. In practice, due to the nature of the exponential function e−t, it is
sufficient to compute t over a small range of real numbers such as [−6, +6].
The logistic function finds applications in a range of fields, including artificial neural
networks, biology,biomathematics, demography, economics, chemistry, mathematical
psychology, probability,sociology, political science, and statistics. It has an easily calculated
derivative:
It also has the property that
Thus, the function
is odd.
4- Explain how the system Dynamics model used in inventory control system?
5- What are stochastic variables?
Ans.- a random variable or stochastic variable is, roughly speaking, avariable whose value results
from a measurement on a system that is subject to variations due to chance. Intuitively, a random
variable is a numerical description of the outcome of an experiment (e.g., the possible results of rolling
two dice: (1, 1), (1, 2), etc.). Alternatively, a random variable can be thought of as a quantity whose value
is not fixed, but which can take on different values; a probability distribution is used to describe the
probabilities of different values occurring. Realizations of a random variable are called random variates.
A random variable's possible values might represent the possible outcomes of a yet-to-be-performed
experiment, or the potential values of a quantity whose already-existing value is uncertain (e.g. as a result
of incomplete information or imprecise measurements). Random variables can be classified as
either discrete (i.e. it may assume any of a specified list of exact values) or as continuous (i.e. it may
assume any numerical value in an interval or collection of intervals).
Random variables are usually real-valued, but one can consider arbitrary types such as boolean
values, complex numbers, vectors, matrices, sequences, trees, sets, shapes, manifolds, functions,
and processes. The term random element is used to encompass all such related concepts. A related
concept is the stochastic process, a set of indexed random variables (typically indexed by time or space).
The formal mathematical treatment of random variables is dealt with in the subject of probability theory. In
that context, random variables are defined in terms of functions defined on a probability space.
6-
What is a design factor?
7- List and describe the mathematical solutions of Queuing problems.
Ans.- Queueing models have been used to investigate industrial problems for many years.
In the 1940s, queueing models were used to solve a variety of machine interference
problems, i.e., how many repairpersons to assign to maintain a system, or how many
telephone operators to handle traffic calls.Queueing models are used to analyze tradeoffs
concerning the number of servers versus the waiting time of customers. Clearly, if the
number of servers is high, the cost of the servers is high, but the waiting time (cost of
customer idle time) is low. Notice that this is the same kind of tradeoff discussed in the
basic inventory order quantity decision discussed earlier.Some kinds of queueing problems
involve determining the appropriate number of service facilities to cover expected demand,
as well as determining the efficiency of servers and the number of servers of different types
at the service facilities. (See Hillier and Lieberman, 2005) These are design problems and
decisions are made in order to provide an appropriate level of service. Suri (1998) suggests
using queueing theory to provide quick solutions to industrial problems.Simulation is a
potentially very detailed modeling tool that is widely used to evaluate the solutions to many
industrial problems. Many measures of the performance of a system are available. A great
benefit of simulation is that a model can often be very close to reality. This can sometimes
result in a complicated simulation model that can take a long time to run. Another
drawback is that (without perturbations analysis), a simulation can model only one system
at a time, with one set of parameters. It is difficult to generalize the results from a
simulation.
However, with the detailed modeling capability of simulation, the results from the model of
a particular system can be quite accurate. Simulation has been a widely-used, very useful
modeling tool.
8- Discuss about simulation of a Telephone system.