Figure 1: Classification of different types of simulation
models
There are three model of approaches in simulation
models, i.e. 1) continuous simulation; 2) static,
stochastic simulation (Monte-carlo simulation); and
3) discrete, dynamic, stochastic simulation also called
Discrete Event Simulation (Groenewoud & Rinkel,
2012). In a continuous model, state variables change
continuously as a function of time. In general
analytical method such as inductive mathematical
reasoning is used to define and solve a system.
According to Groenewoud and Rinkel (2012), the
Monte Carlo methods varies, but tends to follow a
particular pattern:
1. Define a domain of possible inputs.
2. Generate inputs randomly from a probability
distribution over the domain.
3. Perform a deterministic computation on the
inputs.
4. Aggregate the results.
Discrete event models represents only those time
steps at which change occurs, and consequently it is
called event base or event driven, where the system
jumps from one event to another, leaving out the
irrelevant behaviour for the model, in between the
events.
Ross (2005) defined the simulation approach
based on a framework which generates the stochastic
mechanisms of the model and then observes the
resultant flow of the model over time as the discrete
event simulation approach. Depending on the reasons
for the simulation, there will be certain quantities of
interest that someone wants to determine.
Furthermore, the key elements in a discrete event
simulation are variables and events. In general, there
are three types of variables that are often utilized, i.e.
the time variable t, refers to the amount of (simulated)
time that has elapsed; counter variables, which keep
a count of the number of times that certain events
have occurred by time t; and the system state variable,
that describes the “state of the system” at the time t.
Whenever an “event” occurs, the values of the above
variables are changed or updated, and any relevant
data of interest are collected as output.
There are a lot of ways to classify simulation
models. Kelton, Sadowski, and Swets (2010), and
also Groenewoud and Rinkel (2012) claimed that one
of the useful ways is along these three dimensions:
1. Static or Dynamic
2. Continuous or Discrete
3. Deterministic or Stochastic
In the static model, time does not play a natural
role but does in dynamics model. The Buffon needle
problem is an example of static model. Most
operational models are dynamic. In a continuous
model, the state of the system can change
continuously over time while in a discrete model,
change can occur only at certain times. An example
of continuous model would be the level of reservoir
as water flows in and is let out, and as precipitation
and evaporation occur. A manufacturing system with
parts arriving and leaving at specific times, machines
going down and coming back up at specific times is
an example of a discrete model. Models that have no
random input are deterministic, a strict appointment
with a booked operation with fixed service time is an
example. On the other hand, stochastic models
operate with at least some inputs being random. An
example is a bank with randomly arriving customers
requiring varying service times.
From traffic simulation models point of view,
there are two common approaches for traffic
modelling i.e., macroscopic and microscopic models.
Macroscopic traffic models are based on gas-kinetic
models and use equations relating to traffic density
and velocity while microscopic traffic models offer a
way of simulating various driver behaviours and it
consists of an infrastructure that is occupied by a set
of vehicles. Each vehicle interacts with its
environment according to its own rules, so different
kinds of behaviour emerge when groups of vehicles
interact (Wiering et al., 2004). Meanwhile
TransModeler (2013) and Salimifard and Ansari
(2013) divided traffic simulation models into three
kinds of models i.e., microscopic, macroscopic and
mesoscopic models. Microscopic models predict the
mood of single and individual vehicles both
continuous and discrete types such as individual
vehicle speed and locations, macroscopic models
make ready an extensive depiction of the traffic flow
simulation, end mesoscopic include the mixed aspects
of both microscopic and macroscopic models.