Simulation and Modelling - Old Questions
12. Write short notes on (any two).( 2 x 2.5 = 5)
a) System and its environment.
b) Simulation run statistics.
a) System and its environment.
- A system is defined as a collection of object join in some regular interaction or interdependency for achievement of a common goal. We can also define a system as organized set of inter-related idea or principles. All system have input, output and feedback and maintain a basic level of equilibrium.
- A system boundary is the line that separate the system and its environment.
- The external components which interact with the system and produce necessary changes are said to constitute the system environment. In modeling systems, it is necessary to decide on the boundary between the system and its environment. This
b) Simulation run statistics
Example:
Consider a system with Kendall’s notation M/M/1/FIFO (i.e. a single server system in which the inter-arrival time is distributed exponentially ;and service time has an exponential and queue discipline is FIFO) and the objective is to measure the mean waiting time.
In simulation run approach, the mean waiting time is estimated by accumulating the waiting time of n successive entities and then it is divided by n. This measures the sample mean such that:
Whenever a waiting line forms, the waiting time of each entity on the line clearly depends upon the waiting time of its predecessors. Such series of data in which one value affect other values is said to be autocorrelated. The sample mean of autocorrelated data can be shown to approximate a normal distribution as the sample size increases.
A simulation run is started with the system in some initial state, frequently the idle state, in which no service is being given and no entities are waiting. The early arrivals then have a more than normal probability of obtaining service quickly, so a sample mean that includes the early arrivals will be biased.