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Tribhuvan university > CSIT - 2074 Syllabus > Simulation and Modelling > Old Questions > 2074

Simulation and Modelling - Old Questions

Syllabus Notes Old Questions Unit Wise Questions Question Bank

7.  Define confidence interval and I.I.D in output analysis. How do you use simulation run statistics in simulation output analysis? Explain.

5 marks | Asked in 2074
The confidence interval is the range of possible values for the parameter based on a set of data (e.g. the simulation results). Confidence intervals are based on the premise that the data being produced by the simulation is represented well by a probability model.

Infinite population has a stationary probability distribution with a finite mean μ and finite variance σ². Sample variable and time does not affect population distribution Random .variables that meet all these conditions are called independently and identically distributed (I.I.D)

Simulation run statistics
In the estimation method, it is assumed that the observations are mutually independent and the distribution from which they are draws is stationary. Unfortunately many statistics of interest in simulation do not meet these conditions. An example of such case is queuing system. Correlation is necessary to analyze such scenario.  In such cases, simulation run statistics method is used.

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.