this is the slide of simulation run statistics.In this slide you will learn how actually simulation run statistics

1. Simulation Run Statistics
Presented by:
Chandan Sharma

2. Why simulation run
statistics required?
• Data’s are independent
• Identically distributed
• Normal distribution
Previous
assumptions
are
Many statistics of interest in a simulation do
not meet above conditions

3. Goal
To compute
• X=Random variable representing the performance
of the system
• E=Expectation or average
• µ=Mean
µ = E(X)

4. Example
• M= inter-arrival time is distribution exponentially
• M= the service time is distributed exponentially
• 1= one server
Single server
system( M/M/1)
First-in , first-out with no priority.
• To measure the mean waiting timeObjective:

5. Mean
waiting time
The simplest approach is to estimate waiting time is
X̅(n)=
1
𝑛 𝑖=1
𝑛
𝑋𝑖
•X(n)=Sample mean
• 𝑋𝑖 =Individual waiting time
Waiting time is dependent
Data are autocorrelated
Variance of autocorrelated data is not related to population variance
Positive term is added for this system but in other system it can be negative

6. Another Example
Distribution may not be stationary
A simulation run starts in idle condition in initial state
In this case no service is given and there is no entities in queue
The early arrivals obtains service quickly.
Thus, they bias from sample mean as the length of simulation run is extended
When the sample size increases, the effect of bias will die out

8. Description
Sample mean depends upon the sample length for M/M/1 system
System starting from an initial empty state with
server utilization = 0.9
Steady state mean = 8.1
Mean value biased below steady state mean
As sample size increase bias diminishes but even sample =2000 mean only reached 95% of steady state value

9. Thank You
Any Questions?