1. Simulation examples
Presented by:
Md. Habibur Rahman (11-94853-2)
Adnan Mehedi (12-95467-1)
Course:
Simulation and Modeling Techniques
Instructor:
Dr. Md. Shamim Akhter

2.  Example: Bagha
• Today, Bilal works alone at the bar at Bagha in
Gulshan 2, Road 44
• When a customer arrives, he/she is served if Bilal
is free.
• Otherwise, he/she joins the queue.
• Customers are served using a “first come, first
served” logic.
• When Bilal has finished serving a customer,
• he starts serving the next customer in line, or
• waits for the next customer to arrive if the
queue is empty.
Discrete-Event Simulation

3.  The amount of time required by Bilal to
serve a customer is a random variable Xs
with pdf fs.
 unt of time between the arrival of two
customers is a random variable Xa with
pdf fa.
 Bagha does not accept the arrival of
customers after time T.
Discrete-Event Simulation (cont.)

4. Possible questions:
 In average, how much time does a
customer wait after his/her arrival, until
being served?
 Data needed:
• Inter-arrival times of customers
• Service times
Discrete-Event Simulation (cont.)

5.  Consider this scenario at Bagha
 Simulation clock: 15
Discrete-Event Simulation (cont.)
Arrival
interval
Customer
arrives
Begin
service
Service
duration
Service
complete
5 5 5 2 7
1 6 7 4 11
3 9 11 3 14
3 12 14 1 15

6.  What can we calculate at the end of
simulation?
 Average waiting time for a customer: 1.25
 P(customer has to wait): 0.75
 P(Server busy): 0.66
 Average queue length: 0.33
Statistics – Performance Measures

7. Average Wait time for a customer
= total time customers wait in queue
total number of customers
Average wait time of those who wait
= total time of customers who wait in queue
number of customers who wait
Statistics – Performance Measures

8. Proportion of server busy time
= number of time units server busy
total time units of simulation
Average service Time
= total service time
number of customers serviced
More Statistics

9. Average time customer spends in system
= total time customers spend in system
total number of customers
Probability a customer has to wait in queue
= number of customers who wait
total number of customers
More Statistics

10.  One possible problem formulation:
• "Customers have to wait too long in my bank"
 A typical objective:
• Determine the effect of an additional cashier
on the mean queue length
The queue in the bank

11. A typical simulation result

12.  Event notice: A data record specifying an
event
• The event notice must contain all the
information necessary to execute the event (in
particular the time it is scheduled to occur)
 (Future) event list: A list of event notices
for future events
• The event list is the main data structure in a
discrete-event simulator
Event Notice, Event List

13.  The (future) event list (FEL) controls the
simulation
 The FEL contains all future events that are
scheduled
 The FEL is ordered by increasing time of
event notice
 Example FEL (at some simulation time ≤ t1):
The Event List

14.  Example: Simulation of the Mensa:
 Some state variables:
• # people in line 1
• # people at meal line 1 & 2
• # people at cashier 1 & 2
• # people eating at tables
The Event List

15. The Event List
 Operations on the FEL:
• Insert an event into FEL (at appropriate
position!)
• Remove first event from FEL for processing
• Delete an event from the FEL
 The FEL is thus usually stored as a linked
list

16. Simulation Algorithm

17. Simulation Algorithm

18.  Usually, activities last for varying amounts
of time:
• Inter-arrival times at bank
• Service times at bank
• Time to failure for a machine
• Time that a user program runs
 Such times are random or stochastic
Timing

19.  The simulator will need to use random
variables
 We will need to do some statistics
 For event list, we will need more advanced
data structures (trees): O(log n)
 Improve understanding of system
 Study new designs without interrupting
real system
Conclusion

20. Thank you 