1. Analysis of workflows: Verification, validation, and performance analysis.
Wil van der Aalst
Eindhoven University of Technology
Faculty of Technology Management
Department of Information and Technology
P.O. Box 513
5600 MB Eindhoven
The Netherlands

2. نکات مهم فصل چهارم

3. نکات مهم فصل چهارم

4. نکات مهم فصل چهارم

5. نکات مهم فصل چهارم

6. نکات مهم فصل چهارم

7. نکات مهم فصل چهارم

8. نکات مهم فصل چهارم

9. نکات مهم فصل چهارم

10. نکات مهم فصل چهارم

11. نکات مهم فصل چهارم

12. نکات مهم فصل چهارم

13. نکات مهم فصل چهارم

14. نکات مهم فصل چهارم

15. نکات مهم فصل چهارم

16. Queuing models service waiting arrivals l c m Basic characteristics:
average number of arrivals per time unit: l (mean arrival rate)
average number that can be handled by one server per time unit: m (mean service rate)
number of servers: c

17. W (S) = average time in queue (system)
Queuing models (2) l c m
W,Lq
S,L
W (S) = average time in queue (system)
Lq (L) = average number in queue (system)
Basic relationships:
average time between arrivals: 1/l
average service time: 1/m
occupation rate: r = l/(c*m)
average number being served: r = l/m
L = Lq + r
S = W + 1/m
Lq = l * W
L = l * S (Little’s formula)

18. Also formulas for M/Er/1, M/G/1, M/M/c, ... !
M/M/1 queue l 1 m
Assumptions:
time between arrivals and service time follow a negative expontential distribution
1 server (c = 1)
FIFO
Lq = (l* l)/(m * (m-l))
L = l/(m-l) = r/(1-r)
W = r/(m-l)
S = 1/(m-l)
Also formulas for M/Er/1, M/G/1, M/M/c, ... !

19. Exercise Calculate: Increase the occupation rate until 90%:
1 resource, average
service time of 8 minutes
difficult cases
1 resource, average
6 difficult
service time of 2
c21
cases per hour
minutes
task1a c1
c23
task2 c3
18 easy cases
task1b
c22
per hour
easy cases
1 resource, average
service time of 2.66 minutes
Calculate:
occupation rates,
average waiting time,
average throughput time,
average number in system.
Increase the occupation rate until 90%:
average waiting time,
average throughput time,
average number in system.

20. Simulation Random walk through the reachability graph
Computer experiment
pseudo random numbers
random generator
Validation
Statistical aspects
start run
subruns
Animation
Flexible
No proof!