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Workflow Analysis: Verification, Validation, and Performance in Queuing Models

This document provides a comprehensive analysis of workflows, focusing on the verification, validation, and performance evaluation of queuing models. Key metrics such as the average number of arrivals, service rates, and occupation rates are explored. It includes essential relationships and formulas, including Little's law, to understand system dynamics under various conditions. The text also presents exercise problems aimed at calculating occupation rates, waiting times, and throughput times, assisting students in applying theoretical knowledge to practical scenarios.

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Workflow Analysis: Verification, Validation, and Performance in Queuing Models

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  1. Eindhoven University of Technology Faculty of Technology Management Department of Information and Technology P.O. Box 513 5600 MB Eindhoven The Netherlands w.m.p.v.d.aalst@tm.tue.nl Analysis of workflows: Verification, validation, and performance analysis. Wil van der Aalst

  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 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 waiting arrivals l c m

  17. 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 Queuing models (2) l c m W,Lq S,L W (S) = average time in queue (system) Lq (L) = average number in queue (system) • L = Lq + r • S = W + 1/m • Lq = l * W • L = l * S (Little’s formula)

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

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

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