Wil van der Aalst Eindhoven University of Technology

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Presentation transcript:

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 w.m.p.v.d.aalst@tm.tue.nl

نکات مهم فصل چهارم

نکات مهم فصل چهارم

نکات مهم فصل چهارم

نکات مهم فصل چهارم

نکات مهم فصل چهارم

نکات مهم فصل چهارم

نکات مهم فصل چهارم

نکات مهم فصل چهارم

نکات مهم فصل چهارم

نکات مهم فصل چهارم

نکات مهم فصل چهارم

نکات مهم فصل چهارم

نکات مهم فصل چهارم

نکات مهم فصل چهارم

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

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)

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, ... !

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.

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