Analysis of workflows : Verification, validation, and performance analysis .

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

نکات مهم فصل چهارم

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

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)

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, ... !

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.

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

Analysis of workflows : Verification, validation, and performance analysis .