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

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

Wil van der Aalst

Eindhoven University of TechnologyFaculty of Technology ManagementDepartment of Information and TechnologyP.O. Box 513 5600 MB EindhovenThe [email protected]

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نکات مهم فصل چهارم

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Queuing models

Basic characteristics:• average number of arrivals per time unit: (mean arrival rate)• average number that can be handled by one server per time unit:

(mean service rate)• number of servers: c

arrivals waiting service

c

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Queuing models (2)

Basic relationships:• average time between arrivals: 1/• average service time: 1/• occupation rate: c*)• average number being served: r

c

W,Lq

S,LW (S) = average time in queue (system)Lq (L) = average number in queue (system)

• L = Lq + r• S = W + 1/• Lq = * W• L = * S (Little’s formula)

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M/M/1 queue

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• Lq = (• L = • W = • S =

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, ... !

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Exercise

Calculate:• occupation rates, • average waiting time, • average throughput time,• average number in system.

task1b

task1a

c3

c1

c216 difficultcases per hour

c23

c22

1 resource, averageservice time of 8 minutes

1 resource, averageservice time of 2.66 minutes

task2

1 resource, averageservice time of 2minutes

18 easy casesper hour

difficult cases

easy cases

Increase the occupation rate until 90%:• average waiting time, • average throughput time,• average number in system.

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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 .

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