Occupation / queue sizeD/D/1: Constant arrivals, constant duration.M/D/1: Exponential arrivals, constant duration.

0.6 0.8 0.9 1 occupationrate

queuesize

a

2a

4a

Arena experimentsM/D/1 queues.

D/D/1 queues.

Tandem queues.

Assignment 2Goal: obtain Arena knowledge.Modeling+experimenting.

Various models are possible.Several modeling pitfalls.

Use of expression builder.Repeated test vs. "hold" block.

Modeling: parameter choiceProblemdefinition

Modeling

Validation

Experiment

Interpret

Conceptualimpl: Arena CPN Tools

parameterization

Modeling: parameters

- observations (direct / video recordings),

- event logs (e.g. SAP): often interpretation needed,

Select a distribution that accords with theoryand matches measured averages.Example: "create" blockM measured arrivals in N time units;exponential distribution with intensity M / N.

- interviews.

Parameters for a model obtained by a combination of

DCT arrivals

Model should differentiate between B/F/BF trucks:three generators with three different intensities.

Intensities may stay the same or fluctuate.first 108 B trucks 0-265, next 108 265-678first 49 BF trucks 13-363, next 49 368-681first 90 F trucks 1-427, next 90 427-686.There may be reasons for fluctuations (e.g. traffic);look for confirmation by interviews!

DCT trace: arrival 1 at 0.00, 500 at 687.835.exp., avg interarrival time 687.835 / 499.

Import trace into spreadsheet.

Arena input analyzer

Example with interarrival times for B trucks.However, no variable-intensity exponential distribution.So, divide in subparts and analyze separately.Keep asking questions!Listen to answers given!

Trace file is imported into spreadsheet and sorted.

Export selected data to text file,which can be read by input analyzer.

Processing timesInferring processing times from trace.Problem with assessing duration for steps needingresources. Suppose step needs a resource R.

Idle time of R in between?Look at predecessor job(s)!

Job id start B rdy B123 8.79 10.01127 11.26 13.10136 13.24 14.67132 14.87 16.25

Assess resource occupation

Job id rdy A start B rdy B123 8.58 8.79 10.01127 11.13 11.26 13.10136 12.09 13.24 14.67132 13.12 14.87 16.25

When is resource R idle?

Apparently, R not immediately available after rdy B.

t

u

Resource usage modeling

rdy A

Job id rdy A start B rdy B123 8.58 8.79 10.01127 11.13 11.26 13.10136 12.09 13.24 14.67132 13.12 14.87 16.25

A2B st B rdy B

0.21

1.22

?

0.13

1.84

0.14

?

1.43

0.20

?

1.38

?

B-queue empty ↔ t can be timed ↔ u cannot be timed

DCT processingImportant for keeper occupation:arrival (ar), start (sk), error (er), approved (ap), fail (fl).

ar sk er ap fl

31.84 34.70 - 37.32 -

34.85 37.42 39.49 - 44.70

35.42 39.55 - 40.79 -

47.33 56.06 - 56.78 -

47.68 56.85 58.26 63.31 -

47.89 58.31 - 59.11 -

50.33 59.16 - 61.19 -

51.84 63.40 - 64.33 -

42(B)43(F)

44(BF)

45(B)46(BF)

32(B)31(B)

30(BF)

......

extrakeeperoccupation

Keeper process Keeper busytime(ap) - time(sk) + plm. 0.07 if OKtime(er) - time(sk) + plm. 0.07 if failure time(er) - time(sk) + ?(extra) if corrected

Assumption:extra time equals normal check time

DCT processingImportant for crane occupation: mv/d, s1/2, gt/p, pt/p, rd.

19(B)

ap mv gt mv rd pp

23.70 - 24.19 24.38 24.38 24.84

25.52 - 27.29 27.50 27.50 27.93

28.41 - 30.77 30.94 30.94 31.30

29.00 31.53 32.06 32.29 32.29 32.93

21(B)

22(F)

24.36 25.05 25.33 25.05 25.33 25.94 26.16 26.31 26.44 26.68 27.10 27.28

20(BF)

23(F)

24(B) 25(B)

ap mv gt mv gt pp md s1 gp mv pt rd

ap mv md s2 gp mv pt rd

26.22 - 28.12 - 28.27 28.47 28.86 29.10

26.89 29.11 - 29.60 29.80 29.98 30.53 30.75

0.21 0.19

0.23

Crane process Six different paths:B, F, BF, with and without extra first move.F and BF have an optional s1/s2 step for obtainingthe needed container.

Two modeling options:1. Model each step; fit distributions for each step. Do not forget the extra time after "pp" step.2. Aggregate and use a bit of analysis to approximate distribution(s).

Simulation can be used to find out whether option 2is appropriate.