1. Occupation / queue size D/D/1: Constant arrivals, constant duration. M/D/1: Exponential arrivals, constant duration. 0.60.80.91 occupation rate queue size a 2a 4a

2. Arena experiments M/D/1 queues. D/D/1 queues. Tandem queues.

3. Assignment 2 Goal: obtain Arena knowledge. Modeling+experimenting. Various models are possible. Several modeling pitfalls. Use of expression builder. Repeated test vs. "hold" block.

4. Modeling: parameter choice Problem definition Modeling Validation Experiment Interpret Conceptual impl: Arena CPN Tools parameterization

5. Modeling: parameters - observations (direct / video recordings), - event logs (e.g. SAP): often interpretation needed, Select a distribution that accords with theory and matches measured averages. Example: "create" block M measured arrivals in N time units; exponential distribution with intensity M / N. - interviews. Parameters for a model obtained by a combination of

6. 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 108 265-678 first 49 BF trucks 13-363, next 49 368-681 first 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.

7. 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.

8. Processing times Inferring processing times from trace. Problem with assessing duration for steps needing resources. Suppose step needs a resource R. Idle time of R in between? Look at predecessor job(s)! Job idstart Brdy B 123 8.7910.01 12711.2613.10 13613.2414.67 13214.8716.25

9. Assess resource occupation Job idrdy Astart Brdy B 123 8.58 8.7910.01 12711.1311.2613.10 13612.0913.2414.67 13213.1214.8716.25 When is resource R idle? Apparently, R not immediately available after rdy B.

10. Resource usage modeling rdy A Job idrdy Astart Brdy B 123 8.58 8.7910.01 12711.1311.2613.10 13612.0913.2414.67 13213.1214.8716.25 A2Bst Brdy 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

11. DCT processing Important for keeper occupation: arrival (ar), start (sk), error (er), approved (ap), fail (fl). arskerapfl 31.8434.70-37.32- 34.8537.4239.49-44.70 35.4239.55-40.79- 47.3356.06-56.78- 47.6856.8558.2663.31- 47.8958.31-59.11- 50.3359.16-61.19- 51.8463.40-64.33- 42(B) 43(F) 44(BF) 45(B) 46(BF) 32(B) 31(B) 30(BF)...... extra keeper occupation

12. Keeper process Keeper busy time(ap) - time(sk) + plm. 0.07if OK time(er) - time(sk) + plm. 0.07if failure time(er) - time(sk) + ?(extra)if corrected Assumption: extra time equals normal check time

13. DCT processing Important for crane occupation: mv/d, s1/2, gt/p, pt/p, rd. 19(B) apmvgtmvrdpp 23.70-24.1924.38 24.84 25.52-27.2927.50 27.93 28.41-30.7730.94 31.30 29.0031.5332.0632.29 32.93 21(B) 22(F) 24.3625.0525.3325.0525.3325.9426.1626.3126.4426.6827.1027.28 20(BF) 23(F) 24(B) 25(B) apmvgtmvgtppmds1gpmvptrd apmvmds2gpmvptrd 26.22-28.12-28.2728.4728.8629.10 26.8929.11-29.6029.8029.9830.5330.75 0.210.19 0.23

14. Crane process Six different paths: B, F, BF, with and without extra first move. F and BF have an optional s1/s2 step for obtaining the 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 2 is appropriate.