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.

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Presentation transcript:

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

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

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

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

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

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 first 49 BF trucks , next first 90 F trucks 1-427, next There may be reasons for fluctuations (e.g. traffic); look for confirmation by interviews! DCT trace: arrival 1 at 0.00, 500 at exp., avg interarrival time / 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 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

Assess resource occupation Job idrdy Astart Brdy B When is resource R idle? Apparently, R not immediately available after rdy B.

Resource usage modeling rdy A Job idrdy Astart Brdy B A2Bst Brdy B ? ? ? 1.38 ? B-queue empty ↔ t can be timed ↔ u cannot be timed

DCT processing Important for keeper occupation: arrival (ar), start (sk), error (er), approved (ap), fail (fl). arskerapfl (B) 43(F) 44(BF) 45(B) 46(BF) 32(B) 31(B) 30(BF) extra keeper occupation

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

DCT processing Important for crane occupation: mv/d, s1/2, gt/p, pt/p, rd. 19(B) apmvgtmvrdpp (B) 22(F) (BF) 23(F) 24(B) 25(B) apmvgtmvgtppmds1gpmvptrd apmvmds2gpmvptrd

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.