2WB05 Simulation Lecture 6: Process-interaction approach

Transcription

1 2WB05 Simulation Lecture 6: Process-interaction approach Marko Boon December 6, 2012

2 This approach focusses on describing processes; In the event-scheduling approach one regards a simulation as executing a sequence of events ordered in time; but no time elapses within an event. The process-interaction approach provides a process for each entity in the system; and time elapses during a process. In production systems we have processes for: Arrivals Buffers Machines Exit 2/18

3 Example: Single-stage production system 3/18 Arrivals Buffer Machine Exit A single machine processes jobs in order of arrival. The interarrival times and processing times are exponential with parameters λ and µ (with λ < µ). What is the mean waiting time? What is the mean queue length? What is the mean length of a busy period? How does the performance change if we speed up the machine?

4 Arrival process 4/18 Generate arrival after random (exponential) time units arrival

5 Buffer process 5/18 Add job to buffer and remove job from buffer (if there is any) 0 1 n n+1

6 Machine process 6/18 Process job (if there is any) busy idle

7 Exit process 7/18 Accept completed job and do accounting departure accounting

8 The specification language χ: 8/18 Modelling and simulation tool for the design of manufacturing systems The language χ has been developed by the Systems Engineering group For documentation, see

9 9/18 Implementation in χ G a b c B M E Processes: G, B, M, E. Channels: a, b, c. Jobs are generated in G, then they are sent over channel a to B. When M is idle, the first job is sent over channel b to M. After a delay, the job is sent over channel c to exit process E.

10 10/ Mean sojourn time as a function of the number of jobs processed for λ = 1 and µ = 2

11 Example: Single-stage production system with three parallel machines 11/18 G M a b c B M M E

12 Example: Two-stage production system 12/18 Jobs Machine 1 Machine 2 Jobs are processed by two machines in series. Each machine has its own local buffer and processes jobs in order of arrival. The interarrival and processing times of jobs are exponential with parameters λ, µ 1 and µ 2. What is the mean (overall) sojourn time?

13 In the χ program we only have to change the model: 13/18 G a b c B M B d M e E

14 The simulation system Arena 14/18 In Arena you can construct simulation models without programming, but simply with click, drag and drop... At the department of Mathematics and Computer science we have a limited license. See the TU/e software installation page for more details how to get access. Book with CD-ROM: W. David Kelton, Randall P. Sadowski, Deborah A. Sadowski: Simulation with Arena. 3rd ed., London: McGraw-Hill, 2004

15 M M 1 in Arena 15/18

16 M M 3 in Arena 16/18 Just change the capacity of the Service resource from 1 to 3.

17 Two M M 1 queues in series 17/18 Duplicate the server and change the name of the resource of the second server!

18 Mathematica 9 Simulation of a queueing network: network = QueueingNetworkProcess[gamma, P, EB, c]; Table[QueueProperties[{network, i}], {i, 1, Length[EB]}] data = RandomFunction[network, {0, 1000}]; ListLinePlot[data] Table[QueueProperties[{data, i}], {i, 1, Length[EB]}] 18/18