5, (2596) Consider the queueing network shown in the diagram. Jobs arrive at Sta

Question

5, (2596) Consider the queueing network shown in the diagram. Jobs arrive at Station One from the exterior according to a Poisson process at a rate of 12 jobs/hr. Three percent of the jobs processed at this station need to be reprocessed at the same station; the rest of the jobs are sent to StationStation Two. At Station Two, 4% of the jobs need to be One- Two reprocessed at the same station, and 696 need to be sent back for reprocessing at Station One. The rest of the jobs are sent to packaging (which is not part of this network). Assume that Work Station One (WS1) can be modeled as a (MIMI2)(FCFSI00) queue; each server can process 10 jobs r work Station Two (WS2)can be modeled as a (MIM 3) FCFSoo) queue; eachserver can process 7 jobs/hr 15% the number of jobs in process, WIP, in this manufacturing network. Station Two Compute the total arrival rates at each workstation-show your calculations-and use them to estimate a

Explanation / Answer

JOBS/HR JOBS/HR JOBS/HR 12 STATION 1 11.64 STATION 2 10.476 PACKAGING 0.36 (3% OF 12) 0.4656 (4% OF 11.64) 0.6984 (6% OF 11.64) SERVER SERVICE RATE 10 JOBS/HR 7 JOBS/HR NO OF SERVERS 2 3 (SERVICE RATE =SERVER SERVICE RATE * NO OF SERVERS) SERVICE RATE 20 JOBS/HR 21 JOBS/HR A) ARRIVAL RATE AT WS1 = 12 JOBS/HR + 3% OF 12 JOBS/HR + 6% OF (11.64 JOBS/HR) 13.06 JOBS/HR ARRIVAL RATE AT WS2 = 97% OF 12 JOBS/HOUR + 4 % OF 97% OF 12 JOBS/HR 12.11 JOBS/HR SINCE WE HAVE 12 NEW JOBS ARRIVING IN THE SYSTEM/HR AND 10.476 JOB/HR GOING TO PACKAGING, THE WIP IN THE SYSTEM = 12- 10.476 JOBS/HR WIP 1.52 JOBS/HR B) UTILIZATION FACTOR SHOWS THE EPRCENTAGE OF TIME ALL SERVERS ARE BUSY UTILIZATION FACTOR = ARRIVAL RATE/SERVICE RATE WORK STATION ARRIVAL RATE SERVICE RATE UTILIZATION FACTOR WS1 13.06 20 0.65 WS2 12.11 21 0.58 SINCE, THE UTILIZATION FACTOR OF WS1 > UTILIZATION FACTOR OF WS2, THE WS1 IS MORE BUSY THAN WS2, HENCE, NUMBER OF SERVERS SHOULD BE INCREASED IN WS1

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