M/s Queueing Model Case Study
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M/s Queueing Model Case Study
1.) According to the M/M/s Queueing Model, Randy’s estimate of 4 workers does not result in an optimal solution. The results of Randy’s estimate are shown below:
As you can see, the utilization rate exceeds the bottleneck threshold of 85%. Such a high utilization rate (95.9%) will cause a bottleneck and exacerbate an already stressful working environment. The average queue length is also too high. Randy’s recommendation causes over 85% of customers to be waiting (AVG Queue Length/AVG # in System). As discussed with the high utilization rate above, this will add stress to the technicians and cause for inpatient customers. Additionally, the average time in the queue is unreasonably long – over 4 hours.
Little to no customers would be willing to wait that long. Lastly, Randy’s recommendation of having 4 technicians would result in 91% of all customers to wait in the queue. Given that Randy’s background is in an unrelated field, it might be helpful to show him the benefits of simply adding one more technician. These results are as follows:
a.) Utilization:
1.) 4 technicians: 95.9%
2.) 5 technicians: 76.7%
b.) Average Queue Length: 1.) 4 technicians: 21.09
2.) 5 technicians: 1.62
c.) Average Number in System: 1.) 4 technicians: 24.93
2.) 5 technicians: 5.45
d.) Average Time in Queue:
1.) 4 technicians: 4 hours 7 minutes 48 seconds
2.) 5 technicians: 19 minutes 3 seconds
e.) Average Time in System:
1.) 4 technicians: 4 hours 53 minutes 24 seconds
2.) 5 technicians: 1 hour 4 minutes 10 seconds
f.) Percentage who wait: 1.) 4 technicians: 91%
2.) 5 technicians: 49.2%