Question 5: A process has a bottleneck resource that consists of specialized equ

Question

Question 5:
A process has a bottleneck resource that consists of specialized equipment. Jobs arrive to this machine at a rate of 40 per hour (according to a Poisson arrival process). The processing times average 1 minute and are exponentially distributed. Compare the performance (e.g. average cycle time through the bottleneck) of the process for the three following settings.


a. Consider the system as it is currently constructed.
b. Add a second identical machine at the bottleneck. (Hint: This increases the number
of servers from one to two, but the service rate at each machine is just as in case a.)
c. Replace the current machine with one that is twice as fast. (Hint: This doubles the
service rate, but you only have one server.)

Explanation / Answer

a)Using the M|M|S spreadsheet calculator: M/M/s Arrival rate 0.66667 Service rate 1 Number of servers 1 Utilization 66.67% P(0), probability that the system is empty 0.3333 Lq, expected queue length 1.3333 L, expected number in system 2.0000 Wq, expected time in queue 2.0000 W, expected total time in system 3.0000 Probability that a customer waits 0.6667 b)Using the M|M|S spreadsheet calculator: M/M/s Arrival rate .66667 Service rate 1 Number of servers 2 Utilization 33.33% P(0), probability that the system is empty 0.5000 Lq, expected queue length 0.0833 L, expected number in system 0.7500 Wq, expected time in queue 0.1250 W, expected total time in system 1.1250 Probability that a customer waits 0.1667 c)Using the M|M|S spreadsheet calculator: M/M/s Arrival rate .66667 Service rate 2 Number of servers 1 Utilization 33.33% P(0), probability that the system is empty 0.6667 Lq, expected queue length 0.1667 L, expected number in system 0.5000 Wq, expected time in queue 0.2500 W, expected total time in system 0.7500 Probability that a customer waits 0.3333

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