Figure 2 Metal parts for personal gyrocopter engines arrive at a drilling machin

Question

Figure 2

Metal parts for personal gyrocopter engines arrive at a drilling machine at a rate of 8 per minute, following a Poisson distribution. The drilling process is automated, so it takes the same amount of time for each part, and is done at a rate of 11.5 per minute. The calculated system characteristics are shown in the table below.

Arrival Rate- 8 per minute

Service 11.5 per minute

Average service utilization 69.6%

Avergage units in line 0.80 units

Average units in line 1.49

Verae units in system 1.49 units

Average time in line 0.10 minutes

average time in system 0.19

Prob of zero units in system 30.4%

Refer to Figure 2. What is the probability (in percent) that an arriving part will not be drilled immediately?

Explanation / Answer

Average service utilisation = probability that the server is not idle

= mean number of arrivals per time period( per minute) / mean units served per time period ( per minute)

= 8/11.5 = 0.6957 or 69.6%

Thus probability that an arriving part will not be drilled immediately ( that is server is not free to serve immediately) is 69.6%

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