An industrial washing station features a single bay (1 server). Vehicles arrive randomly following a Poisson distribution at a rate of 1 vehicle every 4 minutes. The washing bay takes exactly 5 minutes to process a vehicle (exponentially distributed).
A floor supervisor argues that because the wash takes only 5 minutes, the queue will naturally stabilize. According to queueing theory, what is the exact state of this system, and what is the minimum number of parallel servers ( m ) required to make the system viable?

Question

Answer

The system is viable as is ( U = 0.8 ); minimum  m = 1 .

Answer

The system is overloaded ( U = 1.25 ); minimum  m = 3 .

Answer

The system is viable because arrival rate (15/hr) is less than the processing time (5 mins); minimum  m = 1 .

Answer

The system is overloaded ( U = 1.25 ); minimum  m = 2 .

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An industrial washing station features a single bay (1 server). Vehicles arrive ...

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