There is a single doctor in a primary health centre. Patients arrive at the rate of 32 per hour. The time required to provide service is exponentially distributed with mean of 90 seconds. The mean waiting time of a patient, needing medical checkup facility in the queue, is

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BPSC AE Paper 6 (Mechanical) 14 Oct 2022 Official Paper

Answer 1

Concept:

The mean waiting time of a patient, needing medical checkup facility in the queue, is,

\({W_q} = \frac{\lambda }{{\mu \left( {\mu - \lambda } \right)}}\)

Calculation:

λ = 32 per hour

\(\mu = \frac{{60\; \times \;60}}{{90}} = 40\;{\rm{per\;hour}}\)

\(\therefore {W_q} = \frac{{32}}{{40\left( {40 - 32} \right)}}\)

Wq = 0.1 hour

∴ Wq = 6 minute