Question

A maintenance service facility has Poisson arrival rates, negative exponential service time and operates on a 'first come first served' queue discipline. Break-downs occur on an average of 3 per day with a range of zero to eight. The maintenance crew can service an average of 6 machines per day with a range of zero to seven. The mean waiting time for an item to be serviced would be

• A. 3 day
• B. 1 day
• C. 1/6 day
• D. 1/3 day

Answer 1

The correct option is C 1/6 day

$\text{Given data:}$

$\text{Arrival rate:}\lambda =3\text{per day}$

$\text{Service rate:}\lambda =6\text{per day}$

$\text{Mean waiting time for an item to be serviced}$

$=\frac{\lambda }{\mu (\mu -\lambda )}=\frac{3}{6(6-3)}=\frac{1}{2}\times \frac{1}{3}=\frac{1}{6}day$