A factory y has large g number of semiautomatic machines.On 50% of the working days none of the machines fail. On 30%of the days one machines fails and on 20%of the days two machines fail. The maintenance staff on the average puts 65% of the machines in order in one day, 30% in two days and remaining 5% in three days. Simulate the system y for 30 days y duration and estimate the average length of queue, average waiting time and server loading that is the fraction of time for which server is busy.
the above is the question. according to my knowledge. I did the following
Expected arrival rate=0*.5+1*.3+2*.2=0.7 per day
and
Average service time: 1*.65+2*.3+3*.05=1.4 days
Expected service time: 1/1.4 = 0.714/day
now what is the probability that the system is idle?
I did,
p= 1-(0.7/0.714)=0.019 => 1.9% but the answer is 13.33 %
how is it so?