Answer:
(a) Average number of unit in line = 0.256
(b) Average number of unit in operation= 3.209
(c) Average number of unit being service in operation = 0.535
Explanation:
Given Data:
Number of machine N = 4
Number of attendant (S) = 1
Service time (T)= 5 mins
Time required by the machine before servicing = 30 mins
Calculating the service factor (X) using the formula;
X = T/(T+U)
= 5/(5+30)
= 5/35
= 0.1429
(a) Calculating the average number of unit in line (L) using the formula;
L = N* (1-F)
where, N = Number of unit
F = efficiency factor
L = average number of unit in line
Using the finite queuing table at X = 0.1429 and S = 1,
Efficiency factor = 0.936
Substituting, we have;
L = 4*(1-0.936)
= 4* 0.064
= 0.256
(c) Calculating the average number of unit being service in operation (H) using the formula;
H = N*F*X
= 4 *0.936*0.1429
= 0.535
(b) Calculating the average number of unit in operation using the formula;
Average number of unit in operation= Number of unit-down unit
But down unit = L+H
The formula becomes;
Average number of unit in operation= Number of unit-(L+H)
= 4 - (0.256+0.535)
= 4-0.791
= 3.209
