Respuesta :
Answer:
The following are the answer to the given points:
Explanation:
In point (a):
Calculating the long-distance call cost:
[tex]= 4 \times 5 \times 0.40 \\= 20 \times 0.40\\= 8[/tex]
Calculating the local call cost:
[tex]= 10 \times 3 \times 0.05\\ = 30 \times 0.05\\= 1.5[/tex]
Calculating the overall cost of PSTN:
[tex]= 25 + (4 \times 5 \times 0.40) + (10 \times 3 \times 0.05) + 2000 + 275 \\= 25 + 8 + 1.5 + 2000 + 275 \\= 2309.5[/tex]
In point (b):
Calculating the call rate per second and the average arrival rate:
[tex]\to (\lambda) = 0.2[/tex]
The call average length:
[tex]\to (T_s) = - 8 \\\\ = (8 \times 60) \ seconds \\\\ = 480 \ seconds[/tex]
The complete agent number:
[tex]\to (m) = 9[/tex]
The strength of traffic:
[tex]\to u = \lambda \times T_s \\\\ = (0.2 \times 480) \\\\ = 96[/tex]
The occupancy of the agent:
[tex]\to p = \frac{u}{m} \\\\[/tex]
[tex]= \frac{96}{9} \\ \\= 10.66[/tex]
Calculation of obtained:
[tex]= \frac{(\frac{um}{m!})}{(\frac{um}{m!})} + (1-p) \sum {m-1} _{k=0} \ \frac{uk}{k!}[/tex]
We get = 0.329 to substitute values.
In point (c):
The rate of blocking = [tex]5 \%[/tex]
average call time [tex](T_s) = 480 \ seconds[/tex]
[tex]= 0.05 \times 480 \ seconds \\ = 24 \ second[/tex]
In point (d):
Calculating the number of link, which is required:
[tex]= \frac{275}{5} \\\\ =55[/tex]
In point (e):
Calculating the Line Number:
[tex]= \frac{275}{5} \\\\ =55[/tex]
PSTN line number:
[tex]= (\frac{2000}{55}) \\\\ = 36.3636\\\\= 37[/tex]
In point (f):
The gross design expense = $ 2309. 5
