Question

We assume that ABC Corporation has two business offices. These offices are in the cities of Orlando and Miami. These cities are located 220 miles apart. We assume that there are 3 employees in Orlando and 6 employees in Miami. Further, we assume that each employee calls the other site 4 times a day and talks for an average of 5 minutes. Further, each employee calls others in the same office 10 times a day for an average of 3 minutes. We will assume that 20% of the calls happen in the peak hours of the day. A blocking rate of 5% is acceptable for calls between the 2 sites.
a. What is the cost of PSTN (straightforward) solution?
b. Perform the Erlang calculation
c. Calculate the Blocking
d. Number of links required between these sites with respect to 5% blocking rate.
e. Number of Leased lines and PSTN lines
f. Total cost of your design
The cost of communications services and components
Item Cost
Line to PSTN $25/Month
Local Call $0.05/Minute
Long Distance Call $0.40/Minute
PBX $2000 Purchase Price
Leased Line $275/Month

Answer 1

Answer:

The following are the answer to the given points:

Explanation:

In point (a):

Calculating the long-distance call cost:

$= 4 \times 5 \times 0.40 \\= 20 \times 0.40\\= 8$

Calculating the local call cost:

$= 10 \times 3 \times 0.05\\ = 30 \times 0.05\\= 1.5$

Calculating the overall cost of PSTN:

$= 25 + (4 \times 5 \times 0.40) + (10 \times 3 \times 0.05) + 2000 + 275 \\= 25 + 8 + 1.5 + 2000 + 275 \\= 2309.5$

In point (b):

Calculating the call rate per second and the average arrival rate:

$\to (\lambda) = 0.2$

The call average length:

$\to (T_s) = - 8 \\\\ = (8 \times 60) \ seconds \\\\ = 480 \ seconds$  

The complete agent number:

$\to (m) = 9$

The strength of traffic:

$\to u = \lambda \times T_s \\\\ = (0.2 \times 480) \\\\ = 96$    

The occupancy of the agent:

$\to p = \frac{u}{m}$

      $= \frac{96}{9} \\ \\= 10.66$  

Calculation of obtained:

$= \frac{(\frac{um}{m!})}{(\frac{um}{m!})} + (1-p) \sum {m-1} _{k=0} \ \frac{uk}{k!}$

We get = 0.329 to substitute values.  

In point (c):

The rate of blocking = $5 \%$

average call time $(T_s) = 480 \ seconds$

                                    $= 0.05 \times 480 \ seconds \\ = 24 \ second$

In point (d):

Calculating the number of link, which is required:  

$= \frac{275}{5} \\\\ =55$

In point (e):

Calculating the Line Number:

$= \frac{275}{5} \\\\ =55$

PSTN line number:

$= (\frac{2000}{55}) \\\\ = 36.3636\\\\= 37$

In point (f):

The gross design expense = $ 2309. 5