Question

Given a nodal delay of 53.9ms when there is no traffic on the network (i.e. usage = 0%), what is the effective delay when network usage = 38% ? (Give answer is miliseconds, rounded to one decimal place, without units. So for an answer of 0.10423 seconds you would enter "104.2" without the quotes).

Answer 1

Greetings !

Ans is Effective delay D = 86.9

Explanation:

Relationship between delay and utilization: D = d0 / ( 1 – U ) ………….eq.1

Where D is effective delay, and U is network utilization.(Range of U : 0 <= U <= 1 )

d0 is the delay when network has no other traffic, means U(utilization or usage) = 0

When network utilization is 0, put U=0 in eq.1, you will find D = d0 .

Since a nodal delay (D) of 53.9ms (given in question) when there is no traffic on the network (i.e. usage = 0%).

We have discussed earlier if U =0, it means D = d0

so D = d0 = 53.9 ms

or we can compute simply, network Utilization(U) = 0 (given in question)

Nodal Delay of effective (D) =53.9 ms

since D = d0 / 1- U (formula of efffective delay, discussed earlier)

53.9 = d0 / 1- 0

53.9 = d0

so d0 = 53.9 ms (when netwrok utilization is 0)

Now when U = 38% = .38

We have a value of d0 (53.9 ms) and U (38% = .38), put these value in equation 1 for finding out effective delay.

D = d0 / 1 - U

D = 53.9 / (1 - 0.38)

D = 53.9 / 0.62

D = 86.93 ms

Final answer as per the format mentioned in question = 86.9