Network utility maximisation

Question 1

What is network utility maximisation (NUM)?

Answer 1

maximising utilisation of all flows in network

max U = sum(u_i*x_i) s.t. capacity constaints

Question 2

What is a strict real time utility function?

Answer 2

step graph
need a minimum throughput

Question 3

What is a soft real time utility function?

Answer 3

x^3 graph
increase throughput

Question 4

What is an elastic utility function?

Answer 4

-e^-x graph
no point increasing throughput after certain point as diminishing returns

Question 5

How do we think of bandwidth allocation as an arbitration?

Answer 5

• users request properties of applications
• properties determine solution uniquely
• outcome is Nash axiomatic arbitration solution

Question 6

What is nash arbitration?

Answer 6

properties are axioms of fairness

Question 7

What does taking the log of the objective function mean?

Answer 7

Take log and flow becomes summative of flow weighted by each flow

Question 8

What is Jain’s fairness index?

Answer 8

• applicable to any resource sharing or allocation problem
• independent of amount of resources
• between 0 and 1

Question 9

What does Jain’s fairness index mean?

Answer 9

eg. distribution with fairness 0.1 means it’s unfair to 90% of users

Question 10

What is min max fairness?

Answer 10

• resources allocated equally and in infinitesimal increments to all requested flows
• until one satisfied
• amongst remainder of all flows
• untill all satisfied or capacity exhausted

Question 11

What is the throughput equation for equal utilisation?

Answer 11

Throughput = (n^2+1)/(n+1)

Question 12

What is proportional fair allocation?

Answer 12

not a strict allocation

Question 13

What is weighted proportional fair allocation?

Answer 13

each node given a weight of importance
distributed with certain nodes getting more utilisation

Question 14

How do we choose allocation method based on NUM_obj function?

Answer 14

Max-min: w(i)=1 and alpha->infinity
Prop fair: w(i)=1 and alpha->1
Weighted fair: w(i)not=1 and alpha->1

Question 15

What is the aim of a frequency regulation service?

Answer 15

given:
- Evs/storage units with charge requirements
- electricity generators
- demand profile from non-storage nodes

Aim:
- develop recharging algorithm to improve utilisation of generators

Question 16

What are the features of a frequency regulation service algorithm?

Answer 16

• distributed computation of control policy
• only binary info on frequency deviations
• proportionally fair recharging rates

Question 17

What is the objective function for the EV problem?

Answer 17

Max sum_v(t)[w(t)log(p(t))]
s.t: sum_v(t)[p(t)]<C(t)

v(t) = set of recharging EVs a t
C(t) = net generation capacity used by EVs
w(t) = rate at which i-th EV pays money
p(t) = recharging rate of i-th EV

Question 18

What is the meaning of k?

Answer 18

acts as incentive for demanding energy for autonomous EV agents

Question 19

How is k affected?

Answer 19

• increasing generation costs -> k increases
• EV increases w(i) -> k decreases
• new EVs submit demand-> k decreases