Network Utility Maximisation

Question 1

What constitutes a NUM problem? (Network Utility Maximisation)

Answer 1

Maximising user utility subject to constraints, e.g capacity constraints.

Question 2

What kind of throughput model is often used to model our networks? Draw it

Answer 2

Elastic model

Question 3

In what way can bandwidth allocation be thought of as an arbitration?

Answer 3

• Users request properties of applications
• These properties determine the solution uniquely

Question 4

What is Nash arbitration?

Answer 4

• Properties that users request of applications are used as axioms of fairness
• The outcome of Nash arbitration is a Nash axiomatic arbitration solution

Question 5

How the solution to maximise the utility of n users, each having an objective function of a given resource of (a)xi be written?

Answer 5

= max product from i = 0 to i = n of (a)xi

Question 6

What is the implication of user objective functions being weighted by different values of a?

Answer 6

The different weights act as their bargaining power.

Question 7

How does the price a user is willing to pay affect its objective function?

Answer 7

If amount of money is denoted wi payed at price pi then wi = pi*xi

• xi is the initial user objective function where the user specifies how much of the resource they want (unweighted)
• wi is equivalent to ai in this case –> it is the users bargaining power

Question 8

What is Jain’s Fairness index? (3)

Answer 8

• Applicable to any resource sharing or allocation problem
• Independent of the amount of resources
• Index is always between 0 and 1

Question 9

What does a Jain’s Fairness index of 0.2 indicate?

Answer 9

• That a system is unfair to 80% of its users

Question 10

How do you calculate Jain’s Fairness index? Write it

Answer 10

GAMMA = (sum from i = 1 to n of xi)^2 / (n * sum from i = 1 to n of (xi^2))

Question 11

How does Max-Min Fairness work? Draw using three cups of increasing size.

Answer 11

• Resources are allocated equally and in infinitesimal increments to all requested flows until one is satisfied.
• Then amongst the remainder of requested flows, and so on until all are satisfied or capacity is exhausted.
• I.E give max Utility to smallest requested flow

Question 12

What is the aim of a frequency regulation service?

Answer 12

• Develop EVs distributed recharging algorithm which combines frequency regulation and improves the utilisation of electricity generators.

Question 13

What are features of a frequency regulation algorithm? And what initial information is given?

Answer 13

Initial given:
- set of EVs storage units and state of charge reqs
- set of electricity generators and demand profile from non-storage loads

• Distributed computation of control policy
• Only binary information on frequency deviations is required
• Proportionally fair recharging rates

Question 14

What is the meaning of k in a frequency regulation algorithm and how is it calculated?

Answer 14

k = C(t) / (sum from i to n from set v(t) of wi(t) )

• wi(t) : rate at which i-th EV pays money for recharging
• v(t) : set of recharging EVs at time t
• k is that it is a value that increases when generation is increased
• k decreases when demand is increased
• when k decreases the cost of energy increases (reducing demand)
• when k increases the cost of energy decreases (increasing demand)
• it regulates recharging rates