1

Quiz 3

Communication Networks (EE 706), Spring’14

April 10, 2014; Total: 10 marks; Time: 55 minutesNote:

• You are allowed to use one A4 sheet with handwritten notes on both sides.

QUESTION 1 (1 + 1.5 + 0.5 = 3 MARKS)

Consider a TCP connection for which flow control imposes an upper limit of 1000 packets on

the window-size. Suppose this connection is used to transfer a file of 107 bytes over a single link

that allows infinitely fast transmission and has a propagation delay of 50 ms in either direction.

Suppose each data packet contains 1000 bytes of data. There is no congestion and no lost or

corrupted packets.

(a) How many RTTs does it take until slow start increases the window to 1000 packets?

(b) How many RTTs does it take to complete the file transfer (including the receipt of all ACKs)?

(c) Find the average throughput of the transfer.

QUESTION 2 (2 MARKS)

Give an example in which the asynchronous Bellman-Ford algorithm with poisoned reverse

is used and the count-to-infinity (“bad news travels slowly”) problem still occurs. Assume that

all edge costs are positive.

QUESTION 3 (1.5 + 1.5 = 3 MARKS)

Recall our definition of a max-min fair allocation in the context of a set of sessions P using

a network (directed graph). In the same context, a Pareto efficient allocation is defined as an

allocation r = {rp : p ∈ P}, which is feasible and satisfies the property that the rate rp of any

session p cannot be increased while maintaining feasibility without decreasing the rate rq of

another session q.

For each of the following statements, state whether it is true or false and provide a proof (if

true) or counter-example (if false).

2

(a) Every Pareto efficient allocation is max-min fair.

(b) Every max-min fair allocation is Pareto efficient.

QUESTION 4 (2 MARKS)

Suppose we have a directed graph with N nodes and no directed cycles. Show that the nodes

can be numbered as 1, . . . , N such that there may be an edge from node i to node j only if

i > j.