CS/ECE 438: Communication Networks for Computers Fall 2005
Problem Set 7 Due: start of class, Monday, December 5th
Congestion Control and Performance Analysis
Assigned reading: Peterson and Davie: Chapter 6. All problems carry equal weight. For full credit, show all work.
1. Random Early Detection
Consider a RED gateway with MaxP = 0.015, and with an average queue length halfway between the two thresholds
MinP and MaxP.
a. Find the drop probability Pcount, for count = 1 and count = 50
b. Calculate the probability that none of the 50 packets are dropped.
c. Repeat parts a. with MaxP = 0.025
d. Repeat parts b. with MaxP = 0.025
e. What is the impact of the larger value of MaxP? How will this affect the operation of RED?
2. TCP and Network Delay
Consider the following two causes of a 1-second network delay (assume ACKs return instantaneously).
• One intermediate router with a 1-second outbound per-packet bandwidth delay and no competing
traffic.
• One intermediate router with a 100-ms outbound per-packet bandwidth delay and with a steadily
replenished (from another source) 10 packets in the queue.
a. How might a transport protocol in general distinguish between these two cases?
b. Suppose TCP Vegas sends over the above connections, with an initial CongestionWindow of 3
packets. What will happen to CongestionWindow in each case? Assume BaseRTT = 1 second and
β is one packet per second.
3. Token Bucket
The token bucket scheme places a limit on the length of time at which traffic can depart at the maximum rate. Let
the token bucket be defined by a buck size B octets and a token arrival rate of R octets/sec, and let the maximum
output data rate be M octets/sec.
a. Derive a formula for S, which is the length of the maximum-rate burst. That is, for how long can a
flow transmit at the maximum output rate when governed by a token bucket?
b. What is the value of S for B = 250 KB, R = 2 MBps and M = 25 MBps? (Hint: the formula for S is not
as simple as it might appear, because more tokens arrive while the burst is being output.)
4. TCP Congestion Performance
Consider a TCP system implementing slow start and congestion avoidance with fast retransmit and fast recovery.
When a connection is setup the congestion window is initialized to one segment and the slow start threshold to 64
segments. To simplify the problem, assume that the timeout is equal to the RTT (an exact estimate) and specify time
in units of RTT, such that one time slot is one RTT.
Packet transmissions are such that at each time slot the sender sends all packets in the congestion window. If ACK's
are received in the next time slot, there is no timeout. In addition, to simplify matters either the entire window is
acknowledged or none of its segments are acknowledged.
For a particular connection, ACK's are received in time slots 1-6, 8-22, 24-33, 35-38, and 40-50. Timeouts occur in
slots 7, 23 and 34; in slot 40, three duplicate ACK's are received for the packets sent in time slot 38.
For the system described, plot both the congestion window and the slow start threshold (on the same graph) versus
time (slots). Remember to consider the differences between slow start and congestion avoidance with fast retransmit
and fast recovery when changing the congestion window.
