Telcom 2120 Network Performance Homework 7 Spring 2004
1. (a) Consider an M/M/2 queue with arrival rate service rate , find the mean delay in
the system (b) Consider an M/M/1 queue with the same arrival rate and a single server
that works twice as fast at the servers in part (a) namely 2 , determine the mean delay
and compare the results with (a) as to which system is faster.
2. Consider an T1 link in an campus backbone network, fixed size 53 byte packets arrive
according to a Poisson at a rate of 2,500 cells/sec. (a) Determine the mean delay at the
link. (b) Repeat (a) for the case when the packets are uniformly distributed between 33
bytes and 73 bytes.
3. Consider a virtual-circuit packet-switching network shown below. The network contains
5 packet-switched nodes connecting via unidirectional links. Multiple virtual-circuit (VC)
connections are established over this network where VC source-destination pairs, VC
routing paths, and data rates are listed in the table. If all links operate at 19.2 kbps and
packet size is exponentially distributed with the average of 960 bits. Assuming that traffic
of each VC arrives according to Poisson process.
a
b
c
d
e
5-node network
VC Number Source-Destination VC Path Data Rate
(packets/sec)
VC-1 a b ab 5
VC-2 a c adc 7
VC-3 a d ad 1
VC-4 a e abe 3
VC-5 b c bc 3
VC-6 b e be 5
VC-7 c e ce 10
VC-8 d c dc 3
VC-9 d e dce 1
(a) What is the network-wide packet delay?
(b) What is the average delay experience by a packet traversing the path a-b-c?
4. Consider the two stage queueing system below that models a dual processor router. All
servers have exponentially distributed services rates as shown. Departures from the first
