 ECE466S 2019 COMPUTERNETWORKSII E.pdf-UN...
ECE466S_2019_COMPUTERNETWORKSII_E.pdf-UNIVERSITY OF TORONTO FACULTY OF APPLIED
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ECE466S 2019 COMPUTERNETWORKSII E.p...
ECE466S_2019_COMPUTERNETWORKSII_E.pdf-UNIVERSITY OF TORONTO FACULTY OF APPLIED
##### Page 1
UNIVERSITY OF TORONTO
FACULTY OF APPLIED SCIENCE AND ENGINEERING FINAL EXAM, APRIL 2019
ECE 466: Computer Networks II
Examiner:
J. Liebeherr
Exam Type: D
Permitted aids:
-
Two handwritten aid sheets (standard form, only one side of each sheet can be written)
or one sheet (written on both sides). Content can be any information desired, without
restriction.
-
Calculator (Type 1) and a ruler.
There are six problems. All problems have equal weight (10 marks each).
The duration of the exam is 2.5 hours.
1

##### Page 2
1. Mm-Plus Algebra
(a)
(5 marks)
Assume that
F
and
C
are arbitrary non-negative, non-decreasing, and one-
sided functions. Consider the following expressions for an arbitrary time t > 0:
FØC(t)<F(t),
F®G(t)>F(t).
Show whether the expressions are true or false.
(b)
(5 marks)
Let
F
be defined as
ro,
ti
Provide an expression for
F ® F(t)
for t > 0..
Provide an expression for
F
0
F(t)
for t > 0.
2

##### Page 3
2. Arrivals and Envelopes Consider the following arrival function of a flow:
Io,
I
5k+
A(t)=
2t —3
-
k
1
4t -
9(k +
1),
t<O
4k <t<4k+2
4k+2 <t<4k+3
4k+3 <t
<4k+4
k
=
0,1,2,...
(2 marks)
Provide the values of the arrival function
A(t)
at times t
=
0, 1, 2, 3, 4, 5, 6, 7, 8.
(3
marks)
Provide the values of the minimal envelope E
A
of the arrivals at times t
=
0, 1, 2, 3, 4, 5, 6, 7, 8.
(3
marks)
Suppose that
A(t)
describes the input to a buffered link with rate
C
=
2 (data
units per time unit). Provide the values of the departure function
D(t)
for the traffic
output of the buffered link at times t
=
0, 1, 2, 3, 4, 5, 6, 7, 8.
(2 marks)
Consider an arbitrary arrival function
A
that complies to the traffic enve-
lope
SA
(that is,
A
E4.
Suppose A describes the input to a buffered link with rate
C
=
2 (data units per time unit). Describe how you can use the solution to (b) and/or
(c) to obtain upper bounds for the backlog and delay at the buffered link. Provide the
obtained backlog and delay bounds.
3

##### Page 4
3. Service Curves Consider two network elements in sequence with service curves S
1
and
82,
as shown in the figure. In (a) and (b), derive an expression that describes the service curve
of the sequence of two elements. Show the steps of your solutions.
(5 marks)
Let S
1
and S
2
be given as
lo,
ift1,
S1(t)=l+1
ift>1.
lo,
ift2,
82(t)=13 ift>2.
(5 marks)
Let Si and S
2
be given as
1
0,
t2,
Si(t)= (t-2)
2
, t>2,
( 0,
tO,
and
8
2
(t)
=
2
,
t
> 0
,
4

##### Page 5
4. Traffic Shaping
Consider a traffic shaping algorithm with parameters
b
>
0 and
r
>
0 that operates with a
counter VC.
.
Initially, VC
=
0.
When a packet of size £ bytes arrives at time t:
-
Set the counter to VC
=
max {VC, t} +
-
If VC
-
t, the packet departs immediately.
-
Otherwise, the departure time of the packet is set to VC
-
Assume the shaping parameters are set to
b
=
2000 bits,
r
=
0.5 Mbps.
Consider an arrival scenario of packets with the following arrival times and packet sizes:
Packet index
1
1
2
1
3
1
4
5
6
Arrival time
(ms)
Packet sizes
(bits)
0
1000
1
2000
2
2000
3
1000
12
2000
13
2000
(4
marks)
Provide the departure times of the packets with the given shaping algorithm.
(4
marks)
Provide the departure times of the packets for a token bucket traffic shaper
with burst size
b
=
2000 bits and rate
r
=
0.5 Mbps.
(2 marks)
Compare the two shaping algorithms (used in (a) and (b)) with respect to the
outcome of the departure times and the effort for implementing the shaping algorithms.
5

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