Final Exam Solutions
May 3, 1999
1. (15 points) Give expressionsfor the steady state probabilities of a Random Arrival, Random Departure
(RARD) queue with a queue length of 20, cell arrival probability
:
2 and cell departure probability
:
5.
(
0
)=
:
5
1
,
:
2521
:
75
,
:
5
and
(
j
)=(
:
25
j
=:
5
)
(
0
)
.
Give an expression for the virtual cell discardprobability for a queue carrying traffic from 30 bursty
sources, each with a peak data rate of 8% of the link rate and an average data rate equal to 0.5% of
the link rate.
12 such sources can be on without exceeding the link rate and the probability that any given sources
is on is 1/16. So the virtual cell discard probability is
29
X
i
=
12
29
i
!
(
1
=
16
)(
15
=
16
)
29
,
i
(
:
08
(
i
+
1
)
,
1
)
=
(
:
08
(
i
+
1
))
The IBA model and virtual cell discard probability can be used to estimate the cell loss for bursty
sources. Which is more accurate in each of the following cases? Explain why.
50 bursty sources with peak rate equal to 5% of the link rate, an average rate equal to .5% of the
link rate all sendingdata to a queuelarge enough tohold one average size burst.
Virtual cell discard probability is more accurate in this case. In general, it produces accurate
results when the peak rate of the sources is much smaller than the link rate and the buffer is
small, as is true here. The IBA model works poorly in these situations.
10 bursty sources with peak rate equal to 50% of the link rate, an average rate equal to 5% of
the link rate all sending data to a queuelarge enough to hold 30 average size bursts.
Here the IBA model is better. It gives good results when the buffer is much larger than the
burst size and the peak rate is close to the link rate. The virtual cell discard probability is a poor
estimate for the actual cell discard probability in thiscase.
1
