CCN Activity Session for Section 3.2 – Queuing
A statistical multiplexer is used to connect 3 local machines to a single external networking link as part of a sensor network. The multiplexer has an arrival rate (l) of 125 packets per second, and a service rate (μ) of 500 packets per second.
Question
• What is the load (r) on the multiplexer?
Assume the maximum number of packets in the system (k) is 5. One expression for delay in the system is given by:
! = # = 125 = 0.25 $ 500
Where Ploss is given by:
=𝑃 =(1−r)r$
$
!”= % −()+1)%,-. 1−% 1−%,-.
What is the average packet delay on the network?
(1 − 0.25)0.25′ 1 − 0.25(
Question
The designer of the network would like to reduce the probability of packet loss, while maintaining the transmission rate from the sensors, and the overall rate of transmission on the outgoing link. What steps could be taken to achieve this? Explain your answer.
Increasing the buffer size would reduce the chance of overflows, thereby reducing the probability of packet loss.
1−r$%&
If the average number of packets in the multiplexer is given by:
Question
𝑃 !”##
& (* + 1)&-./ 0.25 6 × 0.257 ![#]=1−&− 1−&-./ =0.75−1−0.257=0.331868
𝑃 =𝑃 = !”## $
=0.000733
![#] = ![&] = 0.331868 = 0.00266 ‘(1 − +,-..) 125 × (1 − 0.000733)