pipantasi4

2022-07-08

A measurement of the traffic generated by the packet source indicates that the average traffic is $\lambda$ [packets/s] and maximum traffic is $\sigma$ [packets/s]. The classic exponential distribution is not appropriate for modeling such a source of traffic, because the exponential distribution contains only one parameter (and two parameters were measured).
To model such a source of motion, you can use the shifted exponential distribution which is described by two parameters ($\gamma ,\delta >0$):
$f\left(\tau \right)=\left\{\begin{array}{cc}0& \tau
Random variable $\tau$ is the time interval between successive packets.
1. Draw a distribution graph (1). What is the relationship between the maximum traffic and $\delta$, for the distribution (#)?
2. Designate a mean value of the distribution (#).
3. Based on measurements of traffic sources $\left(\lambda ,\sigma \right)$ select firstly $\delta$ parameter for distribution (#), then $\gamma$ parameter for distribution (#).

Alec Blake

Expert

Part 1 is simple. If $\delta$ is the minimum interarrival time for consecutive packets, where time is measured in seconds, then at most $1/\delta$ packets can arrive in one second. For instance, if $\delta =0.01$ seconds, meaning that we are assured that the time between packets is at least 0.01 seconds, then the most packets we can observe in one second is 1/0.01=100 packets, and this is $\sigma$. So
$\sigma \delta =1.$
For Part 3, use what you know from Parts 1 and 2 to establish a relationship between $\lambda$ and $\gamma$. The average traffic intensity $\lambda$ is simply the average you found in Part 2. Solve for $\gamma$ in terms of $\lambda$ and $\sigma$.

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