1 Consider a source of packets that can be described by a Po

1. Consider a source of packets that can be described by a Poisson process. Assume that there is only one source with an expected rate of 1 Mpacket ·sec1 .

1.1. Display the formal Poisson distribution for exactly x packets to arrive; x {Z + 0}.

1.2. Display the formal cumulative Poisson distribution for 0 x X packets to arrive.

1.3. How often would you expect to observe 2 Mpacket ·sec1 ? 10 Mpacket ·sec1

1.4. You actually measure 100 packets arriving in one sec – how often would you expect to observe this?

1.5. We discussed self-similarity in the actual trace of traffic arrivals – what does self-similarity mean in this context?

Solution

Poisson distribution = landha^x * e^-landha / x!

1.3. How often would you expect to observe 2 Mpacket ·sec1 ? 10 Mpacket ·sec1

P( x = 2 ) = 1^2 * e^-1    / 2!   = 0.1839