Predicting inter arrival time in Packet Switched Networks

In the world of computer communication networks, a packet-switched network (PSN) operates by transmitting data through small packets. This system allows the sender to efficiently dispatch data or network packets between the source and destination nodes over an internet network channel, enabling the exchange of information among various users and applications. A packet-switched network is referred to as a connection-less network, as it does not establish a continuous connection between source and destination points, distinguishing it from networks that are characterized by perpetual connections.

In packet-switched network, data is chopped up into smaller segments called packets and sent over the network. Apart from the segment of data , each packet contains the originating source, destination information and segment ID pointing to the position of the segment in the original data.

Queuing theory is used to analyze performance in packet-switched switched networks.

In packet-switched networks, events are random

• random packet arrivals
• random packet lengths

At the network layer, more emphasis is given on how long the packet waits in the buffer before being selected for transmission and how large are the buffers in each of the hops in its path to the destination.

Random events

Each packet arrival is a random process due to source variability, network conditions and traffic patterns to name a few.

Typically the packet arrival process is modeled as a Poisson process.

Assumptions: packet arrival time is an independent event. That is packet arriving at a specific time has no knowledge of other packets or their arrival time.

On the time line we can divide it into n sub intervals and at each sub interval there is some probability p that a new packet arrives.

Then on average we would expect np packets arriving in one unit of time.

But ultimately we would like to have n tends to infinity. So we make p=lamda/n , thus average or expected packets arriving on unit time becomes constant lamda.

The Poisson process

• Arrival rate of λ packets per second
• Over a small interval δ, P(exactly one arrival) = λδ + ο(δ) P(0 arrivals) = 1 - λδ + ο(δ) P(more than one arrival) = 0(δ) Where 0(δ)/ δ −> 0 as δ −> 0.
• It can be shown that:

Inter-arrival times

Inter-arrival times = Time that elapses between arrivals (IA)

P(IA <= t) = 1 - P(IA > t)

= 1 - P(0 arrivals in time t)

= 1 - e^(-λt)