A traditional traffic model for circuit switched data as well as packet data is the Poisson process in which the number of incoming packets per time is according to Poisson distribution. It is one of the most widely used and oldest traffic models. In this model the length of each packet is based on exponential distribution and the number of simultaneously ongoing packets is according to Erlang distribution [16].
The Poisson process is characterized as a renewal process. In a Poisson process the inter-arrival times are exponentially distributed with a rate parameter λ: P{An ≤ t} = 1 – exp(-λt).
The Poisson distribution is appropriate if the arrivals are from a large number of independent sources, referred to as Poisson sources. The distribution …show more content…
The traditional assumption of Poisson arrivals has been often justified by arguing that the aggregation of many independent and identically distributed renewal processes tends to a Poisson process when the number increases
Poisson arrivals with mean rate λ are separated by inter arrival times Equivalently, the number of arrivals up to time t is a Markov birth process with all birth rates of λ.
The Poisson arrival process has several properties that make it appealing for analysis.
• It is memoryless in the sense that, given the previous arrival occurred T time ago, the time to the next arrival will be exponentially distributed with mean 1/λ regardless of T.
In other words, the waiting time for the next arrival is independent of the time of the previous arrival. This memoryless property simplifies analysis because future arrivals do not need to take into account the past history of the arrival process.
• The number of arrivals in any interval of length t will have a Poisson probability distribution with mean λt .
• The sum of two independent Poisson arrival processes with rates λ1 and λ2 , is a Poisson process with rate λ1+ λ2. This is convenient for analysis because traffic flows are multiplexed in a
The Poisson process is characterized as a renewal process. In a Poisson process the inter-arrival times are exponentially distributed with a rate parameter λ: P{An ≤ t} = 1 – exp(-λt).
The Poisson distribution is appropriate if the arrivals are from a large number of independent sources, referred to as Poisson sources. The distribution …show more content…
The traditional assumption of Poisson arrivals has been often justified by arguing that the aggregation of many independent and identically distributed renewal processes tends to a Poisson process when the number increases
Poisson arrivals with mean rate λ are separated by inter arrival times Equivalently, the number of arrivals up to time t is a Markov birth process with all birth rates of λ.
The Poisson arrival process has several properties that make it appealing for analysis.
• It is memoryless in the sense that, given the previous arrival occurred T time ago, the time to the next arrival will be exponentially distributed with mean 1/λ regardless of T.
In other words, the waiting time for the next arrival is independent of the time of the previous arrival. This memoryless property simplifies analysis because future arrivals do not need to take into account the past history of the arrival process.
• The number of arrivals in any interval of length t will have a Poisson probability distribution with mean λt .
• The sum of two independent Poisson arrival processes with rates λ1 and λ2 , is a Poisson process with rate λ1+ λ2. This is convenient for analysis because traffic flows are multiplexed in a