For ensuring a given Quality of Service in IP networks for the various packet streams arriving at a link, they are assigned to different queues. By prioritizing the queues or by implementing weighted Round Robin or weighted packet-wise Head of the Line Processor Sharing (weighted fair queueing: WFQ) a corresponding partition of the link capacity to the packet streams to be transported can be ensured.

In the first part, we analyze the delay of the IP packets of a single queue. The arrival process of the packets at the link is modeled by an Interrupted Poisson Process (IPP), where exponentially distributed on and off phases alternate. During the on phases there arrive packets of random length according to a Poisson process, during the off phases there is no packet arrival. The packets are served with constant speed (link rate) according to the FIFO discipline. From a mathematical point of view, the sojourn time in the queueing system IPP/GI/1 is analyzed.

In the second part, we analyze the delay of the IP packets of a marked queue under priority scheduling. For the marked queue priority scheduling means that its service is interrupted after a random duration U, corresponding to an empty period of the higher prior queues, for a random duration D, corresponding to a busy period of the higher prior queues, where the service of a just served packet is finished. As an approximation of this mechanism, phase-type distributed random variables may be chosen for U and D, respectively, whose parameters are determined by means of the first model. The arrival process is modeled by an IPP again, and the length of the packets is modeled by an Erlang distribution (E). From a mathematical point of view, the sojourn time in the queueing system IPP/E/1 with a random environment is analyzed.

In the third part, we investigate the superposition of packet streams. As the superposition of independent IPPs is not an IPP and since in the above models the arrival processes are modeled by IPPs, we have to approximate the superposition of independent IPPs by an appropriate IPP with respect to delay characteristics.

In the fourth part, we investigate the splitting of packet steams. For given weights we search for a splitting of an IPP such that the approximate superposition of the split IPPs reproduces the original IPP and that some constraints are fulfilled.


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