How Different Queuing Systems Affect the Discrete Representation of a Packet Stream

A large number of research articles are devoted to queuing theory and queuing systems. Most of these articles employ a continuous representation of network traffic, in the form of timestamps or interarrival times. In this, there is a contradiction with more recent traffic models capable of capturing the multi-fractal nature of network traffic e.g. the conservative cascade model. These models often represent packet streams in a discrete way by calculating the bin count vector. Directly describing the effect of queuing systems on the variance-time behavior of this discrete representation of traffic is relatively unexplored terrain. This paper presents and analyzes some qualitative results on the altering of a bin count vector when passing it through a queuing system. After the detailed analysis of a basic fixed service time queue, some considerations are made on real networking components. This leads to extending the basic queue model with variable service times, based on the packet size distribution. Finally, the influence of the shape of this distribution on the queuing effects is studied.