The impact of the now widely acknowledged self-similar property of network traffic on cell delay in a single server queueing model is investigated. The analytic traffic model, called N-Burst, uses the superposition of N independent cell streams of ON/OFF type with Power-Tail distributed ON periods. Delay for such arrival processes is mainly caused by over-saturation periods, which occur when too many sources are in their ON-state. The duration of these over-saturation periods is shown to have a Power-Tail distribution, whose exponent fi is in most scenarios different from the tail exponent of the individual ON-period. Conditions on the model parameters, for which the mean and higher moments of the delay distribution become infinite, are investigated. Since these conditions depend on traffic parameters as well as on network parameters, careful network design can alleviate the performance impact of such self-similar traffic. Furthermore, in real networks, a Maximum Burst Size (MBS) leads...

A major challenge in traffic modeling and performance analysis for the Transmission Control Protocol (TCP) stems from the fact that the incoming traffic is not independent of the congestion level in the network. This paper investigates a queueing model where the traffic essentially shows ON/OFF characteristics, i.e. the number of active TCP connections of finite (probabilistic) duration varies as described by a stochastic process. The essential behavior of TCP-like flow-control mechanisms is captured in the analytic model by the feature that the packet-rate of active connections can be throttled in order to avoid that the overall packet-stream exceeds the output-bandwidth of the bottleneck router. By appropriate adjustment of the connection duration, the number of packets in the connections remains unaffected. However, since TCP reacts to existing congestion, the throttling mechanism is only activated when the buffer-occupancy at the bottleneck router exceeds a certain threshold. The impact of such a flowcontrol mechanism on the characteristics of the incoming traffic as well as on the performance behavior at the bottleneck router is discussed and illustrated by numerical results of the analytic model. In particular, the use of (truncated) Power-Tail distributions for the ON periods leads to conclusions about the behavior of long-range dependent traffic under the influence of TCP's flow-control mechanism. Keywords--- TCP flow-control, ON/OFF models, Markov Modulated Poisson Processes, Long-Range Dependence, Truncated Power-Tail Distributions I.

The N-Burst model describes traffic in telecommunication systems as the superposition of N packet (or cell) streams of ON/OFF type, i.e., during its ON-time each source generates packets according to a Poisson Process with intra-burst packet rate p . As such, the N-Burst is an analytic Point-Process modeling network traffic on the packet level. When using Power-Tail Distributions for the duration of the ON periods, self-similar properties are observed. A variety of widely used approximate traffic models are shown to be limiting cases of N-Burst/G/1 queues. For very low intra-burst packet rates, the N-Burst/G/1 model reduces to an M/G/1 queue. For p ! 1 all packets in a burst arrive simultaneously and the model reduces to a Bulk arrival, or M (X) =G=1, queue. In the same limit, the packet-based model can be compared to a model on the burst level, an M/G/1 queue where the individual customers represent complete bursts rather than individual packets. Thus the mean system time describes ...

Let = n be the first time a queueing process like the queue length or workload exceeds a level n. For the M/M/1 queue length process, the mean IE and the Laplace transform IEe \Gammas is derived in closed form using a martingale introduced in Kella & Whitt (1992). For workload processes and more general systems like MAP/PH/1, we use a Markov additive extension given in Asmussen & Kella (2000) to derive sets of linear equations determining the same quantities. Numerical illustrations are presented in the framework of M/M/1 and MMPP/M/1 with an application to performance evaluation of telecommunication systems with long--range dependent properties in the packet arrival process. Different approximations that are obtained from asymptotic theory are compared with exact numerical results.

The impact of the now widely acknowledged self-similar property of network traffic on buffer overflows in a single server queueing model is investigated. The analytic traffic model, called N-Burst, uses the superposition of N independent cell streams of ON/OFF type with Power-Tail distributed ON periods. Due to the high correlation of overflow events for queueing models with self-similar arrival processes, the steady-state buffer overflow probabilities can be misleading, especially when they are rather low. Several transient overflow parameters are introduced to capture the implications of the correlation in the overflow events. A discussion and analysis of those transient parameters for the given aggregated ON/OFF traffic model reveals that the self-similar property leads to a very peculiar behavior, namely that the so-called conditional overflow ratio increases asymptotically with increasing buffer-size. The derivation of the asymptotic behavior provides additional insight into the ...

An analytic queueing model of an ATM switch with the N-Burst arrival process, which exhibits self-similar properties, is used to derive statements about the impact of self-similar traffic on buffer-overflow probabilities. The cell-arrivals of the N-Burst model are generated by multiplexed ON/OFF sources with Power-Tailed ON-times. The analysis shows that in most cases the buffer-overflow probability decays only very slowly with increasing buffer size, namely by a Power-Law whose exponent is derived. Furthermore, the impact of a Maximum Burst Size, implemented by truncations of the Power-Tail distributions, is discussed qualitatively. In the second part of the paper, the cell-loss probability in an N-Burst/M/1/B s loss-system is compared with the overflow probability in an infinite-buffer backup model: both models qualitatively exhibit the same Power-Law behavior, with the overflow probability in the infinite system being an upper bound to the loss probability. In addition, it is s...