Results 1 
6 of
6
Impact of aggregated, selfsimilar ON/OFF traffic on delay in stationary queueing models
 Proceedings of SPIE, Performance and Control of Network Systems III
, 1999
"... The impact of the now widely acknowledged selfsimilar property of network traffic on cell delay in a single server queueing model is investigated. The analytic traffic model, called NBurst, uses the superposition of N independent cell streams of ON/OFF type with PowerTail distributed ON periods. ..."
Abstract

Cited by 12 (5 self)
 Add to MetaCart
The impact of the now widely acknowledged selfsimilar property of network traffic on cell delay in a single server queueing model is investigated. The analytic traffic model, called NBurst, uses the superposition of N independent cell streams of ON/OFF type with PowerTail distributed ON periods. Delay for such arrival processes is mainly caused by oversaturation periods, which occur when too many sources are in their ONstate. The duration of these oversaturation periods is shown to have a PowerTail distribution, whose exponent fi is in most scenarios different from the tail exponent of the individual ONperiod. 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 selfsimilar traffic. Furthermore, in real networks, a Maximum Burst Size (MBS) leads...
Behavior of TCPlike elastic traffic at a buffered bottleneck router
, 2001
"... 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 char ..."
Abstract

Cited by 10 (0 self)
 Add to MetaCart
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 TCPlike flowcontrol mechanisms is captured in the analytic model by the feature that the packetrate of active connections can be throttled in order to avoid that the overall packetstream exceeds the outputbandwidth 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 bufferoccupancy 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) PowerTail distributions for the ON periods leads to conclusions about the behavior of longrange dependent traffic under the influence of TCP's flowcontrol mechanism. Keywords TCP flowcontrol, ON/OFF models, Markov Modulated Poisson Processes, LongRange Dependence, Truncated PowerTail Distributions I.
Comparison of the Analytic NBurst Model with Other Approximations to Selfsimilar Telecommunications Traffic
, 1999
"... The NBurst model describes traffic in telecommunication systems as the superposition of N packet (or cell) streams of ON/OFF type, i.e., during its ONtime each source generates packets according to a Poisson Process with intraburst packet rate p . As such, the NBurst is an analytic PointProcess ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
The NBurst model describes traffic in telecommunication systems as the superposition of N packet (or cell) streams of ON/OFF type, i.e., during its ONtime each source generates packets according to a Poisson Process with intraburst packet rate p . As such, the NBurst is an analytic PointProcess modeling network traffic on the packet level. When using PowerTail Distributions for the duration of the ON periods, selfsimilar properties are observed. A variety of widely used approximate traffic models are shown to be limiting cases of NBurst/G/1 queues. For very low intraburst packet rates, the NBurst/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 packetbased 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 ...
Exact Buffer Overflow Calculations for Queues Via Martingales
, 2000
"... 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 ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
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 longrange dependent properties in the packet arrival process. Different approximations that are obtained from asymptotic theory are compared with exact numerical results.
Transient buffer overflow in queueing models with aggregated, selfsimilar ON/OFF traffic
"... The impact of the now widely acknowledged selfsimilar property of network traffic on buffer overflows in a single server queueing model is investigated. The analytic traffic model, called NBurst, uses the superposition of N independent cell streams of ON/OFF type with PowerTail distributed ON pe ..."
Abstract
 Add to MetaCart
The impact of the now widely acknowledged selfsimilar property of network traffic on buffer overflows in a single server queueing model is investigated. The analytic traffic model, called NBurst, uses the superposition of N independent cell streams of ON/OFF type with PowerTail distributed ON periods. Due to the high correlation of overflow events for queueing models with selfsimilar arrival processes, the steadystate 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 selfsimilar property leads to a very peculiar behavior, namely that the socalled conditional overflow ratio increases asymptotically with increasing buffersize. The derivation of the asymptotic behavior provides additional insight into the ...
Buffer Size Issues in the Presence of . . .
 IFIP WORKSHOP ON TRAFFIC MANAGEMENT AND DESIGN OF ATM NETWORKS
, 1999
"... An analytic queueing model of an ATM switch with the NBurst arrival process, which exhibits selfsimilar properties, is used to derive statements about the impact of selfsimilar traffic on bufferoverflow probabilities. The cellarrivals of the NBurst model are generated by multiplexed ON/OFF sou ..."
Abstract
 Add to MetaCart
An analytic queueing model of an ATM switch with the NBurst arrival process, which exhibits selfsimilar properties, is used to derive statements about the impact of selfsimilar traffic on bufferoverflow probabilities. The cellarrivals of the NBurst model are generated by multiplexed ON/OFF sources with PowerTailed ONtimes. The analysis shows that in most cases the bufferoverflow probability decays only very slowly with increasing buffer size, namely by a PowerLaw whose exponent is derived. Furthermore, the impact of a Maximum Burst Size, implemented by truncations of the PowerTail distributions, is discussed qualitatively. In the second part of the paper, the cellloss probability in an NBurst/M/1/B s losssystem is compared with the overflow probability in an infinitebuffer backup model: both models qualitatively exhibit the same PowerLaw behavior, with the overflow probability in the infinite system being an upper bound to the loss probability. In addition, it is s...