Closed-form expressions on the geometric tail behavior of statistical multiplexers with heterogeneous traffic

Hwang, Gang Uk; Choi, Bong Dae

doi:10.1109/26.737393

IEEE Trans. Commun.

1998

DOI: 10.1109/26.737393

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Closed-form expressions on the geometric tail behavior of statistical multiplexers with heterogeneous traffic

Gang Uk Hwang

Bong Dae Choi²

Abstract: In this paper, we consider a statistical multiplexer fed by heterogeneous ON and OFF sources. We provide closedform results on the tail behavior of the queue-length distribution for statistical multiplexers, where the tail behavior can be expressed in terms of traffic parameters such as the first and second moments of ON and OFF periods for individual sources. Since our results are of simple closed-form, they can be used to provide a simple and efficient way to predict the tail behavior and the impact of traff… Show more

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Cited by 8 publications

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“…Other types of arrival processes incorporate time correlation usually without the notion of higher-level messages. A simple class are on/off-type arrivals [36,41,22,14,24], where a finite number of users generate one packet per slot during on-periods and no packets during offperiods. Another important class of correlated arrival processes are the Markovian Arrival Processes (MAP), studied in [35,29,30,3,9].…”

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Performance analysis of buffers with train arrivals and correlated output interruptions

Feyaerts¹,

Vuyst²,

Bruneel³

et al. 2015

Journal of Industrial &Amp; Management Optimization

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In this paper, we study a discrete-time buffer system with a timecorrelated packet arrival process and one unreliable output line. In particular, packets arrive to the buffer in the form of variable-length packet trains at a fixed rate of exactly one packet per slot. The packet trains are assumed to have a geometric length, such that each packet has a fixed probability of being the last of its corresponding train. The output line is governed by a Markovian process, such that the probability that the line is available during a slot depends on the state of the underlying J-state Markov process during that slot.First, we provide a general analysis of the state of the buffer system based on a matrix generating functions approach. This also leads to an expression for the mean buffer content. Additionally, we take a closer look at the distributions of the packet delay and the train delay. In order to make matters more concrete, we next present a detailed and explicit analysis of the buffer system in case the output line is governed by a 2-state Markov process. Some numerical examples help to visualise the influence of the various model parameters.

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mentioning

confidence: 99%

Performance analysis of buffers with train arrivals and correlated output interruptions

Feyaerts¹,

Vuyst²,

Bruneel³

et al. 2015

Journal of Industrial &Amp; Management Optimization

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Discrete-time buffer systems with session-based arrival streams

Hoflack¹,

Vuyst²,

Wittevrongel³

et al. 2010

Performance Evaluation

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The paper considers a discrete-time buffer system with infinite storage capacity and one single output channel. Users can start and end sessions during which they are active and send packets to the buffer system. In this paper we study a simple model for the resulting session-based arrival process: we assume that each active user generates a random but strictly positive number of packets per time slot. Furthermore it is assumed that the time (expressed in slots) needed to transmit a packet is geometrically distributed. The distribution of the session lengths is also geometrical. This model can be applied to study the traffic of a file server, where one file download by a user is considered to be one session. The probability generating functions of the steady-state number of active sessions, the buffer occupancy and the packet delay are derived. We also derive an approximation for the tail probabilities of the buffer occupancy. Furthermore, an expression for the mean session delay is obtained. This allows us to study the influence of the different system parameters: some examples are presented. We end by applying the model to a web server, based on actual web traffic.

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2000

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Closed-form expressions on the geometric tail behavior of statistical multiplexers with heterogeneous traffic

Cited by 8 publications

References 10 publications

Performance analysis of buffers with train arrivals and correlated output interruptions

Performance analysis of buffers with train arrivals and correlated output interruptions

Discrete-time buffer systems with session-based arrival streams

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