scholarly journals Modeling network traffic by a cluster Poisson input process with heavy and light-tailed file sizes

2010 ◽  
Vol 66 (4) ◽  
pp. 313-350 ◽  
Author(s):  
Vicky Fasen
Keyword(s):  
Network Traffic ◽  
Input Process ◽  
Poisson Input

On the distribution of attributes in organizations

1974 ◽  
Vol 11 (03) ◽  
pp. 529-543
Author(s):  
Horand Störmer
Keyword(s):  
Input Process ◽  
Organization Model ◽  
Generalized Poisson ◽  
Poisson Input

The paper deals with a stochastic organization model described by a generalized Poisson input process and given probabilities of entering individuals obtaining certain attributes in this organization. The distribution of attributes at any given instant is derived. Examples illustrate the application of obtained results.

Single-server queues with impatient customers

1984 ◽  
Vol 16 (4) ◽  
pp. 887-905 ◽  
Author(s):  
F. Baccelli ◽  
P. Boyer ◽  
G. Hebuterne
Keyword(s):  
Waiting Time ◽  
Queueing System ◽  
Distribution Functions ◽  
Single Server ◽  
Waiting Time Distribution ◽  
Input Process ◽  
Poisson Input ◽  
Virtual Waiting Time ◽  
Random Threshold ◽  
The Stability

We consider a single-server queueing system in which a customer gives up whenever his waiting time is larger than a random threshold, his patience time. In the case of a GI/GI/1 queue with i.i.d. patience times, we establish the extensions of the classical GI/GI/1 formulae concerning the stability condition and the relation between actual and virtual waiting-time distribution functions. We also prove that these last two distribution functions coincide in the case of a Poisson input process and determine their common law.

Exponential ergodicity in Markovian queueing and dam models

1979 ◽  
Vol 16 (4) ◽  
pp. 867-880 ◽  
Author(s):  
Pekka Tuominen ◽  
Richard L. Tweedie
Keyword(s):  
Transition Probabilities ◽  
Continuous Process ◽  
Typical Result ◽  
Input Process ◽  
Exponential Ergodicity ◽  
Poisson Input ◽  
State Dependent ◽  
Input Size ◽  
Drift Condition ◽  
Storage Processes

We investigate conditions under which the transition probabilities of various Markovian storage processes approach a stationary limiting distribution π at an exponential rate. The models considered include the waiting time of the M/G/1 queue, and models for dams with additive input and state-dependent release rule satisfying a ‘negative mean drift' condition. A typical result is that this exponential ergodicity holds provided the input process is ‘exponentially bounded'; for example, in the case of a compound Poisson input, a sufficient condition is an exponential bound on the tail of the input size distribution. The results are proved by comparing the discrete-time skeletons of the Markov process with the behaviour of a random walk, and then showing that the continuous process inherits the exponential ergodicity of any of its skeletons.

Exponential ergodicity in Markovian queueing and dam models

1979 ◽  
Vol 16 (04) ◽  
pp. 867-880 ◽  
Author(s):  
Pekka Tuominen ◽  
Richard L. Tweedie
Keyword(s):  
Transition Probabilities ◽  
Continuous Process ◽  
Typical Result ◽  
Input Process ◽  
Exponential Ergodicity ◽  
Poisson Input ◽  
State Dependent ◽  
Input Size ◽  
Drift Condition ◽  
Storage Processes

We investigate conditions under which the transition probabilities of various Markovian storage processes approach a stationary limiting distribution π at an exponential rate. The models considered include the waiting time of the M/G/1 queue, and models for dams with additive input and state-dependent release rule satisfying a ‘negative mean drift' condition. A typical result is that this exponential ergodicity holds provided the input process is ‘exponentially bounded'; for example, in the case of a compound Poisson input, a sufficient condition is an exponential bound on the tail of the input size distribution. The results are proved by comparing the discrete-time skeletons of the Markov process with the behaviour of a random walk, and then showing that the continuous process inherits the exponential ergodicity of any of its skeletons.

scholarly journals A fluid cluster Poisson input process can look like a fractional Brownian motion even in the slow growth aggregation regime

2009 ◽  
Vol 41 (2) ◽  
pp. 393-427 ◽  
Author(s):  
Vicky Fasen ◽  
Gennady Samorodnitsky
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Communication Networks ◽  
Slow Growth ◽  
Input Process ◽  
Fluid Queue ◽  
Stable Motion ◽  
Poisson Input ◽  
Growth Regime ◽  
Poisson Arrivals

We show that, contrary to common wisdom, the cumulative input process in a fluid queue with cluster Poisson arrivals can converge, in the slow growth regime, to a fractional Brownian motion, and not to a Lévy stable motion. This emphasizes the lack of robustness of Lévy stable motions as ‘birds-eye’ descriptions of the traffic in communication networks.

scholarly journals A fluid cluster Poisson input process can look like a fractional Brownian motion even in the slow growth aggregation regime

2009 ◽  
Vol 41 (02) ◽  
pp. 393-427
Author(s):  
Vicky Fasen ◽  
Gennady Samorodnitsky
Keyword(s):  
Brownian Motion ◽  
Fractional Brownian Motion ◽  
Communication Networks ◽  
Slow Growth ◽  
Input Process ◽  
Fluid Queue ◽  
Stable Motion ◽  
Poisson Input ◽  
Growth Regime ◽  
Poisson Arrivals

We show that, contrary to common wisdom, the cumulative input process in a fluid queue with cluster Poisson arrivals can converge, in the slow growth regime, to a fractional Brownian motion, and not to a Lévy stable motion. This emphasizes the lack of robustness of Lévy stable motions as ‘birds-eye’ descriptions of the traffic in communication networks.

On the distribution of attributes in organizations

1974 ◽  
Vol 11 (3) ◽  
pp. 529-543
Author(s):  
Horand Störmer
Keyword(s):  
Input Process ◽  
Organization Model ◽  
Generalized Poisson ◽  
Poisson Input

The paper deals with a stochastic organization model described by a generalized Poisson input process and given probabilities of entering individuals obtaining certain attributes in this organization. The distribution of attributes at any given instant is derived. Examples illustrate the application of obtained results.

Single-server queues with impatient customers

1984 ◽  
Vol 16 (04) ◽  
pp. 887-905 ◽  
Author(s):  
F. Baccelli ◽  
P. Boyer ◽  
G. Hebuterne
Keyword(s):  
Waiting Time ◽  
Queueing System ◽  
Distribution Functions ◽  
Single Server ◽  
Waiting Time Distribution ◽  
Input Process ◽  
Poisson Input ◽  
Virtual Waiting Time ◽  
Random Threshold ◽  
The Stability

We consider a single-server queueing system in which a customer gives up whenever his waiting time is larger than a random threshold, his patience time. In the case of a GI/GI/1 queue with i.i.d. patience times, we establish the extensions of the classical GI/GI/1 formulae concerning the stability condition and the relation between actual and virtual waiting-time distribution functions. We also prove that these last two distribution functions coincide in the case of a Poisson input process and determine their common law.

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