### Abstract

We consider the problem of allocation of network resources for a Variable Bit Rate connection requiring a probabilistic bound on cell delay. We only make the standard assumption that the connection has a deterministically controlled shape as specified by a (σ, ρ) constraint, simultaneously with a (0, π) (or peak-rate) constraint. This paper settles one instance of this open problem raised by Doshi which is motivated by the need to obtain worst-case probabilistic bounds, and is particularly applicable to situations where no statistical descriptors of network traffic are available. In other words, instead of an approach based on traffic modeling and effective bandwidths, we describe an approach using `worst-case' bounds assuming only these deterministic constraints. In particular, we describe that traffic pattern (among all stationary-ergodic and deterministically constrained arrival processes) which maximizes the `overflow probability' P(Q_{0}>b), for a given buffer level b, where {Q_{t}} is the buffer occupancy process, in steady-state, when the service rate is some constant c between ρ and π. This result could be used for resource provisioning of connections or for performance evaluation of network devices.

Original language | English (US) |
---|---|

Pages (from-to) | 545-550 |

Number of pages | 6 |

Journal | Proceedings of the IEEE Conference on Decision and Control |

Volume | 1 |

State | Published - 1998 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Control and Systems Engineering
- Safety, Risk, Reliability and Quality
- Chemical Health and Safety

### Cite this

*Proceedings of the IEEE Conference on Decision and Control*,

*1*, 545-550.

}

*Proceedings of the IEEE Conference on Decision and Control*, vol. 1, pp. 545-550.

**Shape-controlled traffic patterns that maximize overflow probabilities in high-speed networks.** / Kesidis, George; Konstantopoulos, Takis.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Shape-controlled traffic patterns that maximize overflow probabilities in high-speed networks

AU - Kesidis, George

AU - Konstantopoulos, Takis

PY - 1998

Y1 - 1998

N2 - We consider the problem of allocation of network resources for a Variable Bit Rate connection requiring a probabilistic bound on cell delay. We only make the standard assumption that the connection has a deterministically controlled shape as specified by a (σ, ρ) constraint, simultaneously with a (0, π) (or peak-rate) constraint. This paper settles one instance of this open problem raised by Doshi which is motivated by the need to obtain worst-case probabilistic bounds, and is particularly applicable to situations where no statistical descriptors of network traffic are available. In other words, instead of an approach based on traffic modeling and effective bandwidths, we describe an approach using `worst-case' bounds assuming only these deterministic constraints. In particular, we describe that traffic pattern (among all stationary-ergodic and deterministically constrained arrival processes) which maximizes the `overflow probability' P(Q0>b), for a given buffer level b, where {Qt} is the buffer occupancy process, in steady-state, when the service rate is some constant c between ρ and π. This result could be used for resource provisioning of connections or for performance evaluation of network devices.

AB - We consider the problem of allocation of network resources for a Variable Bit Rate connection requiring a probabilistic bound on cell delay. We only make the standard assumption that the connection has a deterministically controlled shape as specified by a (σ, ρ) constraint, simultaneously with a (0, π) (or peak-rate) constraint. This paper settles one instance of this open problem raised by Doshi which is motivated by the need to obtain worst-case probabilistic bounds, and is particularly applicable to situations where no statistical descriptors of network traffic are available. In other words, instead of an approach based on traffic modeling and effective bandwidths, we describe an approach using `worst-case' bounds assuming only these deterministic constraints. In particular, we describe that traffic pattern (among all stationary-ergodic and deterministically constrained arrival processes) which maximizes the `overflow probability' P(Q0>b), for a given buffer level b, where {Qt} is the buffer occupancy process, in steady-state, when the service rate is some constant c between ρ and π. This result could be used for resource provisioning of connections or for performance evaluation of network devices.

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UR - http://www.scopus.com/inward/citedby.url?scp=0032268914&partnerID=8YFLogxK

M3 - Article

VL - 1

SP - 545

EP - 550

JO - Proceedings of the IEEE Conference on Decision and Control

JF - Proceedings of the IEEE Conference on Decision and Control

SN - 0191-2216

ER -