scholarly journals Tail Asymptotics for Monotone-Separable Networks

2007 ◽  
Vol 44 (02) ◽  
pp. 306-320
Author(s):  
Marc Lelarge
Keyword(s):  
Queueing Network ◽  
Network Models ◽  
Moment Generating Function ◽  
Stochastic Petri Nets ◽  
Arrival Process ◽  
Polling Systems ◽  
Tail Asymptotics ◽  
State Variables ◽  
Monotone Functions ◽  
Jackson Networks

A network belongs to the monotone separable class if its state variables are homogeneous and monotone functions of the epochs of the arrival process. This framework contains several classical queueing network models, including generalized Jackson networks, max-plus networks, polling systems, multiserver queues, and various classes of stochastic Petri nets. We use comparison relationships between networks of this class with independent and identically distributed driving sequences and the GI/GI/1/1 queue to obtain the tail asymptotics of the stationary maximal dater under light-tailed assumptions for service times. The exponential rate of decay is given as a function of a logarithmic moment generating function. We exemplify an explicit computation of this rate for the case of queues in tandem under various stochastic assumptions.

scholarly journals Tail Asymptotics for Monotone-Separable Networks

2007 ◽  
Vol 44 (02) ◽  
pp. 306-320
Author(s):  
Marc Lelarge
Keyword(s):  
Queueing Network ◽  
Network Models ◽  
Moment Generating Function ◽  
Stochastic Petri Nets ◽  
Arrival Process ◽  
Polling Systems ◽  
Tail Asymptotics ◽  
State Variables ◽  
Monotone Functions ◽  
Jackson Networks

A network belongs to the monotone separable class if its state variables are homogeneous and monotone functions of the epochs of the arrival process. This framework contains several classical queueing network models, including generalized Jackson networks, max-plus networks, polling systems, multiserver queues, and various classes of stochastic Petri nets. We use comparison relationships between networks of this class with independent and identically distributed driving sequences and the GI/GI/1/1 queue to obtain the tail asymptotics of the stationary maximal dater under light-tailed assumptions for service times. The exponential rate of decay is given as a function of a logarithmic moment generating function. We exemplify an explicit computation of this rate for the case of queues in tandem under various stochastic assumptions.

scholarly journals Tail Asymptotics for Monotone-Separable Networks

2007 ◽  
Vol 44 (2) ◽  
pp. 306-320 ◽  
Author(s):  
Marc Lelarge
Keyword(s):  
Queueing Network ◽  
Network Models ◽  
Moment Generating Function ◽  
Stochastic Petri Nets ◽  
Arrival Process ◽  
Polling Systems ◽  
Tail Asymptotics ◽  
State Variables ◽  
Monotone Functions ◽  
Jackson Networks

A network belongs to the monotone separable class if its state variables are homogeneous and monotone functions of the epochs of the arrival process. This framework contains several classical queueing network models, including generalized Jackson networks, max-plus networks, polling systems, multiserver queues, and various classes of stochastic Petri nets. We use comparison relationships between networks of this class with independent and identically distributed driving sequences and the GI/GI/1/1 queue to obtain the tail asymptotics of the stationary maximal dater under light-tailed assumptions for service times. The exponential rate of decay is given as a function of a logarithmic moment generating function. We exemplify an explicit computation of this rate for the case of queues in tandem under various stochastic assumptions.

Queueing network models for intelligent manufacturing units with dual-resource constraints

2021 ◽  
pp. 105213
Author(s):  
Hui-Yu Zhang ◽  
Qing-Xin Chen ◽  
James MacGregor Smith ◽  
Ning Mao ◽  
Yong Liao ◽  
...  
Keyword(s):  
Resource Constraints ◽  
Queueing Network ◽  
Network Models ◽  
Intelligent Manufacturing ◽  
Queueing Network Models

scholarly journals Limitations of demand- and pressure-driven modeling for large deficient networks

2017 ◽  
Vol 10 (2) ◽  
pp. 93-98 ◽  
Author(s):  
Mathias Braun ◽  
Olivier Piller ◽  
Jochen Deuerlein ◽  
Iraj Mortazavi
Keyword(s):  
Water Distribution ◽  
Network Models ◽  
Distribution Networks ◽  
Computer Applications ◽  
State Variables ◽  
Modeling Process ◽  
Uniqueness Of The Solution ◽  
Basic Equations ◽  
Physical Phenomena ◽  
Pressure Driven

Abstract. The calculation of hydraulic state variables for a network is an important task in managing the distribution of potable water. Over the years the mathematical modeling process has been improved by numerous researchers for utilization in new computer applications and the more realistic modeling of water distribution networks. But, in spite of these continuous advances, there are still a number of physical phenomena that may not be tackled correctly by current models. This paper will take a closer look at the two modeling paradigms given by demand- and pressure-driven modeling. The basic equations are introduced and parallels are drawn with the optimization formulations from electrical engineering. These formulations guarantee the existence and uniqueness of the solution. One of the central questions of the French and German research project ResiWater is the investigation of the network resilience in the case of extreme events or disasters. Under such extraordinary conditions where models are pushed beyond their limits, we talk about deficient network models. Examples of deficient networks are given by highly regulated flow, leakage or pipe bursts and cases where pressure falls below the vapor pressure of water. These examples will be presented and analyzed on the solvability and physical correctness of the solution with respect to demand- and pressure-driven models.

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