NECESSARY AND SUFFICIENT CONDITIONS FOR THE STOCHASTIC COMPARISON OF JACKSON NETWORKS

2003 ◽  
Vol 17 (1) ◽  
pp. 143-151 ◽  
Author(s):  
Antonis Economou
Keyword(s):  
Continuous Time ◽  
Stochastic Order ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Stochastic Comparison ◽  
Jackson Networks ◽  
Continuous Time Markov Chains ◽  
Service Rates ◽  
Necessary And Sufficient

External and internal monotonicity properties for Jackson networks have been established in the literature with the use of coupling constructions. Recently, Lopez et al. derived necessary and sufficient conditions for the (strong) stochastic comparison of two-station Jackson networks with increasing service rates, by constructing a certain Markovian coupling. In this article, we state necessary and sufficient conditions for the stochastic comparison of L-station Jackson networks in the general case. The proof is based on a certain characterization of the stochastic order for continuous-time Markov chains, written in terms of their associated intensity matrices.

Stochastic domination and Markovian couplings

2000 ◽  
Vol 32 (4) ◽  
pp. 1064-1076 ◽  
Author(s):  
F. Javier López ◽  
Servet Martínez ◽  
Gerardo Sanz
Keyword(s):  
Markov Chains ◽  
Continuous Time ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Sufficient Conditions ◽  
Stochastic Domination ◽  
Jackson Networks ◽  
Partially Ordered ◽  
Continuous Time Markov Chains ◽  
Necessary And Sufficient

For continuous-time Markov chains with semigroups P, P' taking values in a partially ordered set, such that P ≤ stP', we show the existence of an order-preserving Markovian coupling and give a way to construct it. From our proof, we also obtain the conditions of Brandt and Last for stochastic domination in terms of the associated intensity matrices. Our result is applied to get necessary and sufficient conditions for the existence of Markovian couplings between two Jackson networks.

On the stochastic domination for batch-arrival, batch-service and assemble-transfer queueing networks

2003 ◽  
Vol 40 (04) ◽  
pp. 1103-1120 ◽  
Author(s):  
Antonis Economou
Keyword(s):  
Continuous Time ◽  
Queueing Networks ◽  
Stochastic Order ◽  
Batch Arrival ◽  
Batch Service ◽  
Stochastic Monotonicity ◽  
Stochastic Domination ◽  
Jackson Networks ◽  
Continuous Time Markov Chains

Stochastic monotonicity properties for various classes of queueing networks have been established in the literature mainly with the use of coupling constructions. Miyazawa and Taylor (1997) introduced a class of batch-arrival, batch-service and assemble-transfer queueing networks which can be thought of as generalized Jackson networks with batch movements. We study conditions for stochastic domination within this class of networks. The proofs are based on a certain characterization of the stochastic order for continuous-time Markov chains, written in terms of their associated intensity matrices.

On geometric and algebraic transience for block-structured Markov chains

2020 ◽  
Vol 57 (4) ◽  
pp. 1313-1338
Author(s):  
Yuanyuan Liu ◽  
Wendi Li ◽  
Xiuqin Li
Keyword(s):  
Markov Chains ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Stability Properties ◽  
System Parameters ◽  
Continuous Time Markov Chains ◽  
Necessary And Sufficient ◽  
Block Structured

AbstractBlock-structured Markov chains model a large variety of queueing problems and have many important applications in various areas. Stability properties have been well investigated for these Markov chains. In this paper we will present transient properties for two specific types of block-structured Markov chains, including M/G/1 type and GI/M/1 type. Necessary and sufficient conditions in terms of system parameters are obtained for geometric transience and algebraic transience. Possible extensions of the results to continuous-time Markov chains are also included.

On the stochastic domination for batch-arrival, batch-service and assemble-transfer queueing networks

2003 ◽  
Vol 40 (4) ◽  
pp. 1103-1120 ◽  
Author(s):  
Antonis Economou
Keyword(s):  
Continuous Time ◽  
Queueing Networks ◽  
Stochastic Order ◽  
Batch Arrival ◽  
Batch Service ◽  
Stochastic Monotonicity ◽  
Stochastic Domination ◽  
Jackson Networks ◽  
Continuous Time Markov Chains

Stochastic monotonicity properties for various classes of queueing networks have been established in the literature mainly with the use of coupling constructions. Miyazawa and Taylor (1997) introduced a class of batch-arrival, batch-service and assemble-transfer queueing networks which can be thought of as generalized Jackson networks with batch movements. We study conditions for stochastic domination within this class of networks. The proofs are based on a certain characterization of the stochastic order for continuous-time Markov chains, written in terms of their associated intensity matrices.

A characterization of the set of local martingale measures

2018 ◽  
Vol 18 (05) ◽  
pp. 1850042 ◽  
Author(s):  
Abdelkarem Berkaoui
Keyword(s):  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Local Martingale ◽  
Probability Measures ◽  
Martingale Measures ◽  
Necessary And Sufficient ◽  
Adapted Process ◽  
Vector Valued

We generalize the results of [1] to continuous time case by stating necessary and sufficient conditions on a set of probability measures to be the set of local martingale measures for a vector valued, locally bounded and adapted process.

scholarly journals On cryptographic properties of (n + 1)-bit S-boxes constructed by known n-bit S-boxes

2020 ◽  
Vol 15 (1) ◽  
pp. 258-265
Author(s):  
Yu Zhou ◽  
Daoguang Mu ◽  
Xinfeng Dong
Keyword(s):  
Sufficient Conditions ◽  
Sum Of Squares ◽  
Basic Component ◽  
Necessary And Sufficient Conditions ◽  
Autocorrelation Functions ◽  
Walsh Spectrum ◽  
Cryptographic Algorithms ◽  
Necessary And Sufficient ◽  
Relationship Of

AbstractS-box is the basic component of symmetric cryptographic algorithms, and its cryptographic properties play a key role in security of the algorithms. In this paper we give the distributions of Walsh spectrum and the distributions of autocorrelation functions for (n + 1)-bit S-boxes in [12]. We obtain the nonlinearity of (n + 1)-bit S-boxes, and one necessary and sufficient conditions of (n + 1)-bit S-boxes satisfying m-order resilient. Meanwhile, we also give one characterization of (n + 1)-bit S-boxes satisfying t-order propagation criterion. Finally, we give one relationship of the sum-of-squares indicators between an n-bit S-box S0 and the (n + 1)-bit S-box S (which is constructed by S0).

The λ-classification of continuous-time birth-and-death processes

2003 ◽  
Vol 35 (04) ◽  
pp. 1111-1130 ◽  
Author(s):  
Andrew G. Hart ◽  
Servet Martínez ◽  
Jaime San Martín
Keyword(s):  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Birth And Death Processes ◽  
Positive Recurrent ◽  
Necessary And Sufficient

We study the λ-classification of absorbing birth-and-death processes, giving necessary and sufficient conditions for such processes to be λ-transient, λ-null recurrent and λ-positive recurrent.

Positive fractional continuous-time linear systems with singular pencils

2012 ◽  
Vol 60 (1) ◽  
pp. 9-12 ◽  
Author(s):  
T. Kaczorek
Keyword(s):  
Linear Systems ◽  
Continuous Time ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Descriptor Systems ◽  
State Variables ◽  
Algebraic Constraints ◽  
Necessary And Sufficient ◽  
Time Linear

Positive fractional continuous-time linear systems with singular pencils A method for checking the positivity and finding the solution to the positive fractional descriptor continuous-time linear systems with singular pencils is proposed. The method is based on elementary row and column operations of the fractional descriptor systems to equivalent standard systems with some algebraic constraints on state variables and inputs. Necessary and sufficient conditions for the positivity of the fractional descriptor systems are established.

scholarly journals Multigenerator Gabor Frames on Local Fields

2018 ◽  
Vol 33 (2) ◽  
pp. 307
Author(s):  
Owais Ahmad ◽  
Neyaz Ahmad Sheikh
Keyword(s):  
Sufficient Conditions ◽  
Complete Characterization ◽  
Necessary And Sufficient Conditions ◽  
Local Fields ◽  
Gabor Frames ◽  
Gabor System ◽  
Necessary And Sufficient

The main objective of this paper is to provide complete characterization of multigenerator Gabor frames on a periodic set $\Omega$ in $K$. In particular, we provide some necessary and sufficient conditions for the multigenerator Gabor system to be a frame for $L^2(\Omega)$. Furthermore, we establish the complete characterizations of multigenerator Parseval Gabor frames.

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