scholarly journals Stability Test of Networked Systems with Multiple Delays

2021 ◽  
Vol 15 ◽  
pp. 102-107
Author(s):  
Yang Xiao ◽  
Jinfeng Kou
Keyword(s):  
Stability Condition ◽  
Networked Systems ◽  
Stability Test ◽  
Multiple Delays ◽  
Characteristic Polynomials ◽  
Sufficient Stability Condition ◽  
Sufficient Stability ◽  
Schur Stability

In this paper, we propose a sufficient stability condition for networked systems with multiple delays based on the 2-D polynomials and 2-D Hurwitz-Schur stability. The main advantage of the new stability condition is that it is applicable to the general case of networked systems with multiple, incommensurate delays yet numerically tractable. The characteristic polynomials of networked systems are mapping into 2-D hybrid polynomials, then to test the Hurwitz-Schur stability can. determine the networked systems, examples including system simulations verify the validity of the proposed test algorithms.

Stability condition for a single-server retrial queue

1993 ◽  
Vol 25 (03) ◽  
pp. 690-701 ◽  
Author(s):  
Huei-Mei Liang ◽  
V. G. Kulkarni
Keyword(s):  
Stability Condition ◽  
Service Time ◽  
Retrial Queue ◽  
Arrival Rate ◽  
Retrial Queues ◽  
Single Server ◽  
Sufficient Stability Condition ◽  
Sufficient Stability ◽  
The Mean ◽  
The Stability

A single-server retrial queue consists of a primary queue, an orbit and a single server. Assume the primary queue capacity is 1 and the orbit capacity is infinite. Customers can arrive at the primary queue either from outside the system or from the orbit. If the server is busy, the arriving customer joins the orbit and conducts a retrial later. Otherwise, he receives service and leaves the system. We investigate the stability condition for a single-server retrial queue. Let λ be the arrival rate and 1/μ be the mean service time. It has been proved that λ / μ < 1 is a sufficient stability condition for the M/G /1/1 retrial queue with exponential retrial times. We give a counterexample to show that this stability condition is not valid for general single-server retrial queues. Next we show that λ /μ < 1 is a sufficient stability condition for the stability of a single-server retrial queue when the interarrival times and retrial times are finite mixtures of Erlangs.

The Control of Leontief Model on Industry Manufacturing Process

2011 ◽  
Vol 187 ◽  
pp. 287-290
Author(s):  
Yong Liang Cui
Keyword(s):  
Linear System ◽  
Discrete Time ◽  
Stability Condition ◽  
Manufacturing Process ◽  
Input Output ◽  
Sufficient Stability Condition ◽  
Sufficient Stability ◽  
Output System ◽  
Leontief Model ◽  
The Stability

The classic Leontief model on industry manufacturing process is investigated. A kind of discrete-time singular dynamic input-output model of industry manufacturing process based on the classic Leontief Model is provided and the stability of this kind of model is researched. By the new mathematic method, the singular dynamic input-output system will not be converted into the general linear system. Finally, a sufficient stability condition under which the discrete-time singular Extended Leontief Model is admissible is proved.

scholarly journals Global Stability of Two-Group Epidemic Models with Distributed Delays and Random Perturbation

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaoming Fan ◽  
Zhigang Wang ◽  
Xuelian Xu
Keyword(s):  
Lyapunov Function ◽  
Stability Condition ◽  
Epidemic Model ◽  
Random Perturbation ◽  
Endemic Equilibrium ◽  
Distributed Delays ◽  
Random Fluctuation ◽  
Asymptotically Stable ◽  
Sufficient Stability Condition ◽  
Sufficient Stability

We discuss a two-group SEIR epidemic model with distributed delays, incorporating random fluctuation around the endemic equilibrium. Our research shows that the endemic equilibrium of the model with distributed delays and random perturbation is stochastically asymptotically stable in the large. In addition, a sufficient stability condition is obtained by constructing suitable Lyapunov function.

Stability condition for a single-server retrial queue

1993 ◽  
Vol 25 (3) ◽  
pp. 690-701 ◽  
Author(s):  
Huei-Mei Liang ◽  
V. G. Kulkarni
Keyword(s):  
Stability Condition ◽  
Service Time ◽  
Retrial Queue ◽  
Arrival Rate ◽  
Retrial Queues ◽  
Single Server ◽  
Sufficient Stability Condition ◽  
Sufficient Stability ◽  
The Mean ◽  
The Stability

A single-server retrial queue consists of a primary queue, an orbit and a single server. Assume the primary queue capacity is 1 and the orbit capacity is infinite. Customers can arrive at the primary queue either from outside the system or from the orbit. If the server is busy, the arriving customer joins the orbit and conducts a retrial later. Otherwise, he receives service and leaves the system.We investigate the stability condition for a single-server retrial queue. Let λ be the arrival rate and 1/μ be the mean service time. It has been proved that λ/μ < 1 is a sufficient stability condition for the M/G/1/1 retrial queue with exponential retrial times. We give a counterexample to show that this stability condition is not valid for general single-server retrial queues. Next we show that λ /μ < 1 is a sufficient stability condition for the stability of a single-server retrial queue when the interarrival times and retrial times are finite mixtures of Erlangs.

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