scholarly journals The Stability Analysis of a Double-X Queuing Network Occurring in the Banking Sector

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1957
Author(s):  
Hong Zhang ◽  
Saviour Worlanyo Akuamoah ◽  
Wilson Osafo Apeanti ◽  
Prince Harvim ◽  
David Yaro ◽  
...  
Keyword(s):  
Banking Sector ◽  
Queuing Network ◽  
Fluid Limit ◽  
Customer Interaction ◽  
Sufficient Stability Condition ◽  
Sufficient Stability ◽  
Service Rates ◽  
The Stability ◽  
General Service ◽  
Independent Identically Distributed

We model a common teller–customer interaction occurring in the Ghanaian banking sector via a Double-X queuing network consisting of three single servers with infinite-capacity buffers. The servers are assumed to face independent general renewal of customers and independent identically distributed general service times, the inter-arrival and service time distributions being different for each server. Servers, when free, help serve customers waiting in the queues of other servers. By using the fluid limit approach, we find a sufficient stability condition for the system, which involves the arrival and service rates in the form of a set of inequalities. Finally, the model is validated using an illustrative example from a Ghanaian bank.

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.

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.

A Sufficient Stability Condition for Linear Conservative Gyroscopic Systems

1994 ◽  
Vol 61 (3) ◽  
pp. 715-717 ◽  
Author(s):  
Jinn-Wen Wu ◽  
Tsu-Chin Tsao
Keyword(s):  
Stability Condition ◽  
Entire System ◽  
Stiffness Matrices ◽  
Sufficient Stability Condition ◽  
Sufficient Stability ◽  
The Stability ◽  
Gyroscopic Systems

A sufficient stability condition for linear conservative gyroscopic systems with negative definite stiffness matrices is given. The condition for the stability is stated in terms of the coefficients of system matrices without solving the spectrum of the entire system. An example is given for comparison with existing results.

Further Results on Performance Guarantees in Adaptive Control of Uncertain Systems With Unmodeled Dynamics

2020 ◽  
Author(s):  
K. Merve Dogan ◽  
Tansel Yucelen ◽  
Jonathan A. Muse
Keyword(s):  
Adaptive Control ◽  
Stability Condition ◽  
Closed Loop ◽  
Model Reference Adaptive Control ◽  
Control Architecture ◽  
Unmodeled Dynamics ◽  
Sufficient Stability Condition ◽  
Sufficient Stability ◽  
The Stability ◽  
Model Reference Adaptive

Abstract Adaptive control approaches are effective system-theoretical methods for guaranteeing both the stability and the performance of physical systems subject to uncertainties. However, the stability and performance of these approaches can be severely degraded by the presence of unmodeled dynamics. Motivated by this standpoint, the previous work of the authors introduced a model reference adaptive control architecture based on the direct uncertainty minimization method for systems with additive input uncertainties and unmodeled dynamics. In particular, the proposed approach not only guaranteed the closed-loop stability predicated on a sufficient stability condition but also improved the closed-loop performance. The purpose of this paper is to generalize this previous work of the authors. Specifically, a model reference adaptive control architecture is given and it is system-theoretically analyzed for systems with unmodeled dynamics, and both additive input and control effectiveness uncertainties (we refer to Theorems 1 and 2 of this paper). The sufficient stability condition of the resulting architecture relies on linear matrix inequalities and this architecture can be effective in achieving not only stability but also a desired level of closed-loop system performance. Finally, we also provide an illustrative numerical example, which demonstrates the given theoretical results. (This research was supported by the Air Force Research Laboratory Aerospace Systems Directorate under the Universal Technology Corporation Grant 162642-20-25-C1.)

ON THE ROBUST STABILITY OF DISCRETE-TIME SYSTEMS

1999 ◽  
Vol 09 (01n02) ◽  
pp. 37-50 ◽  
Author(s):  
ÜLO NURGES ◽  
ENNU RÜSTERN
Keyword(s):  
Stability Boundary ◽  
Discrete Version ◽  
Schur Polynomials ◽  
Kharitonov Theorem ◽  
Discrete Time Systems ◽  
Sufficient Stability Condition ◽  
Sufficient Stability ◽  
The Stability ◽  
Time Systems ◽  
Invariant Transformation

A sufficient stability condition for monic Schur polynomials is obtained via the so-called reflection coefficients of polynomials and the discrete version of Kharitonov's weak theorem. The discrete Kharitonov theorem defines only (n - 1)-dimensional stable hyperrectangle for n-degree monic polynomials. By the use of a linear Schur invariant transformation we put stable line segments through vertices of this hyperrectangle and find an n-dimensional stable polytope with all vertices on the stability boundary.

The Systemic Effects of Prudential Regulation Toughening:The Results of a Stress-test for Russian Banks

2012 ◽  
pp. 4-31 ◽  
Author(s):  
M. Mamonov ◽  
A. Pestova ◽  
O. Solntsev
Keyword(s):  
Financial Services ◽  
Banking Sector ◽  
Stress Test ◽  
Credit Market ◽  
Capital Adequacy ◽  
Government Support ◽  
Government Ownership ◽  
Prudential Regulation ◽  
The Government ◽  
The Stability

The stability of Russian banking sector is threatened by three negative tendencies - overheating of the credit market, significant decrease of banks capital adequacy ratios, and growing problems associated with banks lending to affiliated non-financial corporations. The co-existence of these processes reflects the crisis of the model of private investments in Russian banking sector, which was observed during the last 20 years. This paper analyzes the measures of the Bank of Russia undertaken to maintain the stability of the banking sector using the methodology of credit risk stress-testing. Based on this methodology we conclude that the Bank of Russias actions can prevent the overheating of the credit market, but they can also lead to undesirable effects: further expansion of the government ownership in Russian banking sector and substitution of domestic credit supply by cross-border corporate borrowings. The later weakens the competitive positions of Russian banks. We propose a set of measures to harmonize the prudential regulation of banks. Our suggestions rely on design and further implementation of the programs aimed at developing new markets for financial services provided by Russian banks to their corporate and retail customers. The estimated effects of proposed policy measures are both the increase in profitability and capitalization of Russian banks and the decrease of banks demand for government support.

scholarly journals Interpersonal dimension of trust on customer interaction in the banking sector

2020 ◽  
Vol 7 (1) ◽  
pp. 1827525
Author(s):  
Abdulrahman Bello Bada ◽  
Premalatha Karupiah
Keyword(s):  
Banking Sector ◽  
Customer Interaction ◽  
Interpersonal Dimension

Input-Output Analysis of Environmental Protection Industry

2014 ◽  
Vol 1073-1076 ◽  
pp. 2700-2703
Author(s):  
Lei Jiang ◽  
Shou Zhong Hu ◽  
Xiao Xiao Xu
Keyword(s):  
Environmental Protection ◽  
Singular Systems ◽  
Linear Matrix ◽  
Matrix Inequality ◽  
Input Output ◽  
Output Analysis ◽  
Input Output Analysis ◽  
Sufficient Stability Condition ◽  
Sufficient Stability ◽  
Output System

This paper investigates the run of environmental protection industry input-output model. A new mathematic method is applied to study this kind of singular input-output system. With this new method, we need not convert singular systems into general linear systems. A sufficient stability condition under which an environmental protection industry input-output model is stable is proved. This condition is in the form of linear matrix inequality and can be easily tested by computers.

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