Exponential ergodicity in Markovian queueing and dam models

1979 ◽  
Vol 16 (4) ◽  
pp. 867-880 ◽  
Author(s):  
Pekka Tuominen ◽  
Richard L. Tweedie
Keyword(s):  
Transition Probabilities ◽  
Continuous Process ◽  
Typical Result ◽  
Input Process ◽  
Exponential Ergodicity ◽  
Poisson Input ◽  
State Dependent ◽  
Input Size ◽  
Drift Condition ◽  
Storage Processes

We investigate conditions under which the transition probabilities of various Markovian storage processes approach a stationary limiting distribution π at an exponential rate. The models considered include the waiting time of the M/G/1 queue, and models for dams with additive input and state-dependent release rule satisfying a ‘negative mean drift' condition. A typical result is that this exponential ergodicity holds provided the input process is ‘exponentially bounded'; for example, in the case of a compound Poisson input, a sufficient condition is an exponential bound on the tail of the input size distribution. The results are proved by comparing the discrete-time skeletons of the Markov process with the behaviour of a random walk, and then showing that the continuous process inherits the exponential ergodicity of any of its skeletons.

Exponential ergodicity in Markovian queueing and dam models

1979 ◽  
Vol 16 (04) ◽  
pp. 867-880 ◽  
Author(s):  
Pekka Tuominen ◽  
Richard L. Tweedie
Keyword(s):  
Transition Probabilities ◽  
Continuous Process ◽  
Typical Result ◽  
Input Process ◽  
Exponential Ergodicity ◽  
Poisson Input ◽  
State Dependent ◽  
Input Size ◽  
Drift Condition ◽  
Storage Processes

We investigate conditions under which the transition probabilities of various Markovian storage processes approach a stationary limiting distribution π at an exponential rate. The models considered include the waiting time of the M/G/1 queue, and models for dams with additive input and state-dependent release rule satisfying a ‘negative mean drift' condition. A typical result is that this exponential ergodicity holds provided the input process is ‘exponentially bounded'; for example, in the case of a compound Poisson input, a sufficient condition is an exponential bound on the tail of the input size distribution. The results are proved by comparing the discrete-time skeletons of the Markov process with the behaviour of a random walk, and then showing that the continuous process inherits the exponential ergodicity of any of its skeletons.

A Novel Approach for Analyzing Single Buffer Queueing Systems with State-Dependent Vacation and Correlated Input Process under Four Different Service Disciplines

2015 ◽  
Vol 6 (3) ◽  
pp. 19-59 ◽  
Author(s):  
Thomas Yew Sing Lee
Keyword(s):  
Performance Measures ◽  
Probability Generating Function ◽  
Performance Measure ◽  
Idle Time ◽  
Separate Analysis ◽  
Input Process ◽  
State Dependent ◽  
Special Cases ◽  
Service Disciplines ◽  
Different Types

The author presents performance analysis of a single buffer multiple-queue system. Four different types of service disciplines (i.e., non-preemptive, pre-emptive repeat different, state dependent random polling and globally gated) are analyzed. His model includes correlated input process and three different types of non-productive time (i.e., switchover, vacation and idle time). Special cases of the model includes server with mixed multiple and single vacations, stopping server with delayed vacation and stopping server with alternating vacation and idle time. For each of the four service disciplines the key performance measures such as average customer waiting time, loss probability, and throughput are computed. The results permit a detailed discussion of how these performance measures depends on the customer arrival rate, the customer service time, the switchover time, the vacation time, and the idle time. Moreover, extensive numerical results are presented and the four service disciplines are compared with respect to the performance measure. Previous studies of the single buffer multiple-queue systems tend to provide separate analysis for the two cases of zero and nonzero switchover time. The author is able to provide a unified analysis for the two cases. His results generalize and improve a number of known results on single buffer multiple-queue systems. Furthermore, this method does not require differentiation while it is needed if one uses the probability generating function approach. Lastly, the author's approach works for all single buffer multiple-queue systems in which the next queue to be served is determines solely on the basis of the occupancy states at the end of the cycle time.

Some exact results for dams with Markovian inputs

1976 ◽  
Vol 13 (02) ◽  
pp. 329-337
Author(s):  
Pyke Tin ◽  
R. M. Phatarfod
Keyword(s):  
Probability Distribution ◽  
Stationary Distribution ◽  
Special Form ◽  
Geometric Distribution ◽  
Transition Probabilities ◽  
Exact Results ◽  
Input Process ◽  
Largest Eigenvalue ◽  
The Matrix ◽  
Finite Dam

In the theory of dams with Markovian inputs explicit results are not usually obtained, as the theory depends very heavily on the largest eigenvalue of the matrix (pijzj ) where p ij are the transition probabilities of the input process. In this paper we show that explicit results can be obtained if one considers an input process of a special form. The probability distribution of the time to first emptiness is obtained for both the finite and the infinite dam, as well as the stationary distribution of the dam content for the finite dam. Explicit results are given for the case where the stationary distribution of the input process has a geometric distribution.

On the distribution of attributes in organizations

1974 ◽  
Vol 11 (03) ◽  
pp. 529-543
Author(s):  
Horand Störmer
Keyword(s):  
Input Process ◽  
Organization Model ◽  
Generalized Poisson ◽  
Poisson Input

The paper deals with a stochastic organization model described by a generalized Poisson input process and given probabilities of entering individuals obtaining certain attributes in this organization. The distribution of attributes at any given instant is derived. Examples illustrate the application of obtained results.

Some exact results for dams with Markovian inputs

1976 ◽  
Vol 13 (2) ◽  
pp. 329-337 ◽  
Author(s):  
Pyke Tin ◽  
R. M. Phatarfod
Keyword(s):  
Probability Distribution ◽  
Stationary Distribution ◽  
Special Form ◽  
Geometric Distribution ◽  
Transition Probabilities ◽  
Exact Results ◽  
Input Process ◽  
Largest Eigenvalue ◽  
The Matrix ◽  
Finite Dam

In the theory of dams with Markovian inputs explicit results are not usually obtained, as the theory depends very heavily on the largest eigenvalue of the matrix (pijzj) where pij are the transition probabilities of the input process. In this paper we show that explicit results can be obtained if one considers an input process of a special form. The probability distribution of the time to first emptiness is obtained for both the finite and the infinite dam, as well as the stationary distribution of the dam content for the finite dam. Explicit results are given for the case where the stationary distribution of the input process has a geometric distribution.

Single-server queues with impatient customers

1984 ◽  
Vol 16 (4) ◽  
pp. 887-905 ◽  
Author(s):  
F. Baccelli ◽  
P. Boyer ◽  
G. Hebuterne
Keyword(s):  
Waiting Time ◽  
Queueing System ◽  
Distribution Functions ◽  
Single Server ◽  
Waiting Time Distribution ◽  
Input Process ◽  
Poisson Input ◽  
Virtual Waiting Time ◽  
Random Threshold ◽  
The Stability

We consider a single-server queueing system in which a customer gives up whenever his waiting time is larger than a random threshold, his patience time. In the case of a GI/GI/1 queue with i.i.d. patience times, we establish the extensions of the classical GI/GI/1 formulae concerning the stability condition and the relation between actual and virtual waiting-time distribution functions. We also prove that these last two distribution functions coincide in the case of a Poisson input process and determine their common law.

scholarly journals EVALUATION THE COACHING PROGRAM OF TENNIS TEAM OF BANGKA BELITUNG PROVINCE IN PON XIX WEST JAVA 2016

2018 ◽  
Vol 4 (1) ◽  
pp. 1-18
Author(s):  
Kurnia Tahki ◽  
Mulyana Mulyana ◽  
James Tangkudung
Keyword(s):  
Qualitative Method ◽  
Evaluation Model ◽  
Continuous Process ◽  
Evaluation Research ◽  
Input Process ◽  
West Java ◽  
Before And After ◽  
Interactive Data ◽  
Model Context ◽  
Process Product

Coaching in every sport should be a planned and continuous process so as to achieve the expected goal. A well-developed and executed coaching program is also capable of being evaluated in order to make improvements over time. The purpose of this research is to get information about coaching program of Pelatda’s TennisTeam of Bangka Belitung Province in PON XIX West Java 2016. This research was conducted in Jakarta, Bandung and Bangka Belitung from February to December 2016, before and after PON XIX West Java 2016.This evaluation research using qualitative method with evaluation model Context, Input, Process, Product or CIPP according D.Stufflebeam (2002). Data collection was done by interview, observation, documentation study and interactive. Data sources in this research are: Youth and Sports Office of Bangka Belitung Province, KONI of Bangka Belitung Province, coaches of pelatda, PELTI of Bangka Belitung Province.The results concluded that: (1). The evaluation component of context stage is considered sufficient (59.26%). (2). The evaluation component of input stage is considered sufficient (65,63%). (3). The evaluation component of process stages is considered less (42.86%). (4). The evaluation component of product stage is considered to be very less (28,58%).   Keywords:       Evaluation, Coaching Program, Tennis Team of Bangka Belitung Province, PON XIX West Java 2016

scholarly journals DEVELOPMENT OF A MARKOV MODEL OF THE INFORMATION ENVIRONMENT AS A COMMUNICATION SYSTEM IN THE SCIENTIFIC SPHERE

2020 ◽  
Author(s):  
O Kolesnikov ◽  
A. Biloshchytskyi ◽  
A. Gogunskii ◽  
A. Khomiak
Keyword(s):  
Stochastic Systems ◽  
Transition Probabilities ◽  
High Reliability ◽  
Educational Institution ◽  
Continuous Process ◽  
Educational Environment ◽  
Information Environment ◽  
Project Approach ◽  
Communication Processes ◽  
The Project Approach

The paper presents the theoretical foundations of creating the educational environment of an educational institution using the project approach at the stage of building models and displaying communications in the information environment in accordance with GOST R 54869 - 2011. The article considers the Markov process with discrete states, discrete-time, and homogeneous characteristics of transition probabilities. The latter means that the transition probabilities for the series do not change over time. The set of specific values of transition probabilities characterizes the level of organizational maturity of the project. A unified method of transformation of iconographic models of states of complex systems in the Markov chain is developed. The method has sufficient simplicity of the mathematical apparatus and high reliability of the mapping of the phenomenological properties of stochastic systems. The developed model allows us to study the features of communication processes in competently oriented information training systems in the educational environment of educational institutions and to obtain a quantitative assessment of the effectiveness of such systems. The management of educational activities of an educational institution should be considered as a continuous process of improving its activities in the conditions of modern competition in the market of educational services. The proposed model, based on the project approach, will allow the efficient use of material resources, as well as flexibly respond to any changes both within the educational institution and in the external environment.

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