Embedded Markov chain approach to retrial queue with vacation, phase repair and multioptional services

OPSEARCH ◽  
2015 ◽  
Vol 52 (4) ◽  
pp. 782-809
Author(s):  
Madhu Jain ◽  
Amita Bhagat
Keyword(s):  
Markov Chain ◽  
Retrial Queue ◽  
Embedded Markov Chain ◽  
Markov Chain Approach

scholarly journals Insensitive Bounds for the Stationary Distribution of a Single Server Retrial Queue with Server Subject to Active Breakdowns

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Mohamed Boualem
Keyword(s):  
Markov Chain ◽  
Stationary Distribution ◽  
Retrial Queue ◽  
Embedded Markov Chain ◽  
Single Server ◽  
Waiting Room ◽  
Monotonicity Properties

The paper addresses monotonicity properties of the single server retrial queue with no waiting room and server subject to active breakdowns. The obtained results allow us to place in a prominent position the insensitive bounds for the stationary distribution of the embedded Markov chain related to the model in the study. Numerical illustrations are provided to support the results.

A BAYESIAN APPROACH TO FIND RANDOM-TIME PROBABILITIES FROM EMBEDDED MARKOV CHAIN PROBABILITIES

2007 ◽  
Vol 21 (4) ◽  
pp. 551-556 ◽  
Author(s):  
Winfried K. Grassmann ◽  
Javad Tavakoli
Keyword(s):  
Markov Chain ◽  
Bayesian Approach ◽  
Queuing Theory ◽  
Classical Method ◽  
Renewal Theory ◽  
Random Time ◽  
Embedded Markov Chain ◽  
Markov Chain Approach ◽  
Complex Approach ◽  
Markov Renewal Theory

The embedded Markov chain approach is widely used in queuing theory, in particular in M/G/1 and GI/M/c queues. In these cases, one has to relate the embedded equilibrium probablities to the corresponding random-time probabilities. The classical method to do this is based on Markov renewal theory, a rather complex approach, especially if the population is finite or if there is balking. In this article we present a much simpler method to derive the random-time probabilities from the embedded Markov chain probabilities. The method is based on conditional probability. Our approach might also be applicable in such situations.

An embedded Markov chain approach to stock rationing

2010 ◽  
Vol 38 (6) ◽  
pp. 510-515 ◽  
Author(s):  
Mehmet Murat Fadıloğlu ◽  
Önder Bulut
Keyword(s):  
Markov Chain ◽  
Embedded Markov Chain ◽  
Markov Chain Approach

An embedded Markov chain approach to stock rationing under batch orders

2019 ◽  
Vol 47 (2) ◽  
pp. 92-98 ◽  
Author(s):  
Mehmet Murat Fadıloğlu ◽  
Önder Bulut
Keyword(s):  
Markov Chain ◽  
Embedded Markov Chain ◽  
Markov Chain Approach

Cost Analysis of Movement-Based Location Management in PCS Networks: An Embedded Markov Chain Approach

2014 ◽  
Vol 63 (4) ◽  
pp. 1886-1902 ◽  
Author(s):  
Xian Wang ◽  
Xianfu Lei ◽  
Pingzhi Fan ◽  
Rose Qingyang Hu ◽  
Shi-Jinn Horng
Keyword(s):  
Markov Chain ◽  
Cost Analysis ◽  
Location Management ◽  
Embedded Markov Chain ◽  
Markov Chain Approach ◽  
Pcs Networks

Stochastic monotonicity approach for a non-Markovian priority retrial queue

2021 ◽  
pp. 2150156
Author(s):  
Mohamed Boualem ◽  
Nassim Touche
Keyword(s):  
Markov Chain ◽  
General Theory ◽  
Joint Distribution ◽  
Retrial Queue ◽  
Stochastic Orders ◽  
Embedded Markov Chain ◽  
Stochastic Monotonicity

This paper considers a non-Markovian priority retrial queue which serves two types of customers. Customers in the regular queue have priority over the customers in the orbit. This means that the customer in orbit can only start retrying when the regular queue becomes empty. If another customer arrives during a retrial time, this customer is served and the retrial has to start over when the regular queue becomes empty again. In this study, a particular interest is devoted to the stochastic monotonicity approach based on the general theory of stochastic orders. Particularly, we derive insensitive bounds for the stationary joint distribution of the embedded Markov chain of the considered system.

scholarly journals Bounds of the stationary distribution in M/G/1 retrial queue with two-way communication and n types of outgoing calls

2019 ◽  
Vol 29 (3) ◽  
pp. 375-391
Author(s):  
Lala Alem ◽  
Mohamed Boualem ◽  
Djamil Aissani
Keyword(s):  
Markov Chain ◽  
Stationary Distribution ◽  
Performance Measures ◽  
Time Distribution ◽  
Retrial Queue ◽  
Main Idea ◽  
Embedded Markov Chain ◽  
Stochastic Comparison ◽  
Service Time Distribution ◽  
Comparison Approach

In this article we analyze the M=G=1 retrial queue with two-way communication and n types of outgoing calls from a stochastic comparison viewpoint. The main idea is that given a complex Markov chain that cannot be analyzed numerically, we propose to bound it by a new Markov chain, which is easier to solve by using a stochastic comparison approach. Particularly, we study the monotonicity of the transition operator of the embedded Markov chain relative to the stochastic and convex orderings. Bounds are also obtained for the stationary distribution of the embedded Markov chain at departure epochs. Additionally, the performance measures of the considered system can be estimated by those of an M=M=1 retrial queue with two-way communication and n types of outgoing calls when the service time distribution is NBUE (respectively, NWUE). Finally, we test numerically the accuracy of the proposed bounds.

Estimation of Interregional Trade Flows: A Markov Chain Approach

1986 ◽  
Vol 18 (1) ◽  
pp. 123-132 ◽  
Author(s):  
I Weksler ◽  
D Freeman ◽  
G Alperovich
Keyword(s):  
Markov Chain ◽  
Trade Flows ◽  
Interregional Trade ◽  
Markov Chain Approach

Loss Probability of a Burst Arrival Finite Queue with Synchronized Service

1992 ◽  
Vol 6 (2) ◽  
pp. 201-216 ◽  
Author(s):  
Masakiyo Miyazawa
Keyword(s):  
Markov Chain ◽  
Loss Probability ◽  
Buffer Size ◽  
Embedded Markov Chain ◽  
Main Concern ◽  
Single Server ◽  
Finite Buffer ◽  
Single Server Queue ◽  
Server Queue ◽  
Computation Algorithm

We are concerned with a burst arrival single-server queue, where arrivals of cells in a burst are synchronized with a constant service time. The main concern is with the loss probability of cells for the queue with a finite buffer. We analyze an embedded Markov chain at departure instants of cells and get a kind of lumpability for its state space. Based on these results, this paper proposes a computation algorithm for its stationary distribution and the loss probability. Closed formulas are obtained for the first two moments of the numbers of cells and active bursts when the buffer size is infinite.

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