scholarly journals Approximation of the steady state system state distribution of the M/G/1 retrial queue with impatient customers

2012 ◽  
Vol 22 (2) ◽  
pp. 285-296 ◽  
Author(s):  
Nadjet Stihi ◽  
Natalia Djellab
Keyword(s):  
Steady State ◽  
Retrial Queue ◽  
Mean Value ◽  
Retrial Queues ◽  
System State ◽  
Impatient Customers ◽  
State Distribution ◽  
Information Theoretic ◽  
Principle Of Maximum Entropy ◽  
Principle Of Maximum

For M/G/1 retrial queues with impatient customers, we review the results, concerning the steady state distribution of the system state, presented in the literature. Since the existing formulas are cumbersome (so their utilization in practice becomes delicate) or the obtaining of these formulas is impossible, we apply the information theoretic techniques for estimating the above mentioned distribution. More concretely, we use the principle of maximum entropy which provides an adequate methodology for computing a unique estimate for an unknown probability distribution based on information expressed in terms of some given mean value constraints.

NUMBER OF RETRIALS IN A FINITE SOURCE RETRIAL QUEUE WITH UNRELIABLE SERVER

2014 ◽  
Vol 31 (02) ◽  
pp. 1440005 ◽  
Author(s):  
VELIKA I. DRAGIEVA
Keyword(s):  
Steady State ◽  
Finite Number ◽  
Retrial Queue ◽  
Life Time ◽  
Retrial Queues ◽  
Single Server ◽  
System State ◽  
Finite Source ◽  
Management Optimization ◽  
Continue Investigation

The object of this paper is to continue investigation of a single server retrial queue with finite number of sources in which the server is subjected to breakdowns and repairs. The server life time as well as the intervals between repetitions are exponentially distributed, while the repair and the service times are generally distributed. Using the formulas for the stationary system state distributions, obtained by Wang et al. [in Wang, J, L Zhao and F Zhang (2011). Analysis of the finite source retrial queues with server breakdowns and repairs. Journal of Industrial and Management Optimization, 7, 655–676.] we investigate the distribution of the number of retrials, made by a customer before he reaches the server free. Recurrent schemes for computing this distribution in steady state as well as any arbitrary of its moments are established. Numerical results for five different distributions of the service and repair times are also presented.

BALKING AND RENEGING IN M/G/s SYSTEMS EXACT ANALYSIS AND APPROXIMATIONS

2008 ◽  
Vol 22 (3) ◽  
pp. 355-371 ◽  
Author(s):  
Liqiang Liu ◽  
Vidyadhar G. Kulkarni
Keyword(s):  
Steady State ◽  
Single Server ◽  
Impatient Customers ◽  
Operating Characteristics ◽  
Steady State Distribution ◽  
State Distribution ◽  
Numerical Examples ◽  
Exact Analysis ◽  
Analytical Results ◽  
Server System

We consider the virtual queuing time (vqt, also known as work-in-system, or virtual-delay) process in an M/G/s queue with impatient customers. We focus on the vqt-based balking model and relate it to reneging behavior of impatient customers in terms of the steady-state distribution of the vqt process. We construct a single-server system, analyze its operating characteristics, and use them to approximate the multiserver system. We give both analytical results and numerical examples. We conduct simulation to assess the accuracy of the approximation.

On the thermodynamic stability of steady-state adiabatic systems

1988 ◽  
Vol 189 ◽  
pp. 509-529 ◽  
Author(s):  
L. F. Henderson
Keyword(s):  
Steady State ◽  
Local Thermodynamic Equilibrium ◽  
Equilibrium System ◽  
Adiabatic Flow ◽  
Total Enthalpy ◽  
Principle Of Maximum Entropy ◽  
System A ◽  
The Subject ◽  
Principle Of Maximum ◽  
Oblique Shocks

This paper begins by reviewing Bethe's (1942) work on the subject. He considered the propagation of a normal shock wave in a medium with an arbitrary equation of state. Difficulties arise if one attempts to extend his theory to systems containing plane oblique shocks or the reflection or refraction of such shocks. The object of the present paper is to resolve these difficulties. General conditions for the local thermodynamic equilibrium and thermodynamie stability, of a non-equilibrium system in steady-state, adiabatic, flow are summarized by the principle of maximum entropy production, which gives \[ \Delta s\geqslant 0;\quad {\rm d}(\Delta s)= 0;\quad {\rm d}^2(\Delta s) < 0, \] for ht, constant, where s is the specific entropy and ht is the specific total enthalpy; it is deduced from the second law. Conversely the consequences of Δs < 0, d(Δs) ≠ 0, d2(Δs) = 0, are discussed and may lead to either an impossibility or to some form of instability such as unsteadiness, or a change in the structure of the system (a catastrophe).

MEAN VALUE ANALYSIS OF SINGLE SERVER RETRIAL QUEUES

2010 ◽  
Vol 27 (03) ◽  
pp. 335-345 ◽  
Author(s):  
J. R. ARTALEJO ◽  
J. A. C. RESING
Keyword(s):  
Performance Measures ◽  
Retrial Queue ◽  
Mean Value ◽  
Retrial Queues ◽  
Queueing Models ◽  
Single Server ◽  
Value Analysis ◽  
Mean Value Analysis

Mean value analysis is an elegant tool for determining mean performance measures in queueing models. In this paper we show how mean value analysis can be applied to retrial queues. First, we illustrate the technique for the standard M/G/1 retrial queue with exponential retrial times. After that we show how the relations can be adapted to obtain mean performance measures in more advanced M/G/1-type retrial queues.

FRACTAL LIMIT DISTRIBUTIONS IN RANDOM TRANSPORTS

Fractals ◽  
1996 ◽  
Vol 04 (03) ◽  
pp. 257-264 ◽  
Author(s):  
HIDEKI TAKAYASU ◽  
TAKUO KAWAKAMI ◽  
Y. -H. TAGUCHI ◽  
TOMOO KATSUYAMA
Keyword(s):  
Steady State ◽  
Transport Model ◽  
Mean Value ◽  
Symmetric Case ◽  
Continuous Change ◽  
Steady State Distribution ◽  
State Distribution ◽  
Fluid Turbulence ◽  
Scalar Quantity ◽  
The Mean

We analyze a random transport model of a scalar quantity on a discrete space-time. By changing a parameter which is a portion of the quantity transported at a time, we observe a continuous change of steady-state distribution of fluctuations from Gaussian to a power-law when the mean value of the scalar quantity is not zero. In the symmetric case with zero mean, the steady-state converges either to a trivial no fluctuation state or to a Lorentzian fluctuation state with diverging variance independent of the parameter. We discuss a possible origin of the intermittent behaviors of fully-developed fluid turbulence as an application.

scholarly journals On the performance of the M1,M2/G1,G2/1 retrial queue with pre-emptive resume policy

2015 ◽  
Vol 25 (1) ◽  
pp. 153-164 ◽  
Author(s):  
Leila Boutarfa ◽  
Natalia Djellab
Keyword(s):  
Manufacturing System ◽  
Numerical Study ◽  
Retrial Queue ◽  
System State ◽  
State Distribution ◽  
Supplementary Variables ◽  
Scheduling Method ◽  
To Receive ◽  
Service Priority

Priority mechanism is an invaluable scheduling method that allows customers to receive different quality of service. Service priority is clearly today a main feature of the operation of any manufacturing system. We are interested by an M1,M2/G1,G2/1 priority retrial queue with pre-emptive resume policy. For model in question, we discuss the problem of ergodicity and, by using the method of supplementary variables, find the partial generating functions of the steady state system state distribution. Moreover, some pertinent performance measures are obtained and numerical study is also performed.

Kinetics of diffusive phase transformations: From local equilibrium to mobility-driven migration of thick interfaces

2011 ◽  
Vol 83 (5) ◽  
pp. 1105-1112
Author(s):  
Ernst Gamsjäger
Keyword(s):  
Steady State ◽  
Phase Transformations ◽  
Evolution Equations ◽  
Local Equilibrium ◽  
Time Dependent ◽  
Dependent Development ◽  
Principle Of Maximum Entropy ◽  
Kinetics Of ◽  
Principle Of Maximum ◽  
Satisfactory Manner

It is a prerequisite for the occurrence of diffusive phase transformations that the system is in an off-equilibrium condition. The time-dependent development of the variables until equilibrium or steady-state conditions are reached can be calculated by solving the evolution equations that can be derived from the principle of maximum entropy production. These equations provide the theoretical framework for the kinetics of diffusive phase transformations. In this work, the development from sharp interface-local equilibrium (SI-LE) models to thick interface-finite mobility (TI-FM) models is reviewed and presented in the light of the above-mentioned principle. Experimental results indicate that the kinetics of diffusive solid-state phase transformations can, at least in certain ranges of composition and temperature, be modeled in a satisfactory manner by the TI-FM approach only.

scholarly journals Analysis of a Multiserver Queueing-Inventory System

2015 ◽  
Vol 2015 ◽  
pp. 1-16 ◽  
Author(s):  
A. Krishnamoorthy ◽  
R. Manikandan ◽  
Dhanya Shajin
Keyword(s):  
Steady State ◽  
Service Time ◽  
Conditional Distribution ◽  
Retrial Queue ◽  
Form Solution ◽  
Inventory System ◽  
Inventory Level ◽  
Steady State Distribution ◽  
State Distribution ◽  
Number Of Customers

We attempt to derive the steady-state distribution of theM/M/cqueueing-inventory system with positive service time. First we analyze the case ofc=2servers which are assumed to be homogeneous and that the service time follows exponential distribution. The inventory replenishment follows the(s,Q)policy. We obtain a product form solution of the steady-state distribution under the assumption that customers do not join the system when the inventory level is zero. An average system cost function is constructed and the optimal pair(s,Q)and the corresponding expected minimum cost are computed. As in the case ofM/M/cretrial queue withc≥3, we conjecture thatM/M/cforc≥3, queueing-inventory problems, do not have analytical solution. So we proceed to analyze such cases using algorithmic approach. We derive an explicit expression for the stability condition of the system. Conditional distribution of the inventory level, conditioned on the number of customers in the system, and conditional distribution of the number of customers, conditioned on the inventory level, are derived. The distribution of two consecutivestostransitions of the inventory level (i.e., the first return time tos) is computed. We also obtain several system performance measures.

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