scholarly journals Vacation Queueing Model for Performance Evaluation of Multiple Access Information Transmission Systems without Transmission Interruption

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1508
Author(s):  
Alexander Dudin ◽  
Sergei Dudin ◽  
Valentina Klimenok ◽  
Yuliya Gaidamaka
Keyword(s):  
Multiple Access ◽  
Queueing System ◽  
Stable Operation ◽  
Polling System ◽  
Queueing Model ◽  
World Systems ◽  
Realistic Assumption ◽  
Transmission Interruption ◽  
Access Information ◽  
System States

We consider a MAP/PH/1-type queueing system with server vacations as a model that is useful for the analysis of multiple access systems with polling discipline without transmission interruption. Vacation of the server corresponds to the service providing competitive information flows to the polling system. In this paper, we consider a vacation queueing model under pretty general assumptions about the probabilistic distributions describing the behavior of the system and the realistic assumption, in many real-world systems, that ongoing service cannot be terminated ahead of schedule. We derive the criterion of the stable operation of the system and the stationary distributions of the system states and the waiting time. An illustrative numerical example is presented.

scholarly journals Asymmetry underlies stability in power grids

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Ferenc Molnar ◽  
Takashi Nishikawa ◽  
Adilson E. Motter
Keyword(s):  
Symmetry Breaking ◽  
Real World ◽  
Power Grids ◽  
Stable Operation ◽  
World Systems ◽  
Symmetric State ◽  
Network Systems ◽  
Additional Improvement ◽  
The Stability ◽  
General Method

AbstractBehavioral homogeneity is often critical for the functioning of network systems of interacting entities. In power grids, whose stable operation requires generator frequencies to be synchronized—and thus homogeneous—across the network, previous work suggests that the stability of synchronous states can be improved by making the generators homogeneous. Here, we show that a substantial additional improvement is possible by instead making the generators suitably heterogeneous. We develop a general method for attributing this counterintuitive effect to converse symmetry breaking, a recently established phenomenon in which the system must be asymmetric to maintain a stable symmetric state. These findings constitute the first demonstration of converse symmetry breaking in real-world systems, and our method promises to enable identification of this phenomenon in other networks whose functions rely on behavioral homogeneity.

Transient analysis of M/M/1 queues in discrete time by general server vacations

1994 ◽  
Vol 31 (A) ◽  
pp. 115-129 ◽  
Author(s):  
W. Böhm ◽  
S. G. Mohanty
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Transient Analysis ◽  
Queueing System ◽  
Queueing Model ◽  
Discrete Parameter ◽  
Server Vacations ◽  
Special Case ◽  
Combinatorial Methods ◽  
Transient And Steady State

In this contribution we consider an M/M/1 queueing model with general server vacations. Transient and steady state analysis are carried out in discrete time by combinatorial methods. Using weak convergence of discrete-parameter Markov chains we also obtain formulas for the corresponding continuous-time queueing model. As a special case we discuss briefly a queueing system with a T-policy operating.

An Uncertain Single-Server Queueing Model

2021 ◽  
pp. 2150001
Author(s):  
Kai Yao
Keyword(s):  
Queueing Theory ◽  
Busy Period ◽  
Queueing System ◽  
Single Server ◽  
Queueing Model ◽  
Uncertainty Distribution ◽  
Uncertain Variables ◽  
Service Efficiency ◽  
Service Times ◽  
Interarrival Times

In the queueing theory, the interarrival times between customers and the service times for customers are usually regarded as random variables. This paper considers human uncertainty in a queueing system, and proposes an uncertain queueing model in which the interarrival times and the service times are regarded as uncertain variables. The busyness index is derived analytically which indicates the service efficiency of a queueing system. Besides, the uncertainty distribution of the busy period is obtained.

COST ANALYSIS OF THE R-UNRELIABLE-UNLOADER QUEUEING SYSTEM

2008 ◽  
Vol 25 (01) ◽  
pp. 57-73
Author(s):  
KUO-HSIUNG WANG ◽  
CHUN-CHIN OH ◽  
JAU-CHUAN KE
Keyword(s):  
Sensitivity Analysis ◽  
Steady State ◽  
Queueing System ◽  
Cost Model ◽  
Analytic Solutions ◽  
Queueing Model ◽  
Exponential Distributions ◽  
System Parameters ◽  
Optimal Values ◽  
The Cost

This paper analyzes the unloader queueing model in which N identical trailers are unloaded by R unreliable unloaders. Steady-state analytic solutions are obtained with the assumptions that trip times, unloading times, finishing times, breakdown times, and repair times have exponential distributions. A cost model is developed to determine the optimal values of the number of unloaders and the finishing rate simultaneously, in order to minimize the expected cost per unit time. Numerical results are provided in which several steady-state characteristics of the system are calculated based on assumed numerical values given to the system parameters and the cost elements. Sensitivity analysis is also studied.

Throughput maximization in a loss queueing system with heterogeneous servers

1990 ◽  
Vol 27 (03) ◽  
pp. 693-700 ◽  
Author(s):  
Matthew J. Sobel
Keyword(s):  
Queueing System ◽  
Blocking Probability ◽  
Cost Structure ◽  
Throughput Maximization ◽  
Queueing Model ◽  
Heterogeneous Servers ◽  
Waiting Room ◽  
Discounted Cost ◽  
Long Run ◽  
Poisson Arrivals

Assigning each arriving customer to the fastest idle server is shown to maximize throughput (equivalently, minimize blocking probability) in a queueing model with Poisson arrivals, heterogeneous exponential servers, and no waiting room. If a cost structure is imposed on this model, under specified conditions the same policy minimizes the expected discounted cost and the long-run average cost per unit time.

scholarly journals Analysis of Multiserver Retrial Queueing System with Varying Capacity and Parameters

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Alexander N. Dudin ◽  
Olga S. Dudina
Keyword(s):  
Markov Chain ◽  
Continuous Time ◽  
Queueing System ◽  
Optimization Problems ◽  
The State ◽  
Arrival Process ◽  
Continuous Time Markov Chain ◽  
Retrial Queueing System ◽  
Retrial Queueing ◽  
System States

A multiserver queueing system, the dynamics of which depends on the state of some external continuous-time Markov chain (random environment, RE), is considered. Change of the state of the RE may cause variation of the parameters of the arrival process, the service process, the number of available servers, and the available buffer capacity, as well as the behavior of customers. Evolution of the system states is described by the multidimensional continuous-time Markov chain. The generator of this Markov chain is derived. The ergodicity condition is presented. Expressions for the key performance measures are given. Numerical results illustrating the behavior of the system and showing possibility of formulation and solution of optimization problems are provided. The importance of the account of correlation in the arrival processes is numerically illustrated.

Comparison Results for Markov-Modulated Recursive Models

1997 ◽  
Vol 11 (2) ◽  
pp. 203-217 ◽  
Author(s):  
Nicole Bäuerle ◽  
Ulrich Rieder
Keyword(s):  
Transition Matrix ◽  
Stochastic Ordering ◽  
Queueing Model ◽  
Recursive Models ◽  
Comparison Results ◽  
External Process ◽  
Consumption Model ◽  
System States ◽  
Markov Modulated ◽  
Time Division

We consider a general discrete-time stochastic recursive model that is influenced by an external Markov chain. Our aim is to investigate the effect that the transition matrix of the external process has on the system states of the model. To answer this question, we use new stochastic ordering concepts. Especially interesting are the results for infinite-stage Markov-modulated models. We illustrate our main results by three applications: an inventory model, a consumption model, and a queueing model for a time division multiplexing system.

scholarly journals Non-Orthogonal Multiple Access Assisted Device-to-Device Communication: Best Helping Base Station Approach

2018 ◽  
Vol 12 (2) ◽  
pp. 803
Author(s):  
Huu-Phuc Dang ◽  
Minh-Sang Nguyen ◽  
Dinh-Thuan Do
Keyword(s):  
Data Transmission ◽  
System Performance ◽  
Multiple Access ◽  
Signal To Noise Ratio ◽  
Base Station ◽  
Selection Scheme ◽  
Channel Condition ◽  
Expected Performance ◽  
Realistic Assumption ◽  
Device To Device

<span>It can be studied in this paper that a cooperative non-orthogonal multiple access (NOMA) helps device-to-device (D2D) communication system through base station (BS). In particular, we investigate BS selection scheme as a best channel condition for dedicated devices where a different data transmission demand on each device is resolved. The analysis on amplifying-and forward (AF) relay is proposed to evaluate system performance of the conventional cooperative NOMA scheme. Under the realistic assumption of perfect channel estimation, the achievable outage probability of both devices is investigated, and several impacts on system performance are presented. The mathematical formula in closed form related to probability has also been found. By implementing Monte-Carlo simulation, the simulation results confirm the accuracy of the derived analytical results. Also, the proposed D2D cooperative NOMA system introduces expected performance on reasonable selected parameters in the moderate signal to noise ratio (SNR) regime.</span>

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