Semi-Markovian Model of Two-Line Queuing System with Losses

In the present paper, to build model of two-line queuing system with losses GI/G/2/0, the approach introduced by V.S. Korolyuk and A.F. Turbin, is used. It is based on application of the theory of semi-Markov processes with arbitrary phase space of states. This approach allows us to omit some restrictions. The stationary characteristics of the system have been defined, assuming that the incoming flow of requests and their service times have distributions of general form. The particular cases of the system were considered. The used approach can be useful for modeling systems of various purposes.

Application of Convex Optimization to Queuing Systems

On the basis of the queuing theory, a nonlinear optimal load allocation model is proposed. A novel transformafion method for the optimization variables is also presented, and the constraints are properly combined so as to make this model convex. The interior-point method for convex optimization is presented as an efficient computational tool. Finally, this model is evaluated by a real example,from which the following conclusions are drawn： the optimum result can ensure the full utilization of machines and the smallest amount of WIP （work-in-progress） in queuing systems; the interior-point method needs a few iterations with significant computational savings; other performance measures of queuing systems can also be optimized in a similar way.

Coordinated scheduling model for intermodal transit hubs based on GI/M^K/1 queuing system

Coordinated scheduling of multimode plays a pivotal role in the rapid gathering and dissipating of passengers in transport hubs. Based on the survey data, the whole-day reaching time distribution at transfer points of passengers from the dominant mode to the connecting mode was achieved. A GI/M K/1 bulk service queuing system was constituted by putting the passengers' reaching time distribution as the input and the connecting mode as the service institution. Through queuing theory, the relationship between average queuing length under steady-state and headway of the connecting mode was achieved. By putting the minimum total cost of system as optimization objective, the headway as decision variable, a coordinated scheduling model of multimode in intermodal transit hubs was established. At last, a dynamic scheduling strategy was generated to cope with the unexpected changes of the dominant mode. The instance analysis indicates that this model can significantly reduce passengers' queuing time by approximately 17% with no apparently increase in departure frequency, which provides a useful solution for the coordinated scheduling of different transport modes in hubs.

Modeling and analysis of multiservice queuing system for WiMAX network

An analytical queuing model is proposed for the classified services of WiMAX network. Simulation model is also developed that corresponds to the Markovian analytical model using Java modeling tool （JMT）. This is a new and efficient discrete event tool for queuing network modeling and workload analysis. QoS metrics have been evaluated for the multi-rate traffic in multiple scenari- os. Results obtained from simulation are compared for validation and analysis. Outcomes show that the proposed model is more efficient than the conventional method by improving residence time, re- sponse time, increasing system throughput and efficiency at queuing level with a slight degradation in call acceptance factor.

On One Model of Complex Technical Queuing System with Unreliable Devices and with Time Redundancy

The given article deals with the development of analytical model of request service process by multichannel technical system with unreliable, repaired and reconfigured service facilities. It is assumed that the system is functioning in service mode of random length random request flows. The system considers the existence of time redundancy for afterservice of calls, the service of which is interrupted with refusal, non-depreciating the performed part of the task. Special probability functions are introduced which on the basis of probability reasoning allow to make the systems of integral equations describing the dynamics of request service process.

Ergodicity and Invariance of Flows in Queuing Systems

In this paper, we investigate the flow of customers through queuing systems with randomly varying intensities. The analysis of the Kolmogorov-Chapman system of stationary equations for this model showed that it is not possible to construct a convenient symbolic solution. In this paper an attempt is made to circumvent this requirement by referring to the ergodicity theorems, which gives the conditions for the existence of the limit distribution in the service processes, but do not require knowledge of them.

Improving Queuing System Throughput Using Distributed Mean Value Analysis to Control Network Congestion

In this paper, we have used the distributed mean value analysis (DMVA) technique with the help of random observe property (ROP) and palm probabilities to improve the network queuing system throughput. In such networks, where finding the complete communication path from source to destination, especially when these nodes are not in the same region while sending data between two nodes. So, an algorithm is developed for single and multi-server centers which give more interesting and successful results. The network is designed by a closed queuing network model and we will use mean value analysis to determine the network throughput (b) for its different values. For certain chosen values of parameters involved in this model, we found that the maximum network throughput for β≥0.7?remains consistent in a single server case, while in multi-server case for β≥ 0.5?throughput surpass the Marko chain queuing system.

On One Analytical Model of a Probability Estimation of Quality and Efficiency of Functioning of Complex Technical Queuing Systems

The work is dedicated to the development of analytical model of probability estimation of reliability, productivity, quality and efficiency of functioning of the complex technical queuing system consisting of the arbitrary number of marked groups of the service devises (channels, facilities, servers) differing with reliable characteristics (parameters of refusals and restorations) of forming their composition (also of arbitrary number) marked, identical, unreliable and restorable serving channels in which for serving come in requirements with intensities depending on marking of channels. In the considered system it is supposed that the currents of refusals of serving devices and currents of coming requirements are subdued to Poisson, and the currents of restorations of refused devices and the currents of services of coming requirements—exponential laws of distribution of probabilities. A stochastic process of transfers of a system by that is Markovian process with continuous time and discrete states. Correlations linking the basic parameters and exit characteristics of the systems of the pointed out type are obtained in a view of probabilities of the system location in the given moment of time in one of the possible states.

On One Model of Multichannel Queuing System with Unreliable Repairable Servers and Input Memory

The work deals with the development of analytical model of multichannel technical queuing system with unreliable servers and input memory where server failure flows and incoming request flows comply with Poissonian laws, while the flows of failed facilities repairs and flows of incoming requests comply with exponential laws of probability distribution. Random process of system change-over is a Markovian process with continuous time and discrete states. Relations binding basic parameters and output characteristics of the system indicated are obtained as probabilities of system staying in the given moment in one of the possible states. The proposed model is the most generalized compared to some models known in literature which could be considered as special cases of the considered model.

Performance Analysis of Two Priority Queuing Systems in Tandem

In this paper, we consider a tandem of two head-of-line (HOL) non-preemptive priority queuing systems, each with a single server and a deterministic service-time. Two classes of traffic are considered, namely high priority and low priority traffic. By means of a generating function approach, we present a technique to derive closed-form expressions for the mean buffer occupancy at each node and mean delay. Finally, we illustrate our solution technique with some numerical examples, whereby we illustrate the starvation impact of the HOL priority scheduling discipline on the performance of the low-priority traffic stream. Our research highlights the important fact that the unfairness of the HOL priority scheduling becomes even more noticeable at the network level. Thus this priority mechanism should be used with caution.

Mathematical Modeling in Heavy Traffic Queuing Systems

In this article, modeling in queuing systems with heavy traffic customer flows is reviewed. Key areas include their limiting distributions, asymptotic behaviors, modeling issues and applications. Heavy traffic flows are features of queuing in modern communications, transportation and computer systems today. Initially, we reviewed the onset of asymptotic modeling for heavy traffic single server queuing systems and then proceeded to multi server models supporting diffusion approximations developed recently. Our survey shows that queues with heavy traffic customer flows have limiting distributions and extreme value maximum. In addition, the diffusion approximation can conveniently model performance characters such as the queue length or the waiting time distributions in these systems.

Research and Simulate the Queuing Systems Based on the Markov Chain

This paper shows the researches of the queuing theory,especially the Markov Chainand the Poison Process,and implements the efficient way of designing the queuing system.Then simulating the queuing systems based on the“Simply package”in the“Python”programming language.And the paper would discuss and analyze the differences between different queuing systems.

The MAP/PH(PH/PH)/1 Discrete-time Queuing System with Repairable Server

In this paper, we discuss a discrete time repairable queuing system with Markovian arrival process, where lifetime of server, service time and repair time of server are all discrete phase type random variables. Using the theory of matrix geometric solution, we give the steady state distribution of queue length and waiting time. In addition, the stable availability of the system is also provided.

Integration of naval distributed tactical training simulation system based on advanced message queuing protocol

Aiming at the problems of unreliable data transmission,poor steadiness,nonsupport of complex data types,direct couple between data transmission and exchange,a high-level method based on advanced message queuing protocol( AMQP) is proposed to integrate naval distributed tactical training simulation system after serious consideration with current information exchange features of military combat system. Transferring layer in traditional user datagram protocol is implemented by publishing and subscribing scheme of message middleware. By creating message model to standardize message structure,integration architecture is formulated to resolve potential information security risks from inconsistent data type and express data transmission. Meanwhile,a communication model is put forward based on AMQP,which is in the center position of the whole transmission framework and responsible for reliably transferring battlefield data among subsystems. Experiments show that the method can accurately post amounts of data to the subscriber without error and loss,and can get excellent real-time performance of data exchange.

Performance Analysis for Multimedia Communication Systems with a Multilayer Queuing Network Model

Software performance evaluation in multimedia communication systems is typically formulated into a multi-layered client-server queuing network(MLCSQN) problem. However, the existing analytical methods to MLCSQN model cannot provide satisfactory solution in terms of accuracy, convergence and consideration of interlocking effects. To this end, this paper proposes a heuristic solving method for MLCSQN model to boost the performance prediction of distributed multimedia software systems. The core concept of this method is referred to as the basic model, which can be further decomposed into two sub-models: client sub-model and server sub-model. The client sub-model calculates think time for server sub-model, and the server sub-model calculates waiting time for client sub-model. Using a breadthfirst traversal from leaf nodes to the root node and vice versa, the basic model is then adapted to MLCSQN, with net sub-models iteratively resolved. Similarly, the interlocking problem is effectively addressed with the help of the basic model. This analytical solver enjoys advantages of fast convergence, independence on specific average value analysis(MVA) methods and eliminating interlocking effects.Numerical experimental results on accuracy and computation efficiency verify its superiority over anchors.

On Equilibrium in a Constant Retrial Queuing System with Reserved Time and Vacations

This paper investigates an M/M/1 constant retrial queue with reserved time and vacations.A new arriving customer will take up the server and accept service immediately if the server is idle.Otherwise,if the server is busy or on vacation,customers have to join a retrial orbit and wait for retry.Once a service is completed,the server will reserve a random time to seek a customer from the orbit at a constant retrial rate.If there is no arrivals(from the orbit or outside)during the idle period,to save energy,the server will take a vacation.This paper studies the fully unobservable case.First,the steady-state condition of the system is analyzed by using the Foster’s criterion,and the customers’expected waiting time is obtained based on the generating function technique.And then,by introducing an appropriate revenue structure,the equilibrium strategies of customers and the socially optimal strategy are all derived.Furthermore,a comparison between them is made and the effect of some main system parameters is studied.

Modelling priority queuing systems with varying service capacity

Many studies have been conducted to investigate the performance of priority queuing （PQ） systems with constant service capacity. However, due to the time-varying nature of wireless channels in wireless communication networks, the service capacity of queuing systems may vary over time. Therefore, it is necessary to investigate the performance of PQ systems in the presence of varying service capacity. In addition, self-similar traffic has been discovered to be a ubiquitous phenomenon in various communication networks, which poses great challenges to performance modelling of scheduling systems due to its fractal-like nature. Therefore, this paper develops a flow-decomposition based approach to performance modelling of PQ systems subject to self-similar traffic and varying service capacity. It specifically proposes an analytical model to investigate queue length distributions of individual traffic flows. The validity and accuracy of the model is demonstrated via extensive simulation experiments.

Performance Assessment and Configuration Analysis in the Study of SCADA System (Supervisory Control and Data Acquisition)

Queuing models are used to assess the functionality and aesthetics of SCADA systems for supervisory control and data collection.Here,the main emphasis is on how the queuing theory can be used in the system’s design and analysis.The analysis’s findings indicate that by using queuing models,cost-performance ratios close to the ideal might be attained.This article discusses a novel methodology for evaluating the service-oriented survivability of SCADA systems.In order to evaluate the state of service performance and the system’s overall resilience,the framework applies queuing theory to an analytical model.As a result,the SCADA process is translated using the M^(X)/G/1 queuing model,and the queueing theory is used to evaluate this design’s strategy.The supplemental variable technique solves the queuing problem that comes with the subsequent results.The queue size,server idle time,utilization,and probabilistic generating factors of the distinct operating strategies are estimated.Notable examples were examined via numerical analysis using mathematical software.Because it is used frequently and uses a statistical demarcation method,this tactic is completely acceptable.The graphical representation of this perspective offers a thorough analysis of the alleged limits.

Effects of pooling,specialization,and discretionary task completion on queueing performance

Pooling,unpooling/specialization,and discretionary task completion are typical operational strategies in queueing systems that arise in healthcare,call centers,and online sales.These strategies may have advantages and disadvantages in different operational environments.This paper uses the M/M/1 and M/M/2 queues to study the impact of pooling,specialization,and discretionary task completion on the average queue length.Closed-form solutions for the average M/M/2 queue length are derived.Computational examples illustrate how the average queue length changes with the strength of pooling,specialization,and discretionary task completion.Finally,several conjectures are made in the paper.

Effect of quality uncertainty of parts on performance of reprocessing system in remanufacturing environment

Aimed at the problem of stochastic routings for reprocessing operations and highly variable processing times,an open queuing network is utilized to model a typical reprocessing system.In the model,each server is subject to breakdown and has a finite buffer capacity,while repair times,breakdown times and service time follow an exponential distribution.Based on the decomposition principle and the expansion methodology,an approximation analytical algorithm is proposed to calculate the mean reprocessing time,the throughput of each server and other parameters of the processing system.Then an approach to determining the quality of disassembled parts is suggested,on the basis of which the effect of parts quality on the performance of the reprocessing system is investigated.Numerical examples show that there is a negative correlation between quality of parts and their mean reprocessing time.Furthermore,marginal reprocessing time of the parts decrease with the drop in their quality.