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.

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 scenarios. 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,response 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.

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.

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.

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.

Pedestrian flow through exit:Study focused on evacuation pattern

Experiments are conducted on the evacuation rate of pedestrians through exits with queued evacuation pattern and random evacuation pattern. The experimental results show that the flow rate of pedestrians is larger with the random evacuation pattern than with the queued evacuation pattern. Therefore, the exit width calculated based on the minimum evacuation clear width for every 100 persons, which is on the assumption that the pedestrians pass through the exit in one queue or several queues, is conservative. The number of people crossing the exit simultaneously is greater in the random evacuation experiments than in the queued evacuation experiments, and the time interval between the front row and rear row of people is shortened in large-exit conditions when pedestrians evacuate randomly. The difference between the flow rate with a queued evacuation pattern and the flow rate with a random evacuation pattern is related to the surplus width of the exit, which is greater than the total width of all accommodated people streams. Two dimensionless quantities are defined to explore this relationship. It is found that the difference in flow rate between the two evacuation patterns is stable at a low level when the surplus width of the exit is no more than 45% of the width of a single pedestrian stream. There is a great difference between the flow rate with the queued evacuation pattern and the flow rate with the random evacuation pattern in a scenario with a larger surplus width of the exit. Meanwhile, the pedestrians crowd extraordinarily at the exit in these conditions as well, since the number of pedestrians who want to evacuate through exit simultaneously greatly exceeds the accommodated level. Therefore, the surplus width of exit should be limited especially in the narrow exit condition, and the relationship between the two dimensionless quantities mentioned above could provide the basis to some extent.

Coordinated Voltage Control of Distribution Network ConsideringMultiple Types of Electric Vehicles

The couple between the power network and the transportation network(TN)is deepening gradually with the increasing penetration rate of electric vehicles(EV),which also poses a great challenge to the traditional voltage control scheme.In this paper,we propose a coordinated voltage control strategy for the active distribution networks considering multiple types of EV.In the first stage,the action of on-load tap changer and capacitor banks,etc.,are determined by optimal power flow calculation,and the node electricity price is also determined based on dynamic time-of-use tariff mechanism.In the second stage,multiple operating scenarios of multiple types of EVs such as cabs,private cars and buses are considered,and the scheduling results of each EV are solved by building an optimization model based on constraints such as queuing theory,Floyd-Warshall algorithm and traffic flow information.In the third stage,the output power of photovoltaic and energy storage systems is fine-tuned in the normal control mode.The charging power of EVs is also regulated in the emergency control mode to reduce the voltage deviation,and the amount of regulation is calculated based on the fair voltage control mode of EVs.Finally,we test the modified IEEE 33-bus distribution system coupled with the 24-bus Beijing TN.The simulation results show that the proposed scheme can mitigate voltage violations well.

Development of an Analytical Model of the Process of Cybersecurity Protection of Distributed Information Systems of Critical Infrastructure

This article is dedicated to the creation of the analytical model of quantitative estimation of cybersecurity of Information Systems of Critical Infrastructure (ISCI). The model takes into consideration the existence, in the discussed ISCI, of both the intelligent tools of detection, analysis and identification of threats and vulnerabilities and means for restauration and elimination of their consequences. The development of the model also takes into consideration probabilistic nature of flow of events happening in ISCI and transferring the system between different states of cybersecurity. Among such probabilistic events we mean any operational perturbations (that can cause extreme situations) happening in ISCI under the influence of cyber-threats, as well as events concerning restoration and elimination of consequences of such cyber-threats. In this work, as methods of modelling, there have been used methods of system-oriented analysis based on theory of probability, theory of reliability and theory of queues. These methods enabled to describe analytically dependence of effectiveness indices of ISCI operation on abovementioned probabilistic processes.

Optimization Scheme of Large Passenger Flow in Huoying Station,Line 13 of Beijing Subway System

This paper focuses on the distribution of passenger flow in Huoying Station,Line 13 of Beijing subway system.The transformation measures taken by Line 13 since operation are firstly summarized.Then the authors elaborate the facilities and equipment of this station,especially the node layout and passenger flow field.An optimization scheme is proposed to rapidly distribute the passenger flow in Huoying Station by adjusting the operation time of the escalator in the direction of Xizhimen.The authors adopt Queuing theory and Anylogic simulation software to simulate the original and the optimized schemes of Huoying Station to distribute the passenger flow.The results of the simulation indicate that the optimized scheme could effectively alleviate the traffic congestion in the hall of Huoying Station,and the pedestrian density in other places of the hall is lowered;passengers could move freely in the hall and no new congestion points would form.The rationality of the scheme is thus proved.

IoT-Enabled Autonomous System Collaboration for Disaster-Area Management

Timely investigating post-disaster situations to locate survivors and secure hazardous sources is critical,but also very challenging and risky.Despite first responders putting their lives at risk in saving others,human-physical limits cause delays in response time,resulting in fatality and property damage.In this paper,we proposed and implemented a framework intended for creating collaboration between heterogeneous unmanned vehicles and first responders to make search and rescue operations safer and faster.The framework consists of unmanned aerial vehicles(UAVs),unmanned ground vehicles(UGVs),a cloud-based remote control station(RCS).A light-weight message queuing telemetry transport(MQTT)based communication is adopted for facilitating collaboration between autonomous systems.To effectively work under unfavorable disaster conditions,antenna tracker is developed as a tool to extend network coverage to distant areas,and mobile charging points for the UAVs are also implemented.The proposed framework’s performance is evaluated in terms of end-to-end delay and analyzed using architectural analysis and design language(AADL).Experimental measurements and simulation results show that the adopted communication protocol performs more efficiently than other conventional communication protocols,and the implemented UAV control mechanisms are functioning properly.Several scenarios are implemented to validate the overall effectiveness of the proposed framework and demonstrate possible use cases.

Application of the Queuing Theory in Characterizing and Optimizing the Passenger Flow at the Airport Security

This paper presents mathematics models that describe and optimize the passenger flow at the airport security checkpoints by applying the queuing theory. Firstly, a Poisson process is used to estimate the flow of passengers waiting for going through the security. Then, the Poisson distribution is combined with a multiple M/M/s model. Following that, an arrival model (passengers’ arriving at the checkpoints preparing for security examination and departure) with Gumbel extreme value estimation is described that predicts the busiest time in the busiest airport. Real case data collected from several major airports worldwide is used for creating a hybrid Poisson model to generate the simulation of passenger volume. At last, Markov Chain theory is applied to the analysis to randomly simulate the flow of enplaned passengers again, and the results of these two simulations are compared and discussed, revealing that the hybrid Poisson model is the more accurate one. After successfully characterizing the passenger flow mathematically, two methods for optimizing the passenger flow are then provided in two different respects: one is bypassing passengers and creating an express pass;while the other one promotes Pre-Check service application.

Using Poisson Modeling and Queuing Theory to Optimize Staffing and Decrease Patient Wait Time in the Emergency Department

Introduction: Studies have shown Emergency Department (ED) crowding contributes to reduced quality of patient care, delays in starting treatments, and increased number of patients leaving without being seen. This analysis shows how to theoretically and optimally align staffing to demand. Methods: The ED value stream was identified and mapped. Patients were stratified into three resource-driven care flow cells based on the severity indices. Time observations were conducted for each of the key care team members and the manual cycle times and service rate were calculated and stratified by severity indices. Using X32 Healthcare’s Online Staffing Optimization (OSO) tool, staffing inefficiencies were identified and an optimal schedule was created for each provider group. Results: Lower Severity Indices (higher acuity patient) led to longer times for providers, nurses, patient care assistants, and clerks. The patient length of stay varied from under one hour to over five hours. The flow of patients varied considerably over the 24 hours’ period but was similar by day of the week. Using flow data, we showed that we needed more nurses, more care team members during peak times of patient flow. Eight hour shifts would allow better flexibility. We showed that the additional salary hours added to the budget would be made up for by increased revenue recognized by decreasing the number of patients who leave without being seen. Conclusion: If implemented, these changes will improve ED flow by using lean tools and principles, ultimately leading to timeliness of care, reduced waits, and improved patient experience.