Optimal policy for controlling two-server queueing systems with jockeying

This paper studies the optimal policy for joint control of admission, routing, service, and jockeying in a queueing system consisting of two exponential servers in parallel.Jobs arrive according to a Poisson process.Upon each arrival, an admission/routing decision is made, and the accepted job is routed to one of the two servers with each being associated with a queue.After each service completion, the servers have an option of serving a job from its own queue, serving a jockeying job from another queue, or staying idle.The system performance is inclusive of the revenues from accepted jobs, the costs of holding jobs in queues, the service costs and the job jockeying costs.To maximize the total expected discounted return, we formulate a Markov decision process(MDP) model for this system.The value iteration method is employed to characterize the optimal policy as a hedging point policy.Numerical studies verify the structure of the hedging point policy which is convenient for implementing control actions in practice.

An Algorithm for Estimating the Expected Number of Customers for a Class of Markovian Queueing Systems

An algorithm is presented for estimating the expected number of customers for a class of Markovian queueing systems. The class is characterized by those systems whose transition matrix for the underlying customer arrival and departure process is finite, irreducible, and aperiodic. The algorithm does not depend on a closed-form solution for the limiting behavior of the queue. The expected number of customers is frequently used as a measure of effectiveness to describe the behavior of the system or to optimize its design or control. To calculate such a quantity one must usually obtain a closed-form expression for the steady-state probabilities. Unfortunately, of the myriad of Markovian queueing systems, only a few have known closed-form expressions for their steady-state probabilities. The most well-known, using Kendall’s notation, are the M/M/1 and the M/M/c system. The algorithm described below estimates the expected number in the system under steady-state without a need for closed form steady-state probabilities. All that is needed is the transition matrix for the underlying Markov chain.

Effects of Reneging, Server Breakdowns and Vacation on a Batch Arrival Single Server Queueing System with Three Fluctuating Modes of Service

This article examines the effects of reneging, server breakdown and server vacation on the various states of the batch arrivals queueing system with single server providing service to customers in three fluctuating modes. In this queueing system, any batch arrival joins the queue if the server is busy or on vacation or under repair. However, if the server is free, one customer from the arriving batch joins the service immediately while others join the queue. In case of server breakdown, the customer whose service is interrupted returns back to the head of the queue. As soon as the server has is repaired, the server attends to the customer in mode 1. For this queueing system, customers that are impatient due to breakdown and server vacation may renege (leave the queue without getting service). Due to fluctuating modes of service delivery, the system may provide service with complete or reduced efficiency. Consequently, we construct the mathematical model and derive the probability generating functions of the steady state probabilities of several states of the system including the steady state queue size distribution. Further, we discuss some particular cases of the proposed queueing model. We present numerical examples in order to demonstrate the effects of server vacation and reneging on the various states of the system. The study revealed that an increase in reneging and a decrease in server vacation results in a decrease in server utilization and an increase in server’s idle time provided rates of server breakdown and repair completion are constant. In addition, the probability of server vacation, the probability of system is under repair and the probabilities that the server provides service in three fluctuating modes decreases due to an increase in reneging and a decrease in vacation completion rates.

M/G/1 Vacation Queueing Systems with Server Timeout

We consider a single-server vacation queueing system that operates in the following manner. When the server returns from a vacation, it observes the following rule. If there is at least one customer in the system, the server commences service and serves exhaustively before taking another vacation. If the server finds the system empty, it waits a fixed time c. At the expiration of this time, the server commences another vacation if no customer has arrived;otherwise, it serves exhaustively before commencing another vacation. Analytical results are derived for the mean waiting time in the system. The timeout scheme is shown to be a generalized scheme of which both the single vacation and multiple vacations schemes are special cases, with c=∞and c=0, respectively. The model is extended to the N-policy vacation queueing system.

A Non-Preemptive Priority Queueing System with a Single Server Serving Two Queues M/G/1 and M/D/1 with Optional Server Vacations Based on Exhaustive Service of the Priority Units

We study a vacation queueing system with a single server simultaneously dealing with an M/G/1 and an M/D/1 queue. Two classes of units, priority and non-priority, arrive at the system in two independent Poisson streams. Under a non-preemptive priority rule, the server provides a general service to the priority units and a deterministic service to the non-priority units. We further assume that the server may take a vacation of random length just after serving the last priority unit present in the system. We obtain steady state queue size distribution at a random epoch. Corresponding results for some special cases, including the known results of the M/G/1 and the M/D/1 queues, have been derived.

Development and Investigation of the Program Model of Multichannel Queueing System with Unreliable Recoverable Servers in Matlab Environment

In real life, in different industries, we often deal with systems designed for multiple use for performing single-type tasks. Processes taking place at this time are called service of requirements, and the systems themselves—Queueing Systems. This article is dedicated to computer software modelling of processes taking place in the systems in question, Markov processes in particular. In this article, by means of Matlab environment, software realization of one of the typical models of queueing service theory-multichannel QS with unreliable recoverable servers and limited number of requirements in the system, is fulfilled. The results of this research are important because it gives the possibility to use received results to determine optimality degree of some real queueing systems that possess Markov property.

Optimal Control Policy of M/G/1 Queueing System with Delayed Randomized Multiple Vacations Under the Modified Min(N,D)-Policy Control

Based on the number of customers and the server’s workload,this paper proposes a modified Min(N,D)-policy and discusses an M/G/1 queueing model with delayed randomized multiple vacations under such a policy.Applying the well-known stochastic decomposition property of the steady-state queue size,the probability generating function of the steady-state queue length distribution is obtained.Moreover,the explicit expressions of the expected queue length and the additional queue length distribution are derived by some algebraic manipulations.Finally,employing the renewal reward theorem,the explicit expression of the long-run expected cost per unit time is given.Furthermore,we analyze the optimal policy for economizing the expected cost and compare the optimal Min(N,D)-policy with the optimal N-policy and the optimal D-policy by using numerical examples.

A NEW AND DIRECT METHOD OF ANALYSIS THE DEPARTURE PROCESSES OF SINGLE SERVER QUEUEING SYSTEMS

ＡＮＥＷＡＮＤＤＩＲＥＣＴＭＥＴＨＯＤＯＦＡＮＡＬＹＳＩＳＴＨＥＤＥＰＡＲＴＵＲＥＰＲＯＣＥＳＳＥＳＯＦＳＩＮＧＬＥＳＥＲＶＥＲＱＵＥＵＥＩＮＧＳＹＳＴＥＭＳＴａｎｇＹｉｎｇｈｕｉ（唐应辉）（Ｄｅｐｔ．ｏｆＡｐｐｌＭａｔｈ．，Ｕｎｉｖ．ｏｆＥｌｅｃｔ...

THE MATCHED QUEUEING SYSTEM GI。PH/PH/1

ＴＨＥＭＡＴＣＨＥＤＱＵＥＵＥＩＮＧＳＹＳＴＥＭＧＩ。ＰＨ／ＰＨ／１ＸＵＧＵＡＮＣＨＵＩ（ＧＵＡＮＧ－ＨＵＩＨＳＶ）（徐光煇）；ＨＥＱＩＭＩＮＧ（何启明）（ＩｎｓｔｉｔｕｔｅｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ｔｈｅＣｈｉｎｅｓｅＡｃａｄｅｍｙ...

MATCHED QUEUEING SYSTEMS WITH A DOUBLE INPUT

In this paper, we study the matched queueing system with a double input, MoM/PH/1,where the two inputs are two independent Poisson processes, and the service time is of PH-distribution.The L.S. transforms and the expectations of the distributions of occupation time and virtual waiting time of the type-Ⅰ customer are derived.The probability that the server is working, the mean non-idle period, and the mean busy period are also derived. The related algorithms are given with numerical results.

MATCHED QUEUEING SYSTEM M·PH/G/1

In this paper,we study the matched queueing system,MoPH/G/1,where the type-Ⅰ input is a Poisson process,the type-Ⅱ input is a PH renewal process, and the service times are i.i.d. random variables. A necessary and sufficient condition for the stationariness of the system is given.The expectations of the length of the non-idle period and the number of customers served in a non-idle period are obtained.

Markov Skeleton Processes and Applications to Queueing Systems

In this paper, we apply the backward equations of Markov skeleton processes to qucueing systems. The transient distribution of the waiting time of a GI/G/1 queueing system, the transient distribution of the length of a GI/G/N queueing system and the transient distribution of the length of queueing networks are obtained.

A Spectrum Occupancy Model for Primary Users in Cognitive Radio Systems

There are abundant research results related to cognitive radio systems (CR systems), but using queueing models to portray CR systems is a new research trend. In this paper, a single-server retrial cognitive radio system with a linear retrial rate has been considered. The system has two types of users: primary users and secondary users. Secondary users have no effect on primary users because primary users have preemptive precedence. As a result, our purpose is to examine some performance indicators such as the expected queue length for primary users, the probability of the system being idle or occupied by a secondary user, and the probability of the system being busy. This paper begins by deriving the expressions for the generating functions based on the balance equations, so that we can calculate our goal conveniently.

Close-in weapon system planning based on multi-living agent theory

The close-in weapon system(CIWS)is a combat system that faces a complex environment full of dynamic and unknown challenges,whose construction and planning require a systematic design method.Multiliving agent(MLA)theory is a methodology for the combat system design,which uses the livelihood degree to evaluate the multi-dimensional long-term operational effectiveness of the system;whereas,there is still no uniform quantization framework for the livelihood degree,and the adjustment methods of livelihood degree need to be further improved.In this paper,we propose the uniform quantization framework for the livelihood degree and detailed discuss the methods of livelihood adjustment.Based on the MLA theory,the multi-dimensional operational effectiveness of the missile-gun integrated weapon system(MGIWS)is analyzed,and the long-term combat effectiveness against the saturation attack is assessed.Furthermore,the planning problem of the equipment deployment and configuration is investigated.Two objectives,including the overall livelihood degree and cost-effectiveness(CE),are proposed,and the optimization method based on genetic algorithm(GA)is studied for the planning problem.

A Maintenance Service Improvement Approach Based on Queue Networks: Application

The quest to increase the performance of production systems that have become complex leads to the transfer to the maintenance function of the responsibility of guaranteeing the availability of such systems. Also, we will never stop saying that maintenance must integrate into all of the company’s initiatives, to affirm its role, which is to ensure greater availability and sustainability of the means of production. The objective of this paper is to evaluate the reliability and availability of a system without knowing the distribution law of the operating times. Among the methods for evaluating dependability criteria (Fault Trees, Petri Nets, etc.), we are interested in queues that have the advantage of taking into account functional dependencies, thus allowing a quantified optimization of maintenance. Indeed, queues make it possible to model parallel or sequential processes, implementing operations taking place at the same time or one after the other, meeting the needs of modeling production systems. The main result of this paper is the study of the influence of availability on the reliability of a multi-state production system.

Python Server Page Performance Analysis and Modeling

Today, in the field of computer networks, new services have been developed on the Internet or intranets, including the mail server, database management, sounds, videos and the web server itself Apache. The number of solutions for this server is therefore growing continuously, these services are becoming more and more complex and expensive, without being able to fulfill the needs of the users. The absence of benchmarks for websites with dynamic content is the major obstacle to research in this area. These users place high demands on the speed of access to information on the Internet. This is why the performance of the web server is critically important. Several factors influence performance, such as server execution speed, network saturation on the internet or intranet, increased response time, and throughputs. By measuring these factors, we propose a performance evaluation strategy for servers that allows us to determine the actual performance of different servers in terms of user satisfaction. Furthermore, we identified performance characteristics such as throughput, resource utilization, and response time of a system through measurement and modeling by simulation. Finally, we present a simple queue model of an Apache web server, which reasonably represents the behavior of a saturated web server using the Simulink model in Matlab (Matrix Laboratory) and also incorporates sporadic incoming traffic. We obtain server performance metrics such as average response time and throughput through simulations. Compared to other models, our model is conceptually straightforward. The model has been validated through measurements and simulations during the tests that we conducted.

Improvement Design for Distributed Real-Time Stream Processing Systems

In the era of Big Data, typical architecture of distributed real-time stream processing systems is the combination of Flume, Kafka, and Storm. As a kind of distributed message system, Kafka has the characteristics of horizontal scalability and high throughput, which is manly deployed in many areas in order to address the problem of speed mismatch between message producers and consumers. When using Kafka, we need to quickly receive data sent by producers. In addition, we need to send data to consumers quickly. Therefore, the performance of Kafka is of critical importance to the performance of the whole stream processing system. In this paper, we propose the improved design of real-time stream processing systems, and focus on improving the Kafka's data loading process.We use Kafka cat to transfer data from the source to Kafka topic directly, which can reduce the network transmission. We also utilize the memory file system to accelerate the process of data loading, which can address the bottleneck and performance problems caused by disk I/O. Extensive experiments are conducted to evaluate the performance, which show the superiority of our improved design.

Open Queueing Network Model of Shanghai Public Transportation Problem

１ＩｎｔｒｏｄｕｃｔｉｏｎＢｅｃａｕｓｅｏｆｔｈｅｆａｓｔｄｅｖｅｌｏｐｍｅｎｔｏｆｅｃｏｎｏｍｙ，ｃｉｔｉｅｓａｒｅｂｅｃｏｍｉｎｇｌａｒｇｅｒａｎｄｌａｒｇｅｒ．Ｔｈｅｔｒａｆｉｃ，ｅｓｐｅｃｉａｌｙｔｈｅｐｕｂｌｉｃｔｒａｎｓｐｏｒｔａｔｉｏｎ...

ON PROPERITIES OF A SERIAL SERVICE SYSTEM OF TWO SERVICE COUNTERS WITH FINITE WAITING SPACE

（喻小军）（罗荣桂）ＯＮＰＲＯＰＥＲＩＴＩＥＳＯＦＡＳＥＲＩＡＬＳＥＲＶＩＣＥＳＹＳＴＥＭＯＦＴＷＯＳＥＲＶＩＣＥＣＯＵＮＴＥＲＳＷＩＴＨＦＩＮＩＴＥＷＡＩＴＩＮＧＳＰＡＣＥ￥ＹｕＸｉａｏｊｕｎ；ＬｕｏＲｏｎｇｇｕｉ（ＷｕｈａｎＵｎｉｖｅｒｓｉｔｙｏ...

Analysis of the WWW System Performance

A simple, high-level, open queueing network model is presented from which several general performance results for WWW server on the Internet are derived. Multiple-Server systems are also analyzed.A theoretical upper bound on the serving capacity of WWW server is defined. The effects of file size,server speed, and network bandwidth on response time are also investigated. In addition, the relative merits of several methods of improving server performance are evaluated.