Queuing network model of uniformly distributed arrivals in a distributed supply chain using subcontracting

In this paper, a supply chain (four-input three-stage queuing network) receives uniformly distributed orders from clients. An input order is represented by two stochastic variables, occurrence time and the quantity of items to be delivered. The objective of this work is to compute the minimum response time, and thus the average number of items (optimum capacity) that can be delivered with this response time. Performance measures such as average queue lengths, average response times, and average waiting times of the jobs in the supply chain, and in the equivalent single-server network are derived, plotted and discussed.     

A hybrid closed queuing network model for multi-threaded dataflow architecture

In this paper, a closed queuing network model with both single and multiple servers has been proposed to model dataflow in a multi-threaded architecture. Multi-threading is useful in reducing the latency by switching among a set of threads in order to improve the processor utilization. Two sets of processors, synchronization and execution processors exist. Synchronization processors handle load/store operations and execution processors handle arithmetic/logic and control operations. A closed queuing network model is suitable for large number of job arrivals. The normalization constant is derived using a recursive algorithm for the given model. State diagrams are drawn from the hybrid closed queuing network model, and the steady-state balance equations are derived from it. Performance measures such as average response times and average system throughput are derived and plotted against the total number of processors in the closed queuing network model. Other important performance measures like processor utilizations, average queue lengths, average waiting times and relative utilizations are also derived.     

The Analysis on Translation System Based on Asymmetric Cyclic Polling

By the imbedded Markov chain theory and the probability generating function method, this paper discusses the queuing model of the switch node at the router and analyzes the derivative characters of first and second order of discrete asymmetric tri-queuing gate polling system. The average waiting time and the average queuing length are explicitly obtained and these results are verified by simulation.     

非强占有限优先权M/G/1排队系统

针对部分数据帧有完全优先权发送的计算机网络数据服务系统存在的网络拥塞风险问题,提出了一种非强占有限优先权M/G/1排队系统模型的方法。该系统模型引入控制完全优先权的参数n,使得数据帧的完全优先权变成有限优先权,考虑了不同优先级队伍之间的公平性,降低了计算机网络数据服务系统拥塞的风险,使得网络系统在有限优先权下有较好的稳定性。在模型研究中,运用全概率拆解方法获得各级队伍平均等待时间、平均逗留时间和平均队长的理论结果。对模型采用Matlab 2010a软件实验仿真,实验得到的各级队伍平均等待时间和理论平均等待时间的平均绝对误差为0.951%。实验中,有限优先权条件下各级顾客的平均等待时间比值显著小于完全优先权条件下各级顾客的平均等待时间比值。实验结果表明对非强占有限优先权M/G/1排队系统模型研究的理论结果是正确的,该模型具有更稳定的系统特性。     

Circuit switching with input queuing: an analysis for thed-dimensional wraparound mesh and the hypercube

We analyze circuit switching in a multiprocessor network, where connection requests (or sessions) arrive at each node of the network according to a Poisson process with rate λ. Each session joins the appropriate input-queue at its source node, and, upon advancing to the head of the queue, transmits a setup packet to establish a connection. If the setup packet is successful, it reserves the links on the path for the duration of the session, and the session is served without interruptions. Otherwise, the connection request remains queued at the source, and subsequent attempts are made to establish the circuit. We analyze the queue of connection requests at the input-buffer of a network link, and obtain analytic expressions for the stability region, the average queuing delay, the average connection time, the average waiting time, and the average total delay, which show how these parameters depend on system variables, such as network dimension and session arrival rate. The queuing analysis focuses on the input-queue of a particular link, and accounts for the interactions with queues of other links through the retrial attempts and the associated probability of success. The queuing analysis is independent of the particular network topology under consideration, as long as the probability that a session arriving at a random time successfully establishes a connection can be calculated for that network. Simulations demonstrate the close agreement between the observed network behavior and that predicted by the analysis     

非强占有限优先权M/M/1排队系统

以计算机网络中实时视频流传输的实际应用为基础,建立非强占有限优先权M/M/1排队系统模型;对该系统模型进行分析研究,推导出顾客在系统内的的平均等待时间、平均逗留时间和平均队长。     

Analysis of the discrete-time Geo/G/1 working vacation queue and its application to network scheduling

In this paper we present an exact steady-state analysis of a discrete-time Geo/G/1 queueing system with working vacations, where the server can keep on working, but at a slower speed during the vacation period. The transition probability matrix describing this queuing model can be seen as an M/G/1-type matrix form. This allows us to derive the probability generating function (PGF) of the stationary queue length at the departure epochs by the M/G/1-type matrix analytic approach. To understand the stationary queue length better, by applying the stochastic decomposition theory of the standard M/G/1 queue with general vacations, another equivalent expression for the PGF is derived. We also show the different cases of the customer waiting to obtain the PGF of the waiting time, and the normal busy period and busy cycle analysis is provided. Finally, we discuss various performance measures and numerical results, and an application to network scheduling in the wavelength division-multiplexed (WDM) system illustrates the benefit of this model in real problems.     

Stationary distributions and optimal control of queues with batch Markovian arrival process under multiple adaptive vacations

We consider an infinite-buffer single server queue with batch Markovian arrival process (BMAP) and exhaustive service discipline under multiple adaptive vacation policy. That is, the server serves until system emptied and after that server takes a random maximum number H different vacations until either he finds at least one customer in queue or the server have exhaustively taken all the vacations. The maximum number H of vacations taken by the server is a discrete random variable. We obtain queue-length distributions at various epochs such as, service completion/vacation termination, pre-arrival, arbitrary, post-departure and pre-service. The proposed analysis is based on the use of matrix-analytic procedure to obtain queue-length distribution at a post-departure epoch. Later we use supplementary variable method and simple algebraic manipulations to obtain the queue-length distribution at other epochs using queue-length distribution at post-departure epoch. Some important performance measures, like mean queue lengths and mean waiting times have been obtained. Several other vacation queueing models can be obtained as a special case of our model, e.g., single-, multiple-vacation model and queues with exceptional first vacation time. Finally, the total expected cost function per unit time is considered to determine a locally optimal multiple adaptive vacation policy at a minimum cost.     

资源同时占有平均值分析方法的C/S系统应用

利用分层排队网络模型对具有资源同时占有的客户/服务器(Client/Server,C/S)系统建模,讨论并提出了一种改进的平均值分析方法———资源同时占有平均值分析方法用于计算响应时间、吞吐率、队列长度等系统性能参数均值。着重讨论该算法用于求解排队网络模型中具有不同选道行为、对各服务结点有不同服务需求的多类顾客的情况。     

A new congestion control algorithm for improving the performance of a broadcast-based multiprocessor architecture

Congestion occurring in the input queues of broadcast-based multiprocessor architectures can severely limit their overall performance. The existing congestion control algorithms estimate congestion based on a node’s output channel parameters such as the number of free virtual channels or the number of packets waiting at the channel queue. In this paper, we have proposed a new congestion control algorithm to prevent congestion on broadcast-based multiprocessor architectures with multiple input queues. Our algorithm performs congestion control at the packet level and takes into account the next input queue number which will be accessed by the processor, which form the fundamental differences between our algorithm and the algorithms based on the idea of virtual channel congestion control. The performance of the algorithm is evaluated by OPNET Modeler with various synthetic traffic patterns on a 64-node Simultaneous Optical Multiprocessor Exchange Bus (SOME-Bus) architecture employing the message passing protocol. Performance measures such as average input waiting time, average network response time and average processor utilization have been collected before and after applying the algorithm. The results show that the proposed algorithm is able to decrease the average input waiting time by 13.99% to 20.39%, average network response time by 8.76% to 20.36% and increase average processor utilization by 1.92% to 6.63%. The performance of the algorithm is compared with that of the other congestion control algorithms and it is observed that our algorithm performs better under all traffic patterns. Also, theoretical analysis of the proposed method is carried out by using queuing networks.     

基于M/M/c排队模型的云计算中心能耗管理策略

由于云计算中心在降低能耗的同时还需要保证服务质量（QoS）,针对用户访问云计算中心的排队机制,给出一种云计算任务排队模型,在此基础上提出一种基于M/M/c排队过程的云计算中心能耗管理算法,通过求解该模型获得了平均等待时间、阻塞概率等性能指标进而建立系统的能耗模型。同时用参量ERP（Energy-Response time Product）作为排队网络的反馈量,引入反馈策略及服务器休眠预留机制,动态调整云计算中心服务器服务数。仿真结果表明,与其他策略进行比较该策略能够在保证QoS值的情况下,有效降低系统的能耗,避免了服务器资源浪费。     

Steady state analysis of the GI/M/1/N queue with a variant of multiple working vacations

This paper studies the GI/M/1/N queue with a variant of multiple working vacations, where the server leaves for a working vacation as soon as the system becomes empty. The server takes at most H consecutive working vacations if the system remains empty after the end of a working vacation. Employing the supplementary variable and embedded Markov chain methods, we obtain the queue length distribution at different time epochs. Based on the various system length distribution, the probability of blocking, mean waiting times and mean system lengths have been derived. Finally, numerical results are discussed.     

A discrete-time single-server queue with a modified N -policy

We consider a discrete-time single-server queue where the idle server waits for reaching a level N in the queue size to start a batch service of N messages, although the following arrivals during the busy period receive single services. We find the stationary distributions of the queue and system lengths as well as some performance measures. The vacation and busy periods of the system and the number of messages served during a busy period are also analyzed. The stationary distributions of the time spent waiting in the queue and in the system are studied too. Finally, a total expected cost function is developed to determine the optimal operating N-policy at minimum cost.     

具有优先权的M/G/1重试可修排队系统

在服务台忙的情况下, 到达服务台的顾客以概率 q 进入无限位置的优先队列而以概率 p 进入无限位置的重试轨道 (orbit), 并且按照先到先服务 (FCFS) 规则排队, 假定只有队首的顾客允许重试, 同时考虑服务台可修的因素, 证明了系统稳态解存在的充要条件. 利用补充变量法求得稳态时两个队列与系统的平均队长、顾客等待时间、服务台的各种状态概率以及可靠性指标.     

Analysis of the M/G/1 queue with discriminatory random order service policy

We consider an M/G/1 queue with different classes of customers and discriminatory random order service (DROS) discipline. The DROS discipline generalizes the random order service (ROS) discipline: when the server selects a customer to serve, all customers waiting in the system have the same selection probability under ROS discipline, whereas customers belonging to different classes may have different selection probabilities under DROS discipline. For the M/G/1 queue with DROS discipline, we derive equations for the joint queue length distributions and for the waiting time distributions of each class. We also obtain the moments of the queue lengths and the waiting time of each class. Numerical results are given to illustrate our results.     

Grids with multiple batch systems for performance enhancement of multi-component and parameter sweep parallel applications

In this work, we evaluate the benefits of using Grids with multiple batch systems to improve the performance of multi-component and parameter sweep parallel applications by reduction in queue waiting times. Using different job traces of different loads, job distributions and queue waiting times corresponding to three different queuing policies (FCFS, conservative and EASY backfilling), we conducted a large number of experiments using simulators of two important classes of applications. The first simulator models Community Climate System Model (CCSM), a prominent multi-component application and the second simulator models parameter sweep applications. We compare the performance of the applications when executed on multiple batch systems and on a single batch system for different system and application configurations. We show that there are a large number of configurations for which application execution using multiple batch systems can give improved performance over execution on a single system.     

Finite capacity priority queues with potential health applications

The queuing processes of interest in this paper are that of waiting lines with two priorities and multiple service channels. The arrival process is assumed Poison and the service time distribution is negative exponential. Arriving units enter service if there is at least one idle channel, otherwise they join a finite queue and are served according to a non-preemptive priority discipline. If a low priority arriving unit finds the queue full, it is not allowed to enter the system and is considered “blocked” or lost. In the first model a high priority arrival may displace a low priority unit from the full queue and may be “blocked” if the queue consists of high priority units only. In the second model the high priority unit may still displace a low priority unit from the full queue but it will never be “blocked” and may wait “outside” the system if the system is full. Thus far there has been no discussion of such models in queuing theory literature. In this paper analytical expressions for average waiting times have been obtained for the two models. Two potential applications of the models are described and the usefulness of the models is illustrated by numerical examples.     

Impatient customers in an M/M/1 queue with single and multiple working vacations

We consider an M/M/1 queue with impatient customers and two different types of working vacations. The working vacation policy is the one in which the server serves at a lower rate during a vacation period rather than completely stop serving. The customer’s impatience is due to its arrival during a working vacation period, in which the customer service rate is lower than the normal busy period. We analyze the queue for two different working vacation termination policies, a multiple working vacation policy and a single working vacation policy. Closed-form solutions and various performance measures like, the mean queue lengths and the mean waiting times are derived. The stochastic decomposition properties are verified for both multiple and single working vacation cases. A comparison of both the models is carried out to capture their performances with the change in system parameters.     

A queuing model for CPU functional unit and issue queue configuration

In a superscalar processor, instructions of various types flow through an execution pipeline, traversing hardware resources which are mostly shared among many different instruction types. A notable exception to shared pipeline resources is the collection of functional units, the hardware that performs specific computations. In a trade-off of cost versus performance, a pipeline designer must decide how many of each type of functional unit to place in a processor’s pipeline. In this paper, we model a superscalar processor’s issue queue and functional units as a novel queuing network. We treat the issue queue as a finite-sized waiting area and the functional units as servers. In addition to common queuing problems, customers of the network share the queue but wait for specific servers to become ready (e.g., addition instructions wait for adders). Furthermore, the customers in this queue are not necessary ready for service, since instructions may be waiting for operands. In this paper we model a novel queuing network that provides a solution to the expected queue length of each type of instruction. This network and its solution can also be generalized to other problems, notably other resource-allocation issues that arise in superscalar pipelines.     

基于两次丢包策略的主动队列管理算法研究

针对网络拥塞现象,基于两次丢包方法建立了一种新的主动队列管理算法TDPQW。该算法利用M/G/1排队模型推导了实际队列长度和等待时间的数学表达式,以此提出在队列头部和队中随机位置进行丢包的策略。同时,通过仿真实验对比分析了该算法与RED、DROP-TAIL算法的性能,结果表明TDPQW具有较好的适应性。