On a single server queue with two-stage heterogeneous service and deterministic server vacations

We analyse a single server queue with Poisson arrivals, two stages of heterogeneous service with different general (arbitrary) service time distributions and binomial schedule server vacations with deterministic (constant) vacation periods. After first-stage service the server must provide the second stage service. However, after the second stage service, he may take a vacation or may decide to stay on in the system. For convenience, we designate our model as M/G ₁, G ₂/D/1 queue. We obtain steady state probability generating function of the queue length for various states of the server. Results for some particular cases of interest such as M/E_{k 1} , E_{k 2} /D/1, M/M ₁, M ₂/D/1, M/E _k /D/1 and M/G ₁, G ₂/1 have been obtained from the main results and some known results including M/E_k /1 and M/G/1 have been derived as particular cases of our particular cases.     

Reducing server data traffic using a hierarchical computation model

Commercial workloads impose heavy demands on memory and storage subsystems in a server and often result in a large amount of traffic in I/O and memory buses. To reduce the data movement between the storage subsystem and the processing units, we propose a hierarchical computing (HC) system that distributes processing elements across the storage hierarchy. We present a programming model that allows us to decompose database queries into simple operations. These operations are then distributed and executed by the different layers of the hierarchy depending on the affinity of the task to a particular layer. Commands percolate down into the lower layers of the hierarchy and partially processed information flows up into the higher layers, where subsequent operations can be performed. We evaluate the effectiveness of the proposed hierarchical computing model by performing full system simulations of a business decision support system (DSS) workload. On a group of TPC-H-like queries, hierarchical computing systems reduce the amount of data transferred over the processor to memory interconnect by 37-58 percent. We also observe that HC configurations show speedups between 1.14x and 1.45x when compared with CC-NUMA with 32 processors.     

Maximum entropy analysis of the M[x]/M/1 queueing system with multiple vacations and server breakdowns

We consider a single unreliable sever in an M^[x]/M/1 queueing system with multiple vacations. As soon as the system becomes empty, the server leaves the system for a vacation of exponential length. When he returns from the vacation, if there are customers waiting in the queue, he begins to serve the customers; otherwise, another vacation is taken. Breakdown times and repair times of the server are assumed to obey a negative exponential distribution. Arrival rate varies according to the server’s status: vacation, busy, or breakdown. Using the maximum entropy principle, we develop the approximate formulae for the probability distributions of the number of customers in the system which is used to obtain various system performance measures. We perform a comparative analysis between the exact results and the maximum entropy results. We demonstrate, through the maximum entropy results, that the maximum entropy principle approach is accurate enough for practical purposes.     

The gravity multiple server location problem

Models for locating facilities and service providers to serve a set of demand points are proposed. The number of facilities is unknown, however, there is a given number of servers to be distributed among the facilities. Each facility acts as an M/M/k queuing system. The objective function is the minimization of the combined travel time and the waiting time at the facility for all customers. The distribution of demand among the facilities is governed by the gravity rule. Two models are proposed: a stationary one and an interactive one. In the stationary model it is assumed that customers do not consider the waiting time at the facility in their facility selection decision. In the interactive model we assume that customers know the expected waiting time at the facility and consider it in their facility selection decision. The interactive model is more complicated because the allocation of the demand among the facilities depends on the demand itself. The models are analyzed and three heuristic solution algorithms are proposed. The algorithms were tested on a set of problems with up to 1000 demand points and 20 servers.     

On a doubly dynamically controlled supermarket model with impatient customers

In this paper, we provide a key generalization of the supermarket model both from the impatient customers and from a doubly dynamic control, which may also be related to the size-based scheduling through the centered management of the customer resource as well as the total service ability. We first use an infinite-dimensional Markov process to express the states of this supermarket model, and set up an infinite-dimensional system of differential equations satisfied by the expected fraction vector. Then we use the operator semigroup to provide a mean-field limit for the sequence of infinite-dimensional Markov processes, which asymptotically approaches a single trajectory identified by the unique and global solution to the infinite-dimensional system of limiting differential equations. Finally, we provide an effective and efficient algorithm for computing the fixed point of the infinite-dimensional system of limiting differential equations, and use the fixed point to give performance analysis of this supermarket model. Also, some numerical examples are given to demonstrate how the performance measures depend on some crucial parameters of this supermarket model. We believe that the mean-field method developed in this paper will be useful and effective for analyzing more complicated supermarket models in many practical areas.     

Note on the article: Maximum entropy analysis of the M/M/1 queueing system with multiple vacations and server breakdowns

Wang et al. [Wang, K. H., Chan, M. C., & Ke, J. C. (2007). Maximum entropy analysis of the M^[x]/M/1 queueing system with multiple vacations and server breakdowns. Computers & Industrial Engineering, 52, 192–202] elaborate on an interesting approach to estimate the equilibrium distribution for the number of customers in the M^[x]/M/1 queueing model with multiple vacations and server breakdowns. Their approach consists of maximizing an entropy function subject to constraints, where the constraints are formed by some known exact results. By a comparison between the exact expression for the expected delay time and an approximate expected delay time based on the maximum entropy estimate, they argue that their maximum entropy estimate is sufficiently accurate for practical purposes. In this note, we show that their maximum entropy estimate is easily rejected by simulation. We propose a minor modification of their maximum entropy method that significantly improves the quality of the estimate.     

The optimal control of an M/G/1 queueing system with server vacations, startup and breakdowns

This paper studies the control policy of the N policy M/G/1 queue with server vacations, startup and breakdowns, where arrivals form a Poisson process and service times are generally distributed. The server is turned off and takes a vacation whenever the system is empty. If the number of customers waiting in the system at the instant of a vacation completion is less than N, the server will take another vacation. If the server returns from a vacation and finds at least N customers in the system, he requires a startup time before providing service until the system is again empty. It is assumed that the server breaks down according to a Poisson process and his repair time has a general distribution. The system characteristics of such a model are analyzed and the total expected cost function per unit time is developed to determine the optimal threshold of N at a minimum cost.     

Optimal replacement policy for a repairable system with multiple vacations and imperfect fault coverage

The present investigation deals with the reliability analysis of a repairable system consisting of single repairman who can take multiple vacations. The system failure may occur due to two types of faults termed as major and minor. When the system has failed due to minor faults, it is perfectly recovered by the repairman. If the system failure is due to major faults, there are some recovery levels/procedures that recover the faults imperfectly with some probability. However, the system cannot be repaired in ‘as good as new’ condition. It is assumed that the repairman can perform some other tasks when either the system is idle or waiting for recovery from the faults. The life time of the system and vacation time of the repairman are assumed to be exponential distributed while the repair time follows the general distribution. By assuming the geometric process for the system working/vacation time, the supplementary variable technique and Laplace transforms approach are employed to derive the reliability indices of the system. We propose the replacement policy to maximize the expected profit after a long run time. The validity of the analytical results is justified by taking numerical illustrations.     

An M/G/1 retrial G-queue with non-exhaustive random vacations and an unreliable server

This paper deals with an M/G/1 retrial queue with negative customers and non-exhaustive random vacations subject to the server breakdowns and repairs. Arrivals of both positive customers and negative customers are two independent Poisson processes. A breakdown at the busy server is represented by the arrival of a negative customer which causes the customer being in service to be lost. The server takes a vacation of random length after an exponential time when the server is up. We develop a new method to discuss the stable condition by finding absorb distribution and using the stable condition of a classical M/G/1 queue. By applying the supplementary variable method, we obtain the steady-state solutions for both queueing measures and reliability quantities. Moreover, we investigate the stochastic decomposition law. We also analyse the busy period of the system. Some special cases of interest are discussed and some known results have been derived. Finally, an application to cellular mobile networks is provided and the effects of various parameters on the system performance are analysed numerically.     

A multiple server location–allocation model for service system design

Service systems are endemic in a service economy, and effective system design is fundamental to the competitiveness of service organizations such as retailers, distributors, and healthcare providers. This is because system design may significantly facilitate (or hinder) the attainment of important organizational objectives such as minimizing system cost and maximizing service level. This paper develops and solves a comprehensive nonlinear location–allocation model for service system design that incorporates several relevant costs and considerations. These include, for instance, transportation, facility, and waiting costs, queuing considerations, multiple servers, multiple order priority levels, multiple service sites, and service distance limits. The model is first converted to an equivalent linear form and then solved using Lagrangian relaxation. A computational study shows problems with 250 service districts, 60 service sites, and 250 candidate locations are solved in about two and a half minutes. An extensive managerial experiment is conducted that evaluates alternative system designs from a number of important perspectives including centralization versus decentralization, system configuration, and service distance limit. Each scenario is evaluated with respect to two fundamental criteria, namely, total cost and service level. The analysis provides insights into important tradeoffs that must be taken into consideration in designing an effective service system.     

Analysis of discrete-time batch service renewal input queue with multiple working vacations

This paper investigates a discrete-time single server batch service queue with multiple working vacations wherein arrivals occur according to a discrete-time renewal process. The server works with a different service rate rather than completely stopping during the vacation period. The service is performed in batches and the server takes a vacation when the system does not have any waiting customers at a service completion epoch or a vacation completion epoch. We present a recursive method, using the supplementary variable technique to obtain the steady-state queue-length distributions at pre-arrival, arbitrary and outside observer’s observation epochs. The displacement operator method is used to solve simultaneous non-homogeneous difference equations. Some performance measures and waiting-time distribution in the system have also been discussed. Finally, numerical results showing the effect of model parameters on key performance measures are presented.     

基于超市模型的网格资源分配方法研究*

针对网格资源管理中的资源分配问题,提出了一种基于超市模型的网格资源管理分配方法.该方法能够实现子资源的快速匹配,从而减少了网格管理开销,更高效地分配了稀缺资源.     

广义模型服务器的设计与实现

模型的管理与运行一直是决策支持系统的核心,为了有效地实现广义模型的管理,组合和运行,文章设计和实现了一个广义模型服务器。它基于TCP／IP协议,采用三层客户／服务器机制,对模型的表示和运行进行了规范化,通过命令语言在客户端进行模型的管理和运行。该服务器可以对模型、算法、实例、工具等决策支持资源进行有效地管理,它既可广泛地应用于各领域的决策支持系统的开发,也可单独作为决策支持工具进行各种领域问题的辅助决策,文中系统地介绍了该服务器的设计和实现的理论和技术问题。     

Human gait simulation with a neuromusculoskeletal model and evolutionary computation

This paper describes a human gait animation system with a precise neuromusculoskeletal model and evolutionary computation. The neuromusculoskeletal model incorporates 14 rigid bodies, 19 degrees of freedom, 60 muscular models, 16 pairs of the neural oscillators, and other neuronal systems. By changing the search parameters and the evaluative criteria of the evolutionary search process, we demonstrate various locomotive patterns, such as normal gait, pathological gait, running and ape‐like walking. The proposed simulation system takes not only kinematic data but also in vivo dynamic data such as energy consumption information into consideration, so that the resultant locomotion patterns are natural and valid from a biomechanical point of view. Hence the simulation system can also be used for finding a biologically appropriate physical model to realize a desired gait by simultaneously modifying the body dynamics parameters with the neuronal parameters. This capability creates a novel application of human gait simulation systems, such as rehabilitation tool design and consultation for physically handicapped people. Copyright © 2003 John Wiley & Sons, Ltd.     

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.     

The uniform memory hierarchy model of computation

TheUniform Memory Hierarchy (UMH) model introduced in this paper captures performance-relevant aspects of the hierarchical nature of computer memory. It is used to quantify architectural requirements of several algorithms and to ratify the faster speeds achieved by tuned implementations that use improved data-movement strategies.A sequential computer's memory is modeled as a sequence M ₀,M ₁,... of increasingly large memory modules. Computation takes place inM ₀. Thus,M ₀ might model a computer's central processor, whileM ₁ might be cache memory,M ₂ main memory, and so on. For each moduleM _u, a busB _u connects it with the next larger module M_u+1. All buses may be active simultaneously. Data is transferred along a bus in fixed-sized blocks. The size of these blocks, the time required to transfer a block, and the number of blocks that fit in a module are larger for modules farther from the processor. The UMH model is parametrized by the rate at which the blocksizes increase and by the ratio of the blockcount to the blocksize. A third parameter, the transfer-cost (inverse bandwidth) function, determines the time to transfer blocks at the different levels of the hierarchy.UMH analysis refines traditional methods of algorithm analysis by including the cost of data movement throughout the memory hierarchy. Thecommunication efficiency of a program is a ratio measuring the portion of UMH running time during which M₀ is active. An algorithm that can be implemented by a program whose communication efficiency is nonzero in the limit is said to becommunication- efficient. The communication efficiency of a program depends on the parameters of the UMH model, most importantly on the transfer-cost function. Athreshold function separates those transfer-cost functions for which an algorithm is communication-efficient from those that are too costly. Threshold functions for matrix transpose, standard matrix multiplication, and Fast Fourier Transform algorithms are established by exhibiting communication-efficient programs at the threshold and showing that more expensive transfer-cost functions are too costly.A parallel computer can be modeled as a tree of memory modules with computation occurring at the leaves. Threshold functions are established for multiplication ofN×N matrices using up to N² processors in a tree with constant branching factor.     

A neural computation model with short-term memory

A study of the memory characteristics of the brain and the computer prompts the creation of a new neuron architecture for neural computation. We hypothesize that neural responses resemble hysteresis loops. The upper and lower halves of the hysteresis loop are described by two sigmoids. Generalizing the two sigmoids to two families of curves accommodates loops of various sizes. This model, which we call the ;hystery model', is capable of memorizing the entire history of its bipolar inputs in an adaptive fashion, with larger memory for longer sequences. We theorize and prove that the hystery model's response converges asymptotically to hysteresis-like loops. A simple application to temporal pattern discrimination demonstrates the nonlinear short-term memory characteristics of the hystery model. This model may have important applications for time-based computations such as control, signal processing and spatiotemporal pattern recognition, especially if it can take advantage of existing hysteresis phenomena in semiconductor materials.     

Steady state analysis and computation of the GI/M/1/L queue with multiple working vacations and partial batch rejection

This paper analyzes a finite-buffer bulk-arrival bulk-service queueing system with multiple working vacations and partial batch rejection in which the inter-arrival and service times are, respectively, arbitrarily and exponentially distributed. Using the supplementary variable and the embedded Markov chain techniques, we obtain the waiting queue-length distributions at pre-arrival and arbitrary epochs. We also present Laplace–Stiltjes transform of the actual waiting-time distribution in the queue. Finally, several performance measures and a variety of numerical results in the form of tables and graphs are discussed.