Queueing Systems with Some Versions of Limited Processor Sharing Discipline (original) (raw)
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The processor-sharing queueing model for time-shared systems with bulk arrivals
Networks, 1971
We consider a model which is applicable to time-muitiplexed systems, such as multiplexed comunication channels and time-shared computing facilities. In this (processor-sharing) queueing model, all jobs currently in the system share equally the processing capability of the server. investigate the processor-sharing model for the case of bulk arrivals. The mean response time of the system as a function of required service time is derived. An example is given to show ths effect of bulk arrivals versus single arrivals for a constant utilization.
Journal of Applied Probability, 2004
We derive in this paper closed formulas for the joint probability generating function of the number of customers in the two virtual FIFO queues of a weighted fair queueing (WFQ) system with two classes of customers arriving according to Poisson processes and requiring exponential service times. Contrary to previous studies published on the WFQ system, we show that it is possible to establish explicit expressions for the generating functions of the number of customers in each queue without calling for a Riemann Hilbert problem formulation. We specifically prove that the problem of determining the unknown functions due to the reflecting conditions on the boundaries of the positive quarter plane can be reduced to a Poisson equation. The explicit formulas are then used to derive some characteristics of the WFQ system (in particular the tails of the probability distributions of the numbers of customers in each virtual queue).
Law of Large Number Limits of Limited Processor-Sharing Queues
Mathematics of Operations Research, 2009
Motivated by applications in computer and communication systems, we consider a processor sharing queue where the number of jobs served is not larger than K. We propose a measure-valued fluid model for this limited processor sharing queue and show that there exists a unique associated fluid model solution. In addition, we show that this fluid model arises as the limit of a sequence of appropriately scaled processor sharing queues. studies of operating systems papers , as well as in more recent Web server design papers , and database implementation papers . So in the modeling of many computer and communication systems, a sharing limit is normally imposed, which results in an LPS model.
On the Influence of High Priority Customers on a Generalized Processor Sharing Queue
Lecture Notes in Computer Science, 2015
In this paper, we study a hybrid scheduling mechanism in discrete-time. This mechanism combines the well-known Generalized Processor Sharing (GPS) scheduling with strict priority. We assume three customer classes with one class having strict priority over the other classes, whereby each customer requires a single slot of service. The latter share the remaining bandwith according to GPS. This kind of scheduling is used in practice for the scheduling of jobs on a processor and in Quality of Service modules of telecommunication network devices. First, we derive a functional equation of the joint probability generating function of the queue contents. To explicitly solve the functional equation, we introduce a power series in the weight parameter of GPS. Subsequently, an iterative procedure is presented to calculate consecutive coefficients of the power series. Lastly, the approximation resulting from a truncation of the power series is verified with simulation results. We also propose rational approximations. We argue that the approximation performs well and is extremely suited to study these systems and their sensitivity in their parameters (scheduling weights, arrival rates, loads ...). This method provides a fast way to observe the behaviour of such type of systems avoiding time-consuming simulations.
Distribution of Occupied Resources on A Discrete Resources Sharing in A Queueing System
International Journal of Engineering Research and, 2021
In this paper, we study discrete resources sharing in a queueing system. We build analytical model of the distribution of occupied resources that can help for resources dimensioning. Both infinite and finite amount of discrete server resources are highlighted and validated with special cases of individual resource requirement following Poisson and Binomial distribution. It is found that there is a peak of usage near the average number of resources requested by customers, and other small peaks with low probability at multiples of this mean. The charging factor of the queue impacts mostly on the resources occupation distribution.
Analysis of a non-work conserving Generalized Processor Sharing queue
We consider in this paper a non work-conserving Generalized Processor Sharing (GPS) system composed of two queues with Poisson arrivals and exponential service times. Using general results due to Fayolle et al, we first establish the stability condition for this system. We then determine the functional equation satisfied by the generating function of the numbers of jobs in both queues and the associated Riemann-Hilbert problem. We prove the existence and the uniqueness of the solution. This allows us to completely characterize the system, in particular to compute the empty queue probability. We finally derive the tail asymptotics of the number of jobs in one queue.
2016
Queueing Theory is one of the most commonly used mathematical tool for the performance evaluation of systems. The aim of the book is to present the basic methods, approaches in a Markovian level for the analysis of not too complicated systems. The main purpose is to understand how models could be constructed and how to analyze them. It is intended not only for students of computer science, engineering, operation research, mathematics but also those who study at business, management and planning departments, too. It covers more than one semester and has been tested by graduate students at Debrecen University over the years. It gives a very detailed analysis of the involved queueing systems by giving density function, distribution function, generating function, Laplace-transform, respectively. Furthermore, Java-applets are provided to calculate the main performance measures immediately by using the pdf version of the book in a WWW environment. I have attempted to provide examples for ...
Priority queueing system with many types of requests and restricted processor sharing
Journal of Ambient Intelligence and Humanized Computing
A priority queueing model with many types of requests and restricted processor sharing is considered. A novel discipline of requests admission and service is proposed. This discipline assumes restriction of the bandwidth (capacity) of the server and the number of requests that can receive service in the system at the same time. This discipline is some kind of realistic hybrid of the traditional discipline of service in a multi-server system and the discipline of the limited processor sharing. The requests of the highest priority can push out from the service the low priority requests. Therefore, the important problem is fitting of the number of requests that can receive service at the same time to the bandwidth of the server. This problem is solved via construction and analysis of a multi-dimensional Markov chain describing operation of the system under any fixed set of the system parameters.
A Queueing Model of General Servers in Tandem with Finite Buffer Capacities
International journal of operations research, 2004
⎯We consider a queueing model with finite capacities. External arrivals follow a Coxian distribution. Due to the limitation of the capacity, arrivals may be lost if the buffer is full. Our goal is to study the probability of blocking. In order to obtain the steady-state probability distribution of this model, we construct an embedded Markov chain at the departure points. The solution is solved analytically and its analysis is extended to semi-Markovian representation of performance measures in queueing networks.
A Finite-Source Queue with Different Customers
Journal of the ACM, 1982
~STRACT A finite-source queuing model (sometimes called the finite-population, machine-interference, or machine-repairman model), which has often been used in analyzing time-sharing systems and multiprogrammed computer systems, is invesugated. The model studied here has two service staUons, a processor (single server) and peripherals (infinite server), and a finite number of customers (or jobs) that have a distract service rate at the processor. The model is in eqmhbnum.