275 research outputs found

    (R1975) MAP/PH(1), PH(2)/2 Queue with Multiple Vacation, Optional Service, Consultations and Interruptions

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    Two types of services are explored in this paper: regular server and main server, both of which provide both regular and optional services. Customers arrive using the Markovian Arrival Process (MAP), and service time is allocated based on phase type. The regular server uses the main server as a resource. Customers’ service at the primary server is disrupted as a result. When the queue size is empty, the main server can take several vacations. This system has been represented as a QBD Process that investigates steady state with the use of matrix analytic techniques, employing finite-dimensional block matrices. Our model’s waiting time distribution has been examined in more detail during the busy times. The system’s key parameters are assessed, and a few graphs and numerical representations are constructed

    Analysis of a multi-server queueing model with vacations and optional secondary services

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    In this paper we study a multi-server queueing model in which the customer arrive according to a Markovian arrival process. The customers may require, with a certain probability, an optional secondary service upon completion of a primary service. The secondary services are offered (in batches of varying size) when any of the following conditions holds good: (a) upon completion of a service a free server finds no primary customer waiting in the queue and there is at least one secondary customer (including possibly the primary customer becoming a secondary customer) waiting for service; (b) upon completion of a primary service, the customer requires a secondary service and at that time the number of customers needing a secondary service hits a pre-determined threshold value; (c) a server returning from a vacation finds no primary customer but at least one secondary customer waiting. The servers take vacation when there are no customers (either primary or secondary) waiting to receive service. The model is studied as a QBD-process using matrix-analytic methods and some illustrative examples arediscussed

    A class of multi-server queueing systems with unreliable servers: Models and application.

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    Where queueing systems with unreliable servers are concerned, most research that has been done focuses on one-server systems or systems with a Poisson arrival process and exponential service time. However, in some situations we need to consider non-exponential service time or service rate changes with the number of available servers. These are the queueing systems that are discussed in this thesis, none of which has ever been discussed in the literature. Since the phase type distribution is more general than the exponential distribution and captures most features of a general distribution, the phase type distributed service time is considered in unreliable queueing systems such as M/PH/n and M/PH/n/c. For the M/PH/n queueing system with unreliable servers, the mathematical model, stability condition analysis, stationary distribution calculation, computer programs and examples are all presented. For the M/PH/n/c queueing system with server failures, a finite birth-and-death mathematical model is built and the stationary distribution and performance evaluation measurements are calculated. Computer programs are developed and an example is given to demonstrate the application of this queueing system. (Abstract shortened by UMI.)Dept. of Industrial and Manufacturing Systems Engineering. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2003 .Y375. Source: Masters Abstracts International, Volume: 43-01, page: 0295. Adviser: Attahiru S. Alfa. Thesis (M.A.Sc.)--University of Windsor (Canada), 2004

    MAP/PH/1 queueing model with working vacation and crowdsourcing

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    Crowdsourcing has been used in different domains such as healthcare, computer science, environmental sciences, business and marketing. However, only recently, queueing models useful in the context of crowdsourcing have been studied. These studies involve queueing models of the type M/M/c, MAP/PH/1, and MAP/PH/c. In this paper we introduce vacation and working vacation in the context of MAP/PH/1 with crowdsourcing and highlight the qualitative aspects of the model through illustrative examples

    Mathematical Analysis of Queue with Phase Service: An Overview

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    We discuss various aspects of phase service queueing models. A large number of models have been developed in the area of queueing theory incorporating the concept of phase service. These phase service queueing models have been investigated for resolving the congestion problems of many day-to-day as well as industrial scenarios. In this survey paper, an attempt has been made to review the work done by the prominent researchers on the phase service queues and their applications in several realistic queueing situations. The methodology used by several researchers for solving various phase service queueing models has also been described. We have classified the related literature based on modeling and methodological concepts. The main objective of present paper is to provide relevant information to the system analysts, managers, and industry people who are interested in using queueing theory to model congestion problems wherein the phase type services are prevalent

    A Multi-Server Retrial Queueing Inventory System With Asynchronous Multiple Vacations

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    This article deals with asynchronous server vacation and customer retrial facility in a multi-server queueing-inventory system. The Poisson process governs the arrival of a customer. The system is comprised of c identical servers, a finite-size waiting area, and a storage area containing S items. The service time is distributed exponentially. If each server finds that there are an insufficient number of customers and items in the system after the busy period, they start a vacation. Once the servers vacation is over and it recognizes there is no chance of getting busy, it goes into an idle state if the number of customers or items is not sufficient, otherwise, it will take another vacation. Furthermore, each server's vacation period occurs independently of the other servers. The system accepts a (s, Q) control policy for inventory replenishment. For the steady state analysis, the Marcel F Neuts and B Madhu Rao matrix geometric approximation approach is used owing to the structure of an infinitesimal generator matrix. The necessary stability condition and R matrix are to be computed and presented. After calculating the sufficient system performance measures, an expected total cost of the system is to be constructed and numerically incorporated with the parameters. Additionally, numerical analyses will be conducted to examine the waiting time of customers in the queue and in orbit, as well as the expected rate of customer loss.Comment: 43 pages, 12 figures, 5 table

    Performance analysis of priority queueing systems in discrete time

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    The integration of different types of traffic in packet-based networks spawns the need for traffic differentiation. In this tutorial paper, we present some analytical techniques to tackle discrete-time queueing systems with priority scheduling. We investigate both preemptive (resume and repeat) and non-preemptive priority scheduling disciplines. Two classes of traffic are considered, high-priority and low-priority traffic, which both generate variable-length packets. A probability generating functions approach leads to performance measures such as moments of system contents and packet delays of both classes

    A MAP/PH/1 PRODUCTION INVENTORY MODEL

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    In this study, a production inventory model with phase type service times where customers join the system occur according to a Markovian arrival process is discussed. When the inventory level is positive, if an arriving customer finds the server idle gets into service immediately. Served customer leaves the system and the on-hand inventory is decreased one unit of item at service completion epoch. Otherwise, the customer enters into a waiting space (queue) of infinite capacity and waits for get served. The production facility produces items according to an (,) policy. The production is switched on when the inventory level depletes to and the production remains on until the inventory level reaches to the maximum level . Once the inventory level becomes , the production process is switched off. Applying the matrix-geometric method, we carry out the steady-state analysis of the production inventory model and perform a few illustrative numerical examples includes the effect of parameters on the system performance measures and an optimization study for the inventory polic
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