102 research outputs found
Analysis of operating characteristics for the heterogeneous batch arrival queue with server startup and breakdowns
In this paper we consider a like-queue production system in which server startup
and breakdowns are possible. The server is turned on (i.e. begins startup)
when N units are accumulated in the system and off when the system is empty.
We model this system by an M[x]/M/1 queue with
server breakdowns and startup time under the N policy. The arrival rate varies according to the server's status:
off, startup, busy, or breakdown.
While the server is working, he is subject to
breakdowns according to a Poisson process. When the server breaks down, he requires repair
at a repair facility, where the repair time follows the negative exponential distribution.
We study the steady-state behaviour of the system size distribution at
stationary point of time as well as the queue size distribution at departure point of time
and obtain some useful results.
The total expected cost function per unit time is developed to determine the optimal operating
policy at a minimum cost. This paper provides the minimum expected cost and the optimal operating
policy based on assumed numerical values of the system parameters. Sensitivity analysis is also provided
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A study of some M[x]/G/1 type queues with random breakdowns and bernouilli schedule server vacations based on a single vacation policy
This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Queueing systems arise in modelling of many practical applications related to computer sciences, telecommunication networks, manufacturing and production, human computer interaction, and so on. The classical queueing system, even vacation queues or queues subject to breakdown, might not be sufficiently realistic. The purpose of this research is to extend the work done on vacation queues and on unreliable queues by studying queueing systems which take into consideration both phenomena. We study the behavior of a batch arrival queueing system with a single server, where the system is subject to random breakdowns which require a repair process, and on the other hand, the server is allowed to take a vacation after finishing a service. The breakdowns are assumed to occur while serving a customer, and when the system breaks down, it enters a repair process immediately while the customer whose service is interrupted comes back to the head of the queue waiting for the service to resume. Server vacations are assumed to follow a Bernoulli schedule under single vacation policy. We consider the above assumptions for different queueing models: queues with generalized service time, queues with two-stages of heterogeneous service, queues with a second optional service, and queues with two types of service. For all the models mentioned above, it is assumed that the service times, vacation times, and repair times all have general arbitrary distributions. Applying the supplementary variable technique, we obtain probability generating functions of queue size at a random epoch for different states of the system, and some performance measures such as the mean queue length, mean waiting time in the queue, proportion of server's idle time, and the utilization factor. The results obtained in this research, show the effect of vacation and breakdown parameters upon main performance measures of interest. These effects are also illustrated using some numerical examples and graphs.This work is funded by the Ministry of Education, Kingdom of Bahrain
Non-Markovian Queueing System, Mx/G/1 with Server Breakdown and Repair Times
This paper deals with the steady state behavior of an MX/G/1 queue with breakdown. It assumed that customers arrive to the system in batches of variable size, but serve one by one. The main new assumption in this paper is that the repair process does not start immediately after a breakdown and there is a delay time waiting for repairs to start. We obtain steady state results in explicit and closed form in terms of the probability generating functions for the number of customers in the queue, the average waiting time in the queue
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On some queueing systems with server vacations, extended vacations, breakdowns, delayed repairs and stand-bys
This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.This research investigates a batch arrival queueing system with a Bernoulli scheduled vacation and random system breakdowns. It is assumed that the repair process does not start immediately after the breakdown. Consequently there maybe a delay in starting repairs. After every service completion the server may go on an optional vacation. When the original vacation is completed the server has the option to go on an extended vacation. It is assumed that the system is equipped with a stand-by server to serve the customers during the vacation period of the main server as well as during the repair process.
The service times, vacation times, repair times, delay times and extended vacation times are assumed to follow different general distributions while the breakdown times and the service times of the stand-by server follow an exponential distribution.
By introducing a supplementary variable we are able to obtain steady state results in an explicit closed form in terms of the probability generating functions. Some important performance measures including; the average length of the queue, the average number of customers in the system, the mean response time, and the value of the traffic intensity are presented.
The professional MathCad 2001 software has been used to illustrate the numerical results in this study
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Analysis of some batch arrival queueing systems with balking, reneging, random breakdowns, fluctuating modes of service and Bernoulli schedulled server vacations.
This thesis was submitted for the award of Doctor of Philosophy and was awarded by Brunel University LondonThe purpose of this research is to investigate and analyse some batch arrival queueing systems with Bernoulli scheduled vacation process and single server providing service. The study aims to explore and extend the work done on vacation and unreliable queues with a combination of assumptions like balking and re-service, reneging during vacations, time homogeneous random breakdowns and fluctuating modes of service. We study the steady state properties, and also transient behaviour of such queueing systems. Due to vacations the arriving units already in the system may abandon the system without receiving any service (reneging). Customers may decide not to join the queue when the server is in either working or vacation state (balking). We study this phenomenon in the framework of two models; a single server with two types of parallel services and two stages of service. The model is further extended with re-service offered instantaneously. Units which join the queue but leave without service upon the absence of the server; especially due to vacation is quite a natural phenomenon. We study this reneging behaviour in a queueing process with a single server in the context of Markovian and non-Markovian service time distribution. Arrivals are in batches while each customer can take the decision to renege independently. The non-Markovian model is further extended considering service time to follow a Gamma distribution and arrivals are due to Geometric distribution. The closed-form solutions are derived in all the cases. Among other causes of service interruptions, one prime cause is breakdowns. We consider breakdowns to occur both in idle and working state of the server. In this queueing system the transient and steady state analysis are both investigated. Applying the supplementary variable technique, we obtain the probability generating function of queue size at random epoch for the different states of the system and also derive some performance measures like probability of server‟s idle time, utilization factor, mean queue length and mean waiting time. The effect of the parameters on some of the main performance measures is illustrated by numerical examples to validate the analytical results obtained in the study. The Mathematica 10 software has been used to provide the numerical results and presentation of the effects of some performance measures through plots and graphs
On some queueing systems with server vacations, extended vacations, breakdowns, delayed repairs and stand-bys
This research investigates a batch arrival queueing system with a Bernoulli scheduled vacation and random system breakdowns. It is assumed that the repair process does not start immediately after the breakdown. Consequently there maybe a delay in starting repairs. After every service completion the server may go on an optional vacation. When the original vacation is completed the server has the option to go on an extended vacation. It is assumed that the system is equipped with a stand-by server to serve the customers during the vacation period of the main server as well as during the repair process. The service times, vacation times, repair times, delay times and extended vacation times are assumed to follow different general distributions while the breakdown times and the service times of the stand-by server follow an exponential distribution. By introducing a supplementary variable we are able to obtain steady state results in an explicit closed form in terms of the probability generating functions. Some important performance measures including; the average length of the queue, the average number of customers in the system, the mean response time, and the value of the traffic intensity are presented. The professional MathCad 2001 software has been used to illustrate the numerical results in this study.EThOS - Electronic Theses Online ServiceGBUnited Kingdo
Unreliable Server Retrial Queue with Optional Service and Multi-Phase Repair
In this paper, the retrial unreliable server queue with batch arrivals is considered. The arrival rates of
the units are different and dependent upon the joining probabilities according to the server status. On arrival, if unit
finds the busy server, he may retry for the service after a random duration of time. The server facilitates the essential
service and optional service, if opted after essential service. Moreover, the server is unreliable and subject to the
breakdown while rendering essential/optional service. The failed server may immediately undergo for the
compulsory multiphase repair or may wait to start the repair due to any technical reasons. The server can also avail
the optional vacation under the Bernoulli schedule after finish the service of each unit or may continue to serve the
next unit. The variables corresponding to elapsed times of general distributed service process, retrial process, repair
process and vacation duration, as supplementary variables and used to frame the governing equations. By using the
probability generating functions of joint distributions of the units at different states of the server, the performance
characteristics of the system are derived. To validate the results, the sensitivity analysis has been performed by taking
the numerical illustration
A multiple channel queueing model under an uncertain environment with multiclass arrivals for supplying demands in a cement industry
In recent years, cement consumption has increased in most Asian countries, including Malaysia. There are many factors which affect the supply of the increasing order demands in the cement industry, such as traffic congestion, logistics, weather and machine breakdowns. These factors hinder smooth and efficient supply,
especially during periods of peak congestion at the main gate of the industry where queues occur as a result of inability to keep to the order deadlines. Basic elements, such as arrival and service rates, that cannot be predetermined must be considered under an uncertain environment. Solution approaches including conventional
queueing techniques, scheduling models and simulations were unable to formulate the performance measures of the cement queueing system. Hence, a new procedure of fuzzy subset intervals is designed and embedded in a queuing model with the consideration of arrival and service rates. As a result, a multiple channel queueing model with multiclass arrivals, (M1, M2)/G/C/2Pr, under an uncertain environment is
developed. The model is able to estimate the performance measures of arrival rates of bulk products for Class One and bag products for Class Two in the cement manufacturing queueing system. For the (M1, M2)/G/C/2Pr fuzzy queueing model, two defuzzification techniques, namely the Parametric Nonlinear Programming and Robust Ranking are used to convert fuzzy queues into crisp queues. This led to three proposed sub-models, which are sub-model 1, MCFQ-2Pr, sub-model 2, MCCQESR-2Pr and sub-model 3, MCCQ-GSR-2Pr. These models provide optimal crisp
values for the performance measures. To estimate the performance of the whole system, an additional step is introduced through the TrMF-UF model utilizing a utility factor based on fuzzy subset intervals and the α-cut approach. Consequently, these models help decision-makers deal with order demands under an uncertain
environment for the cement manufacturing industry and address the increasing quantities needed in future
On the distribution of throughput of transfer lines
Ankara : Department of Industrial Engineering and the Institute of Engineering and Sciences of Bilkent University, 1998.Thesis (Master's) -- Bilkent University, 1998.Includes bibliographical references leaves 86-107A transfer line corresponds to a manufacturing system consisting of a number
of work stations in series integrated into one system by a common transfer
mechanism and a control system. There is a vast literature on the transfer
lines. However, little has been done on the transient analysis of these systems
by making use of the higher order moments of their performance measures
due to the difficulty in determining the evolution of the stochastic processes
under consideration. This thesis examines the transient behavior of relatively
short transfer lines and derives the distribution of the performance measures
of interest. The proposed method based on the analytical derivation of the
distribution of throughput is also applied to the systems with two-part types.
An experiment is designed in order to compare the results of this study with the
state-space representations and the simulation. They are also interpreted from
the point of view of the line behavior and design issue. Furthermore, extensions
are briefly discussed and directions for future research are suggested.Deler, BaharM.S
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