Sreenivasan, C; Dr.Krishnamoorthy,A(Cochin University of Science and Technology, June 16, 2012)
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Abstract:
The thesis entitled “Queueing Models with Vacations and Working Vacations" consists of seven chapters including the introductory chapter. In chapters 2 to 7 we analyze different queueing models highlighting the role played by vacations and working vacations. The duration of vacation is exponentially distributed in all these models and multiple vacation policy is followed.In chapter 2 we discuss an M/M/2 queueing system with heterogeneous servers, one of which is always available while the other goes on vacation in the absence of customers waiting for service. Conditional stochastic decomposition of queue length is derived. An illustrative example is provided to study the effect of the input parameters on the system performance measures. Chapter 3 considers a similar setup as chapter 2. The model is analyzed in essentially the same way as in chapter 2 and a numerical example is provided to bring out the qualitative nature of the model. The MAP is a tractable class of point process which is in general nonrenewal. In spite of its versatility it is highly tractable as well. Phase type distributions are ideally suited for applying matrix analytic methods. In all the remaining chapters we assume the arrival process to be MAP and service process to be phase type. In chapter 4 we consider a MAP/PH/1 queue with working vacations. At a departure epoch, the server finding the system empty, takes a vacation. A customer arriving during a vacation will be served but at a lower rate.Chapter 5 discusses a MAP/PH/1 retrial queueing system with working vacations.In chapter 6 the setup of the model is similar to that of chapter 5. The signicant dierence in this model is that there is a nite buer for arrivals.Chapter 7 considers an MMAP(2)/PH/1 queueing model with a nite retrial group
Description:
Department of
Mathematics, Cochin University of Science and Technology.
Sreenivasan, C; Dr.Krishnamoorthy,A(Cochin University of Science and Technology, August 16, 2012)
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Abstract:
The objective of the study of \Queueing models with vacations and working
vacations" was two fold; to minimize the server idle time and improve the
e ciency of the service system. Keeping this in mind we considered queueing
models in di erent set up in this thesis.
Chapter 1 introduced the concepts and techniques used in the thesis and
also provided a summary of the work done. In chapter 2 we considered an
M=M=2 queueing model, where one of the two heterogeneous servers takes
multiple vacations. We studied the performance of the system with the help
of busy period analysis and computation of mean waiting time of a customer
in the stationary regime. Conditional stochastic decomposition of queue
length was derived. To improve the e ciency of this system we came up
with a modi ed model in chapter 3. In this model the vacationing server
attends the customers, during vacation at a slower service rate. Chapter
4 analyzed a working vacation queueing model in a more general set up.
The introduction of N policy makes this MAP=PH=1 model di erent from
all working vacation models available in the literature. A detailed analysis
of performance of the model was provided with the help of computation of
measures such as mean waiting time of a customer who gets service in normal
mode and vacation mode.
Description:
Department of Mathematics, Cochin University of Science and Technology