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Some time-dependent queuing problems with batch arrivals and departures.


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McNeil, Donald Roy 1964 , 'Some time-dependent queuing problems with batch arrivals and departures.', Research Master thesis, University of Tasmania.

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In this thesis a queue with infinitely many states, compound
Poisson arrivals, bulk service, and batch departures is
investigated. It is shown that the queue-length probabilities
satisfy an infinite system of differential-difference equations
(the "birth and death equations"), which are solved in various
special cases. A closely allied system of equations is found
for the probability distribution function (which may be defective)
of the server's busy period.
In chapter 1 the queue is specified, in terms of the
arrival process, the service discipline, and the departure
process. The birth and death equations are then derived in
their most general form.
In chapter 2 queues with batch arrivals and departures
are investigated. This particular case arises by taking the
general queue and making the arrival and departure processes
independent of the state of the queue. It is here that most
of the original work appears, as the finite-time behaviour of
queues with batch departures does not seem to have been studied
in the literature.
Chapter 3 embodies an exposition of two papers, each by
Karlin and McGregor, which the author has studied in detail.
In this case the arrival and departure processes depend upon the
state of the queue.
In the final chapter the above special cases are considered
... expressions for the probability ,
distribution of a customer's waiting time are also found.

Item Type: Thesis - Research Master
Authors/Creators:McNeil, Donald Roy
Keywords: Queuing theory
Copyright Holders: The Author
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Copyright 1964 the Author - The University is continuing to endeavour to trace the copyright
owner(s) and in the meantime this item has been reproduced here in good faith. We
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Additional Information:

Thesis (M.Sc.) - University of Tasmania, 1965. Includes bibliography

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