Past Seminars

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Queues with Advance Reservations
Professor Peter Taylor
MASCOS, The University of Melbourne
Start time: 3:15 pm
Date: Friday 25 August 2006
Location: Theatre 1, Ground Floor, 111 Barry Street, Carlton

Queues where on "arrival" customers make a reservation for service at some time in the future are endemic in practice and relatively under-analysed in theory. Simulations illustrate some interesting implications of the facility to make such reservations. For example introducing independent and identically distributed reservation periods into an Erlang loss system changes the blocking probability from that given by the Erlang B formula, despite the fact that the process of 'reserved arrivals' is still Poisson. In this talk we shall discuss some preliminary analyses of such queues. In particular, we shall obtain various transient and stationary distributions associated with the "bookings diary" for the infinite server system, and discuss attempts to extend the analysis to blocking probability calculations.

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An Involution for Enumerating Osculating Lattice Paths and Alternating Sign Matrices
Paul Fijn
The University of Melbourne
Start time: 3:15 pm
Date: Wednesday 9 August 2006
Location: AMSI Seminar Room, Ground Floor, 111 Barry Street, Carlton

Enumerative combinatorics is concerned with the establishment of "nice" formulae for the counting of various sets of objects. This talk is primarily concerned with paths on an integer lattice which can share vertices (but not edges) and must remain consistently ordered---osculating lattice paths. It is known that there are many methods of enumerating two osculating lattice paths, and two methods for the problem of three paths. Unfortunately, none of these generalise to the N paths case. An outline of a proof for N paths is given, along with an introduction to basic enumerative techniques. Connections to other areas of statistical mechanics and combinatorics, such as Alternating Sign Matrices, the Bethe Ansatz and the 6-vertex model, will also be briefly discussed.

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Optimal Monitoring for Fox Management
Alana Moore (Ph.D. student)
The University of Melbourne
Start time: 3:45 pm
Date: Friday 4 August 2006
Location: Theatre 1, Ground Floor, 111 Barry Street, Carlton

Since its introduction in the 1900's, the European red fox has had a major negative impact on native Australian fauna and is held responsible for the extinction of several Australian marsupial species. Once established, complete eradication of invasive species such as foxes is usually infeasible and control strategies employed in an attempt to save native species are often expensive and require intensive management programs. It is intuitive that effective management requires information about the system in question, but how much? Given obtaining information is usually difficult and costly, and budgets for park management are limited, it is unclear how effort should be split between monitoring and control in order to most effectively manage fox populations. I present a simple model which may be used to calculate optimal monitoring and management regimes.

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Truncation schemes for Markov chains and QBDs
Allan Motyer (Ph.D. student)
The University of Melbourne
Start time: 3:15 pm
Date: Friday 4 August 2006
Location: Theatre 1, Ground Floor, 111 Barry Street, Carlton

When modelling a random system with an infinite number of states as a Markov chain it may not be possible to find a closed form solution for the equilibrium distribution. In this situation we truncate the state space of the system to a sufficiently large but finite number of states in order to find a numerical solution. It is desirable that as the number of states in the truncated system is increased, the numerical solution converges to the (unknown) solution for the system with infinite states. This is not something that can be taken for granted. I will outline conditions under which such convergence occurs, give examples of when it doesn't, and apply the known results to a special type of Markov chain - the quasi-birth-and-death process.

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Survival Analysis with Long-term Survivors
Xian Zhou
The Hong Kong Polytechnic University
Start time: 1:15 pm
Date: Thursday 27 July 2006
Location: Theatre 2, Old Geology Building, The University of Melbourne

Survival analysis deals with data representing time durations before the occurrence of a certain event of interest, such as death from a particular disease, committing another crime, making an insurance claim, etc. Such data are typically subject to censoring and/or truncation, so that special techniques are required to account for these situations. A long-term survivor is an individual who will never experience the event of interest, such as a cancer patient who has been completely cured of the cancer, a HIV carrier who will never develop AIDS symptoms, and an insurance policyholder who never needs to make a claim, etc. The presence of long-term survivors could have a significant impact on the analysis of survival data. In this talk, we will introduce appropriate statistical models for survival data with long-term survivors. Nonparametric and parametric approaches are used to estimate the distributions and/or parameters under such models. Test for the presence of long-term survivors will also be discussed.

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