McDonald: Preprints
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Preprints of Recent Papers

Electronic approximations to some recent papers can be downloaded by clicking appropriate links below. In general, these files are in postscript format, and they represent the initial form of the paper before copy editing and other improvements made by the publishers.

Of course users of these files should not violate the copyrights of the publishers. The goal is to save postage and save time.

Refereed Papers

The following papers have appeared:

1) Asymptotics of first passage times for random walk in an orthant. This paper has  appeared in the Annals of Applied Probability describes a constructive large deviation theory which applies to many interesting queueing networks. The attached ps and pdf files have incorporated minor corrections suggested by Prof. Jiyeon Lee. 
2) A unified approach to fast teller queues and ATM.  This paper uses the results in 1) to give asymptotic results on the tail of the queue in a discrete time fast teller system.  It also proposes an importance sampling algorithm for simulating buffers buried deep in an ATM switch. This paper appeared in the Journal of Applied Probability.  
3) Accelerated Simulation of ATM switching fabrics. This paper gives the details of the importance sampling algorithm suggested in 2).  
4) VCC cell loss probabilities using the oldest-cell- first discipline. This paper gives the exact asymptotics of an M|D|1 queue using the theory in 1) and uses these results to estimate the cell loss probabilities when the oldest-cell- first discipline is used to manage buffers contending for a link.
5) Rare events for stationary processes. The Palm calculus is used to give the asymptotics of the mean time until a rare event occurs.  
6) Variation Fluctuation Smoothing for ATM Circuit Emulation Service, Conference proceedings ITC-97. This simple paper gives an algorithm for managing contending buffers when the traffic is of CES type.
7) Join the shortest queue: stability and exact asymptotics. This paper extends the theory in 1) and stretches this theory to its limit. The application is the classical join the shortest queue problem.  The exact asymptotics of the two queue system are given and an interesting phenomenon called weak pooling is discovered.
8) An approximation method for complete solutions of Markov-modulated fluid models. The method of induced Dirichlet forms is used to project the complicated Markov-modulated queue onto the model of a queue with a single equivalent bandwidth source .  
9) A comparison of load balancing algorithms like join the shortest queue and join the shortest expected waiting time.

10) My most recent work with Francois Baccelli and Julien Reynier concerns the performance of a bottleneck router implementing RED.  We are able to capture the dynamics of the congestion windows as a random measure. This paper has been accepted for Performance 2002.  We are currently using this model to derive an optimal AQM scheme.

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