The Stochastic Systems Group at ISyE will hold a workshop on February 19 and February 20. The schedule of the talks is as follows:

February 19

Masakiyo Miyazawa 2:00 to 2:40
David McDonald 2:40 to 3:20
Break 3:20 to 3:50
Sunil Kumar 3:50 to 4:30

February 20

Wuqin Lin 9:00 to 9:40
Baris Ata 9:40 to 10:20
Break 10:20 to 10:50
Hayriye Ayhan 10:50 to 11:30

All talks will take place in room 228 (Executive classroom) of the main building. The titles and the abstracts are given below.

Masakiyo Miyazawa, Tokyo University of Sciences

Answers to the tail decay rate problem for a reflected random walk on a positive quadrant

This talk is concerned with a skip free random walk on the two dimensional positive quadrant with homogeneous reflecting transitions at each boundary face. We are interested in the tail decay behavior of its marginal distributions in the steady state. We solve this problem by characterizing the decay rates as the solutions of a certain non linear optimization problem, provided the stationary distribution exists. In general, those decay rates are in the logarithmic sense, referred to as weak decay rates. However, this result with help of existence results also answers to the question when the asymptotic decay is exactly geometric and what happens if it is not the case. We exemplify these results for Jackson networks and their modifications.

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David McDonald, University of Ottawa

A Stochastic Model for the Throughput of HTTP sessions

We introduce a simplified model of an HTTP which consists of a succession of idle and download periods. The file downloads are subject to a fixed packet loss probability. The same TCP connection is used for the download of a random number of files. We assume the files are transmitted in the congestion avoidance regime and we don't consider time outs. We do take into account the effect of slow start at the beginning of a download period with SSTHRESH set to CWND after the last loss in the preceeding download period; i.e. the cycles are dependent. For this stochastic model, we derive a closed form formula for the stationary throughput obtained by a flow. We also derive closed form expressions for the mean time to transfer a file and for the distribution of the throughput. We also briefly discuss how the formulas can be applied to predict bandwidth sharing among competing HTTP flows.

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Sunil Kumar, Stanford University.

Dynamics of New Product Introduction in Closed Rental Systems

We study a rental system where a fixed number of heterogeneous users rent one product at a time from a collection of re-usable products. The online DVD rental firm Netflix provides the motivation. We assume that rental durations of each user are i.i.d. with finite mean. We study transient behavior in this system following the introduction of a new product that is desired by all the users. We represent the usage process for this new product in terms of an empirical distribution. This allows us to characterize the asymptotic behavior of the usage process as the number of users increases without bound, via appropriate versions of Glivenko-Cantelli and Donsker