סמינר: Graduate Seminar

קהילת נשות הנדסת חשמל ומחשבים

Fluid and diffusion limits in queueing and communication networks: measure-valued processes and robustness

Date: March,14,2023 Start Time: 11:30 - 12:30
Location: חדר 861, בניין מאייר, הפקולטה להנדסת חשמל ומחשבים
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Lecturer: Yonatan Shadmi
Affiliations: The Andrew and Erna Viterbi Faculty of Electrical & Computer Engineering

In this talk we describe two lines of research in which new scaling limits are established for models used in queueing and communication theory. In both cases, the scaling limits provide great simplification of extremely complex models.

In the first, we prove the convergence to a fluid limit of a network operating under the scheduling policy Earliest Deadline First. Such results were previously known only for the case of a single node. The limit is described as a dynamic equation in the space of measures. The results provide a bridge between the oblique reflection map in the orthant and the measure-valued Skorohod problem. We also prove the convergence to the fluid limit of a queue with Shortest Job First with Aging policy, whose importance stems from its balance between fairness and small average waiting times, as well as being similar to policies that are used in practical systems. An explicit description of the limit is provided.

In the second, we study a multiclass scheduling problem, or equivalently, a multi-user communication channel, at the diffusion scale, under model uncertainty. This uncertainty is modeled as a zero-sum game between a scheduler and an adversarial player that dynamically controls the probability distributions driving the service times / channel usage time. The cost is associated with weighted delay. The limiting stochastic differential game is fully solved, i.e. its value is characterized through a Hamilton-Jacobi-Bellman equation, and both the optimal adversarial control and scheduler's strategy are found. For the scheduler, the c mu rule is optimal for any adversarial control; and for the adversary, the optimal control depends on a 2-dimensional representation of the infinite-dimensional uncertainty sets.

Ph.D. Under the supervision of Prof. Rami Atar.

 

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