סמינרים

סמינר בסטטיסטיקה: יואב קרנר

תאריך: 
ב', 22/02/2016 - 15:30 עד 16:30

מיקום: 
4412 (חדר הסמינרים)

Rational abnadomnets from an M/G/1 queue

Yoav Kerner, Ben Gurion University of the Negev

 

 

We consider an M/G/1 queue in which the customers, while waiting in line, observe the dynamics of the queue, and may decide reneging it.

 

We show that the Nash equilibrium profile is defined by two sequences of thresholds. 

 

For each customer, the decision is based on the observed past (that determines from what sequence the threshold is taken) and the observed queue length (that determines which element in the chosen sequence). 

 

We construct the set of equations that its solution is the Nash equilibrium and discuss the relation between the properties of the service time distribution and the properties of the Nash equilibrium (e.g. uniqueness, finiteness). 

 

Joint work with Eliran Schertzer

Vladimir Gaitsgory

תאריך: 
ב', 18/01/2016 - 15:30 עד 16:30

מיקום: 
חברה 4412 (חדר סמינרים)


(The seminar will begin after the Yohanan Vax scholarship presentation at 15:00, and may be a few minutes 

after the scheduled time.) 

Speaker: Prof. Vladimir Gaitsgory, Macquarie University


Title: 
 Linear Programming Approach to Optimal Control and Singularly Perturbed Optimal Control Problems 

Abstract: Problems of optimal control (POC) of dynamical systems arise in many applications and enjoy a great deal of attention internationally. Common theoretical tools for analysis and solution of POC are Pontryagin maximum principle and Hamilton-Jacobi-Bellman equations. In this presentation, we will discuss a much less conventional approach to POC. Namely, we will show that, based on occupational measures relaxation, the POC can be “equivalently” reformulated as an infinite-dimensional linear programming (IDLP) problem. We will indicate a way how this IDLP problem and its dual can be solved numerically and how their obtained numerical solutions can be used for a construction of a near optimal control of the underlying POC.  A special attention will be paid to analysis of so-called singularly perturbed POC, in which the state variables change their values with rates of different order of magnitude (so that some of them can be considered to be fast/slow with respect to others). Theoretical developments will be illustrated with some numerical examples.

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