• When & Where: Seminars are generally (please, check the timeline and location before coming!) held on:
    • Wednesday afternoon at LINCS (14h-15h, Salle de Conseil) and
    • Thursday afternoon at Barrault (14h-15h, Amphi Saphir).
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30/04/2014Uri Yechiali (Tel-Aviv University)Tandem Jackson Networks, Asymmetric Inclusion Processes and Catalan Numbers
14/05/2014Thomas Bonald (Telecom ParisTech)Application of queuing theory to traffic engineering

Date:30/04/2014, 14h - 15h
Room:LINCS, Salle du Conseil
Speaker:Uri Yechiali (Tel-Aviv University)
Talk:Tandem Jackson Networks, Asymmetric Inclusion Processes and Catalan Numbers
Abstract:The Tandem Jackson Networkis a system of n sites (queues)in series, where single particles (customers, jobs, packets, etc.) move, one by one anduni-directionally,from one site to the next until they leave the system. (Think, for example, on aproduction line, or on a line in a cafeteria).When each site is a M/M/1 queue, the Tandem Jackson Network is famous for its product-form solution of the multi-dimensional Probability Generating Function of the site occupancies. In contrast, the Asymmetric Inclusion Process (ASIP) is a series of n Markovian queues (sites), each with unbounded capacity, but with unlimited-size batch service. That is, when service is completed at sitek,all particles present there move simultaneously to sitek+1,and form a cluster with the particles present in the latter site. We analyze the ASIP and show that its multi-dimensional Probability Generating Function(PGF) does notposses a product-form solution. We then present a method to calculate this PGF. We further show that homogeneous systems are �optimal� and derive limit laws (when the number of sites becomes large) for various variables (e.g. busy period, draining time, etc.). Considering the occupancies of the sites (queue sizes) we show that occupation probabilities in the ASIP obey a discrete two-dimensional boundary value problem. Solving this problem wefind explicit expressions for the probability that site k is occupied by m particles (m=0,1,2,..).Catalan's numbersare shown to naturally arise in the context of these occupation probabilities. This is a joint work with ShlomiReuveni and IddoEiazar.
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Date:14/05/2014, 14h - 15h
Room:LINCS, Salle du Conseil
Speaker:Thomas Bonald (Telecom ParisTech)
Talk:Application of queuing theory to traffic engineering
Abstract:Traffic engineering refers to the set of techniques used to dimension links and route traffic in IP networks. It relies most often on simplistic traffic models where packets arrive according to a Poisson process at each router, independently of the experienced delays and losses. In this talk, we revisit traffic engineering methods in the light of more realistic traffic models where data transfers are viewed as fluid flows sharing links in an elastic way, mimicking the congestion control algorithms of TCP. The corresponding queuing system is no longer a set of independent FIFO queues but a set of coupled processor-sharing queues. We show that minimizing the mean delay in this system tends to balance load more equally in the network.
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