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Title: Discrete-time TASEP with holdback
Abstract: We study a discrete-time interacting particle system, which can be called a totally asymmetric simple exclusion process with holdback (TASEP-H). There are rho*n particles, rho < 1, moving clockwise, in discrete time, on n sites arranged in a circle. The “holdback" refers to the property that the probability of a particle moving forward to a vacant site depends on the presence of a particle immediately “behind” it. The model is motivated by a communication network with packets moving along a sequence of nodes under a “standard” random access algorithm. Another motivation is a slow-to-start model of car traffic. We focus on the dependence of the steady-state flux (throughput) on the density rho, when n is large. We show that when rho exceeds a certain threshold, a phase transition occurs in that large particle clusters are formed and persist, making the "typical" flux different from the formal one. (Joint work with Seva Shneer, Heriot-Watt Univ.)
Bio: Since 2017 Aleksandr Stolyar is a Founder Professor in the ISE Department and Coordinated Science Lab at UIUC. His research interests are in stochastic processes, queueing theory, and stochastic modeling of information, communication and service systems. He received Ph.D. in Mathematics from the Institute of Control Science, Moscow, in 1989, and was a research scientist at the Institute of Control Science in 1989-1991. In 1992-1998 he was working on stochastic models in telecommunications at Motorola and AT&T Research. From 1998 to 2014 he was with the Bell Labs Mathematical Sciences Research, Murray Hill, New Jersey, working on stochastic networks and resource allocation problems in a variety of applications, including wireless and wireline communications, service systems, network clouds. In 2014-2016 he was a Timothy J. Wilmott Endowed Chair Professor in the ISE Department at Lehigh University. He received INFORMS Applied Probability Society 2004 Best Publication award, SIGMETRICS'96 Best Paper award.
