Year: 2026
Type: article
Abstract: We consider an interacting particle system, which generalizes the classical totally asymmetric simple exclusion process (TASEP), in that each site can contain up to a fixed finite number of particles, and the particle movement is governed by a back-pressure (BP) algorithm (also often called MaxWeight ). There are N sites (with N finite or infinite), each may contain at most c particles, $$1 \le c < \infty $$ 1 ≤ c < ∞ . New particles enter the system at the left-most site 1 as a Poisson process of rate $$\alpha \le 1$$ α ≤ 1 , unless site 1 has c particles. Particles (if any) are removed from the right-most site N as a Poisson process of rate $$\beta \le 1$$ β ≤ 1 . The left-to-right movement of particles between neighboring sites is governed by the BP rule: one particle moves from site n to $$n+1$$ n + 1 at epochs of a rate 1 Poisson process, as long as the former site has strictly more particles than the latter. When $$c=1$$ c = 1 , this is the standard TASEP. Our main results address the asymptotics of the stationary distribution of a finite system, and especially the limit of the flux (current) as $$N\rightarrow \infty $$ N → ∞ . In particular, we prove that interesting non-trivial phase transitions take place in a system with $$c>1$$ c > 1 . For example, if $$c>1$$ c > 1 and $$1/2 \le \beta \le 1$$ 1 / 2 ≤ β ≤ 1 , the maximum limiting flux 1/4 is achieved as long as $$\alpha \ge \alpha _c^*$$ α ≥ α c ∗ , where $$\alpha _c^* < 1/2$$ α c ∗ < 1 / 2 is some non-trivial threshold. (For the standard TASEP the threshold is 1/2.) We also put forward a general conjecture about the stationary distribution asymptotics under an arbitrary parameter setting. We illustrate our formal results and the conjecture by simulations, and identify interesting directions for further research.
Source: Journal of Statistical Physics
Authors: Yuliy Baryshnikov, Alexander L. Stolyar
Institution: University of Illinois Urbana-Champaign
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W7171799552