A stochastic airplane boarding model in a framework of ASEP with distinguishable particles

2018 ◽  
Vol 29 (10) ◽  
pp. 1850093
Author(s):  
ShengJie Qiang ◽  
Bin Jia ◽  
QingXia Huang
Keyword(s):  
Removal Rate ◽  
Exclusion Process ◽  
System Size ◽  
Nonequilibrium Systems ◽  
One Dimensional ◽  
Simple Exclusion Process ◽  
Maximum Current ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion ◽  
The Difference

The asymmetric simple exclusion process (ASEP) is a paradigmatic model for nonequilibrium systems and has been used in many applications. Airplane boarding provides another interesting example where this framework can be applied. We propose a simple model for boarding process, in which a particle moves along a one-dimensional aisle after being injected, and finally is removed at a reserved site. Different from the typical ASEP model, particles are removed in a disorderly or a parallel way. Detailed calculations and discussions of some related characteristics, such as mean boarding time and parallelism indicator, are provided based on Monte-Carlo simulations. Results show that three phases exist in the boarding process: free-flow, jamming and maximum current. Transitions between these phases are governed by the difference between the injection and removal rate. Further analysis shows how the scaling behavior depends on the system size and the boarding conditions. Those results emphasize the importance of utilizing the whole length of the aisle to reduce the boarding time when designing an efficient boarding strategy.

scholarly journals Dynamical Transitions in a One-Dimensional Katz–Lebowitz–Spohn Model

Entropy ◽  
2019 ◽  
Vol 21 (11) ◽  
pp. 1028 ◽  
Author(s):  
Alessandro Pelizzola ◽  
Marco Pretti ◽  
Francesco Puccioni
Keyword(s):  
Finite Size ◽  
Exclusion Process ◽  
Asymmetric Simple Exclusion Process ◽  
Pair Approximation ◽  
Fundamental Diagram ◽  
One Dimensional ◽  
Simple Exclusion Process ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion ◽  
The One

Dynamical transitions, already found in the high- and low-density phases of the Totally Asymmetric Simple Exclusion Process and a couple of its generalizations, are singularities in the rate of relaxation towards the Non-Equilibrium Stationary State (NESS), which do not correspond to any transition in the NESS itself. We investigate dynamical transitions in the one-dimensional Katz–Lebowitz–Spohn model, a further generalization of the Totally Asymmetric Simple Exclusion Process where the hopping rate depends on the occupation state of the 2 nodes adjacent to the nodes affected by the hop. Following previous work, we choose Glauber rates and bulk-adapted boundary conditions. In particular, we consider a value of the repulsion which parameterizes the Glauber rates such that the fundamental diagram of the model exhibits 2 maxima and a minimum, and the NESS phase diagram is especially rich. We provide evidence, based on pair approximation, domain wall theory and exact finite size results, that dynamical transitions also occur in the one-dimensional Katz–Lebowitz–Spohn model, and discuss 2 new phenomena which are peculiar to this model.

THEORETICAL INVESTIGATION OF SYNCHRONOUS TOTALLY ASYMMETRIC SIMPLE EXCLUSION PROCESS WITH DETACHMENT

2011 ◽  
Vol 25 (12) ◽  
pp. 1585-1592
Author(s):  
SONG XIAO ◽  
JIU-JU CAI ◽  
MING-ZHE LIU ◽  
FEI LIU
Keyword(s):  
Stationary Phases ◽  
Mean Field ◽  
Exclusion Process ◽  
Asymmetric Simple Exclusion Process ◽  
Dimensional System ◽  
One Dimensional ◽  
Simple Exclusion Process ◽  
Asymmetric Simple Exclusion ◽  
The Mean ◽  
Simple Exclusion

This paper investigates a synchronous totally asymmetric simple exclusion process (TASEP) with a detachment in a one-dimensional system. In the model, particles can detach irreversibly with probability q from a bulk site which is far away from boundaries. The phase diagram of the model is calculated in the mean-field approach and verified by Monte Carlo simulations. There are five stationary phases in the system. With the increase of q, the regions of the LD/LD and MC/LD phases increase, while the regions of the HD/HD and LD/HD phases decrease. The MC/HD phase corresponds to a critical point.

scholarly journals Mapping TASEP back in time

2021 ◽  
Author(s):  
Leonid Petrov ◽  
Axel Saenz
Keyword(s):  
Markov Process ◽  
Continuous Time ◽  
Exclusion Process ◽  
Discrete Space ◽  
Baxter Equation ◽  
Simple Exclusion Process ◽  
Open Questions ◽  
Asymmetric Simple Exclusion ◽  
Simple Exclusion ◽  
Hammersley Process

AbstractWe obtain a new relation between the distributions $$\upmu _t$$ μ t at different times $$t\ge 0$$ t ≥ 0 of the continuous-time totally asymmetric simple exclusion process (TASEP) started from the step initial configuration. Namely, we present a continuous-time Markov process with local interactions and particle-dependent rates which maps the TASEP distributions $$\upmu _t$$ μ t backwards in time. Under the backwards process, particles jump to the left, and the dynamics can be viewed as a version of the discrete-space Hammersley process. Combined with the forward TASEP evolution, this leads to a stationary Markov dynamics preserving $$\upmu _t$$ μ t which in turn brings new identities for expectations with respect to $$\upmu _t$$ μ t . The construction of the backwards dynamics is based on Markov maps interchanging parameters of Schur processes, and is motivated by bijectivizations of the Yang–Baxter equation. We also present a number of corollaries, extensions, and open questions arising from our constructions.

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