Dresden 2014 – wissenschaftliches Programm
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DY: Fachverband Dynamik und Statistische Physik
DY 8: Critical Phenomena and Phase Transitions
DY 8.11: Vortrag
Montag, 31. März 2014, 18:00–18:15, ZEU 118
Queue with exclusion — •Chikashi Arita1 and Andreas Schadschneider2 — 1Theoretische Physik, Universität des Saarlandes, Saarbrücken, Germany — 2Institut für Theoretische Physik, Universität zu Köln, Köln, Germany
The history of the queueing theory goes back to A K Erlang 1909. The M/M/1 queueing process is one of basic models in which injection and extraction of particles (customers) are imposed. When pedestrians make a queue, they usually proceed when there is a space in front of them. However this excluded-volume effect is neglected in the M/M/1 queue. The ``exclusive queueing process (EQP)'' was introduced to take this effect into account by imposing a new boundary condition on the exclusion process [1,2]. The M/M/1 queue converges (diverges) when the incoming rate is smaller (greater) than the outgoing rate, ``phase transition''. On the other hand, in the EQP, the incoming rate is restricted by the so-called maximal current of the exclusion process for convergence, i.e. ``the queue itself is a bottleneck.'' This property was derived by using an exact stationary state [1,2]. Furthermore, with helps of Monte Carlo Simulations, some time dependent properties of the system length L have been investigated [3,4,5]. Recently an update rule dependent behavior of L was found on the phase transition line [6].
[1] CA: Phys Rev E 80, 051119 (2009) [2] CA & D Yanagisawa: J Stat Phys 141, 829 (2010) [3] CA & AS: Phys Rev E 83, 051128 (2011) [4] CA & AS: Phys Rev E 84, 051127 (2011) [5] CA & AS: J Stat Mech, P12004 (2012) [6] CA & AS: EPL, in press (2013)