exact solution of a 1d asymmetric exclusion model using a matrix formulation several recent works have shown that the one dimensional fully asymmetric exclusion model which describes a system of particles hopping in a preferred direction with hard core interactions can be solved exactly in the case of open boundaries here the authors present a new approach based on representing the weights of each configuration in the steady state as a product of noncommuting matrices with this approach the whole solution of the problem is reduced to finding two matrices and two vectors which satisfy very simple algebraic rules they obtain several explicit forms for these non commuting matrices which are in the general case infinite dimensional their approach allows exact expressions to be derived for the current and density profiles finally they discuss briefly two possible generalizations of their results the problem of partially asymmetric exclusion and the case of a mixture of two kinds of particles

phase transitions in an exactly soluble one dimensional exclusion process we consider an exclusion process with particles injected with rate at the origin and removed with rate at the right boundary of a one dimensional chain of sites the particles are allowed to hop onto unoccupied sites to the right only for the special case of 1 the model was solved previously by derridaet al here we extend the solution to general the phase diagram obtained from our exact solution differs from the one predicted by the mean field approximation

asymmetric simple exclusion model with local inhomogeneity we study a totally asymmetric simple exclusion model with open boundary conditions and a local inhomogeneity in the bulk it consists of a one dimensional lattice with particles hopping stochastically with equal rates to the right at all lattice sites except one where the jump rate is different approximate stationary state solutions and phase diagrams are obtained and compared with monte carlo simulation results

totally asymmetric exclusion processes with particles of arbitrary size the steady state currents and densities of a one dimensional totally asymmetric exclusion process tasep with particles that occlude an integer number d of lattice sites are computed using various mean field approximations and monte carlo simulations taseps featuring particles of arbitrary size are relevant for modelling systems such as mrna translation vesicle locomotion along microtubules and protein sliding along dna we conjecture that the nonequilibrium steady state properties separate into low density high density and maximal current phases similar to those of the standard d 1 tasep a simple mean field approximation for steady state particle currents and densities is found to be inaccurate however we find local equilibrium particle distributions derived from a discrete tonks gas partition function yield apparently exact currents within the maximal current phase for the boundary limited phases the equilibrium tonks gas distribution cannot be used to predict currents phase boundaries or the order of the phase transitions however we employ a refined mean field approach to find apparently exact expressions for the steady state currents boundary densities and phase diagrams of the d 1 tasep extensive monte carlo simulations are performed to support our analytic mean field results

on the stability of the extreme point set in linear optimization this paper analyzes the stability properties of the set of extreme points of a closed convex set described by means of a given linear inequality system sigma we assume that all the coefficients of sigma can be arbitrarily perturbed maintaining the possibly infinite index set as well as the finite dimension of the space of variables and we measure the size of these perturbations by means of the pseudometric of the uniform convergence the paper characterizes the nonemptiness of the extreme point set under sufficiently small perturbations and the berge lower semicontinuity of the extreme point set mapping at sigma it also gives necessary as well as sufficient conditions for the closedness and for the berge upper semicontinuity at sigma which provide characterizations of these properties for finite systems

exact results for one dimensional cellular automata with different types of updates we study two common types of time noncontinuous updates for one dimensional stochastic cellular automata with arbitrary nearest neighbor interactions and arbitrary open boundary conditions we first construct the stationary states using the matrix product formalism this construction then allows to prove a general connection between the stationary states which are produced by the two different types of updates using this connection we derive explicit relations between the densities and correlation functions for these different stationary states

exact results for 2d directed animals on a strip of finite width proves a conjecture giving the exact number of directed animals of s sites with any root on a strip of finite width of a square lattice the authors also rederive more simply some previous results concerning the connective constant and particular eigenvectors of the transfer matrix

characterization of total ill posedness in linear semi infinite optimization this paper deals with the stability of linear semi infinite programming lsip for short problems we characterize those lsip problems from which we can obtain under small perturbations in the data different types of problems namely inconsistent consistent unsolvable and solvable problems the problems of this class are highly unstable and for this reason we say that they are totally ill posed the characterization that we provide here is of geometrical nature and it depends exclusively on the original data i e on the coefficients of the nominal lsip problem our results cover the case of linear programming problems and they are mainly obtained via a new formula for the subdifferential mapping of the support function

exact steady states of disordered hopping particle models with parallel and ordered sequential dynamics a one dimensional driven lattice gas with disorder in the particle hopping probabilities is considered it has previously been shown that in the version of the model with random sequential updating a phase transition occurs from a low density inhomogeneous phase to a high density congested phase here the steady states for both parallel fully synchronous updating and ordered sequential updating are solved exactly the phase transition is shown to persist in both cases with the critical densities being higher than that for random sequential dynamics the steady state velocities are related to the fugacity of a bose system suggesting a principle of minimization of velocity a generalization of the dynamics to the case where the hopping probabilities depend on the number of empty sites in front of the particles is also solved exactly in the case of parallel updating the models have natural interpretations as simplistic descriptions of traffic flow the relation to more sophisticated traffic flow models is discussed

totally asymmetric simple exclusion process with a shortcut in this paper we study the interplay of a totally asymmetric simple exclusion process tasep with a shortcut in its bulk under open boundary conditions two different models are introduced i model a for molecular motor motion and ii model b for vehicular traffic the phase diagrams and density profiles of both models are studied it is found that although the phase diagrams of both models can be classified into three regions the phases corresponding to these regions and the phase boundaries between these regions are quite different in these two models moreover the approximate stationary state solutions of model a have been carried out and it is shown that the analytical results are in good agreement with the results of monte carlo simulations

the fluid limit of an overloaded processor sharing queue this paper primarily concerns strictly supercritical fluid models which arise as functional law of large numbers approximations for overloaded processor sharing queues analogous results for critical fluid models associated with heavily loaded processor sharing queues are contained in gromoll et al 2002 and puha and williams 2004 an important distinction between critical and strictly supercritical fluid models is that the total mass for a solution that starts from zero grows with time for the latter but it is identically equal to zero for the former for strictly supercritical fluid models this paper contains descriptions of each of the following the distribution of the mass as it builds up from zero the set of stationary solutions and the limiting behavior of an arbitrary solution as time tends to infinity in addition a fluid limit result is proved that justifies strictly supercritical fluid models as first order approximations to overloaded processor sharing queues

exact solution of a cellular automaton for traffic we present an exact solution of a probabilistic cellular automaton for traffic with open boundary conditions e g cars can enter and leave a part of a highway with certain probabilities the model studied is the asymmetric exclusion process asep with simultaneous updating of all sites it is equivalent to a special case vmax 1 of the nagel schreckenberg model for highway traffic which has found many applications in real time traffic simulations the simultaneous updating induces additional strong short range correlations compared to other updating schemes the stationary state is written in terms of a matrix product solution the corresponding algebra which expresses a system size recursion relation for the weights of the configurations is quartic in contrast to previous cases in which the algebra is quadratic we derive the phase diagram and compute various properties such as density profiles two point functions and the fluctuations in the number of particles cars in the system the current and the density profiles can be mapped onto the asep with other time discrete updating procedures through use of this mapping our results also give new results for these models

comparison between simultaneous and sequential updating in 2n 1 1 cellular automata properties of cellular automata with packard wolfram code 2n 1 1 have been studied without and with noise on square n 4 and triangular n 6 lattices the outer totalistic rule used assign a central spin opposite to the majority spin of its neighbourhood and flips it in the case of equality starting from random configurations with a variable proportion r of up spins different relaxation behaviours and equilibrium structures are obtained a ferromagnetic f structure and an antiferromagnetic af structure for simultaneous and sequential updatings respectively on a square lattice when the spins are processed simultaneously in the presence of noise a first order transition f af is observed for a square lattice and a second order transition for a triangular lattice the results show similarities with ising models domains but also strong differences magnetization as a function of r

effects of junctional correlations in the totally asymmetric simple exclusion process on random regular networks we investigate the totally asymmetric simple exclusion process on closed and directed random regular networks which is a simple model of active transport in the one dimensional segments coupled by junctions by a pair mean field theory and detailed numerical analyses it is found that the correlations at junctions induce two notable deviations from the simple mean field theory which neglects these correlations 1 the narrower range of particle density for phase coexistence and 2 the algebraic decay of density profile with exponent 1 2 even outside the maximal current phase we show that these anomalies are attributable to the effective slow bonds formed by the network junctions

exact stationary state for an asymmetric exclusion process with fully parallel dynamics the exact stationary state of an asymmetric exclusion process with fully parallel dynamics is obtained using the matrix product ansatz we give a simple derivation for the deterministic case by a physical interpretation of the dimension of the matrices we prove the stationarity via a cancellation mechanism and by making use of an explicit representation of the matrix algebra we easily find closed expressions for the correlation functions in the general probabilistic case asymptotic expressions obtained by making use of earlier results allow us to derive the exact phase diagram

representations of the quadratic algebra and partially asymmetric diffusion with open boundaries we consider the one dimensional partially asymmetric exclusion model with open boundaries the model describes a system of hard core particles that hop stochastically in both directions with different rates at both boundaries particles are injected and extracted by means of the method of derrida et al the stationary probability measure can be expressed as a matrix product state involving two matrices forming a fock like representation of a general quadratic algebra we obtain the representations of this algebra which were unknown in the mathematical literature and use the two dimensional one to derive exact expressions for the density profile and correlation functions using the correspondence between the stochastic model and a quantum spin chain we obtain exact correlation functions for a spin heisenberg xxz chain with non diagonal boundary terms generalizations to other reaction diffusion models are discussed

synchronization of kinks in the two lane totally asymmetric simple exclusion process with open boundary conditions we study the motion of kinks in a two lane model of the totally asymmetric simple exclusion process with open boundaries we analytically study the motion of the kinks by a decoupling approximation in terms of the decoupling approximation we find that the positions of the kinks become synchronized though the difference in the number of particles between lanes remains non zero when the rate of lane change is asymmetric the validity of this result is confirmed for small asymmetric cases through the monte carlo simulation

matrix product ground states for exclusion processes with parallel dynamics we show in the example of a one dimensional asymmetric exclusion process that stationary states of models with parallel dynamics may be written in a matrix product form the corresponding algebra is quadratic and involves three different matrices using this formalism we prove previous conjectures for the equal time correlation functions of the model

law of large number limits of limited processor sharing queues motivated by applications in computer and communication systems we consider a processor sharing queue where the number of jobs served is not larger than k we propose a measure valued fluid model for this limited processor sharing queue and show that there exists a unique associated fluid model solution in addition we show that this fluid model arises as the limit of a sequence of appropriately scaled processor sharing queues

a note on the continuity of solutions of parametric linear programs this note shows that if a parametric linear program min cx ax b1 b2 x 0 has optimal solutions in an interval left underset raise0 3em hbox smash scriptscriptstyle theta bar theta right for then depending on degeneracy the solutions is a continuous vector function or a continuous point to set mapping in the latter case an algorithm is introduced to solve the problem and generate a continuous vector solution in left underset raise0 3em hbox smash scriptscriptstyle theta bar theta right

the asymmetric exclusion process comparison of update procedures the asymmetric exclusion process asep has attracted a lot of interest not only because of its many applications e g in the context of the kinetics of biopolymerization and traffic flow theory but also because it is a paradigmatic model for nonequilibrium systems here we study the asep for different types of updates namely random sequential sequential sublattice parallel and parallel in order to compare the effects of the different update procedures on the properties of the stationary state we use large scale monte carlo simulations and analytical methods especially the so called matrix product ansatz mpa we present in detail the exact solution for the model with sublattice parallel and sequential updates using the mpa for the case of parallel update which is important for applications like traffic flow theory we determine the phase diagram the current and density profiles based on monte carlo simulations we furthermore suggest an mpa for that case and derive the corresponding matrix algebra

sharp lipschitz constants for basic optimal solutions and basic feasible solutions of linear programs the main purpose of this paper to give lipschitz constants for basic optimal solutions or vertices of solution sets and basic feasible solutions or vertices of feasible sets of linear programs with respect to right hand side perturbations the lipschitz constants are given in terms of norms of pseudoinverses of submatrices of the matrices involved and are sharp under very general assumptions there are two mathematical principles involved in deriving the lipschitz constants 1 the local upper lipschitz constant of a hausdorff lower semicontinuous mapping is equal to the lipschitz constant of the mapping and 2 the lipschitz constant of a finite set valued mapping can be inherited by its continuous submappings moreover it is proved that any lipschitz constant for basic feasible solutions can be used as an lipschitz constant for basic optimal solutions feasible solutions and optimal solutions

fluid limits of g g 1 g queues under the nonpreemptive earliest deadline first discipline a single server queueing model is considered with customers that have deadlines if a customer s deadline elapses before service is offered the customer abandons the system customers do not abandon while being served when the server becomes available it offers service to the customer having the earliest deadline among those that are in the queue we obtain a fluid limit of the queue length and abandonment processes and for the occupation measure of deadlines in the form of measure valued processes we characterize the limit by means of a skorohod problem in a time varying domain that has an explicit solution the fluid limits also describe a certain process called the frontier that is well known to play a key role in systems operating under this scheduling policy

on the stability of convex valued mappings and their relative boundary and extreme points set mappings this paper deals with the transmission of the main stability properties lower and upper semicontinuity in berge sense and closedness from a given closed convex valued mapping to its corresponding relative boundary and extreme point set mappings and vice versa the domain of the mappings considered in this paper are locally metrizable spaces and the images range on euclidean spaces important examples of the class of mappings considered in this paper are the feasible set mapping and the optimal set mapping of convex optimization problems for which the space of parameters is the result of perturbing a given nominal problem

totally asymmetric exclusion process with long range hopping generalization of the one dimensional totally asymmetric exclusion process tasep with open boundary conditions in which particles are allowed to jump l sites ahead with the probability p l ensuremath sim 1 l ensuremath sigma 1 is studied by monte carlo simulations and the domain wall approach for ensuremath sigma g1 the standard tasep phase diagram is recovered but the density profiles display additional features when 1l ensuremath sigma l2 at the first order transition line the domain wall is localized and phase separation is observed in the maximum current phase the profile has an algebraic decay with a ensuremath sigma dependent exponent within the ensuremath sigma ensuremath le 1 regime where the transitions are found to be absent analytical results in the continuum mean field approximation are derived in the limit ensuremath sigma ensuremath 1

garden of eden states in traffic models we investigate the allowed configurations in the stationary state of the cellular automaton model for single lane traffic it is found that certain states in the configuration space cannot be reached if one uses parallel dynamics these so called garden of eden goe states do not exist for random sequential dynamics and are responsible for the strong short ranged correlations found in parallel dynamics by eliminating the goe states we obtain a simple and effective approximative description of the model for the exact solution is recovered for this elimination leads to much higher values of the flux compared to the mean field result which are in good agreement with monte carlo simulations

fluid limits for processor sharing queues with impatience we investigate a processor sharing queue with renewal arrivals and generally distributed service times impatient jobs may abandon the queue or renege before completing service the random time representing a job s patience has a general distribution and may be dependent on its initial service time requirement a scaling procedure that gives rise to a fluid model with nontrivial yet tractable steady state behavior is presented this fluid model captures many essential features of the underlying stochastic model and it is used to analyze the impact of impatience in processor sharing queues

totally asymmetric exclusion process on chains with a double chain section in the middle computer simulations and a simple theory computer simulations of the totally asymmetric simple exclusion process on chains with a double chain section in the middle are performed in the case of random sequential update the outer ends of the chain segments connected to the middle double chain section are open so that particles are injected at the left end with rate alpha and removed at the right end with rate beta at the branching point of the graph the left end of the middle section the particles choose with equal probability 1 2 which branch to take and then simultaneous motion of the particles along the two branches is simulated with the aid of a simple theory neglecting correlations at the junctions of the chain segments the possible phase structures of the model are clarified density profiles and nearest neighbor correlations in the steady states of the model at representative points of the phase diagram are obtained and discussed cross correlations are found to exist between equivalent sites of the branches of the middle section whenever they are in a coexistence phase

discrete stochastic models for traffic flow we investigate a probabilistic cellular automaton model which has been introduced recently this model describes single lane traffic flow on a ring and generalizes the asymmetric exclusion process models we study the equilibrium properties and calculate the so called fundamental diagrams flow versus density for parallel dynamics this is done numerically by computer simulations of the model and by means of an improved mean field approximation which takes into account short range correlations for cars with a maximum velocity of 1 the simplest nontrivial approximation gives the exact result for higher velocities the analytical results obtained by iterated application of the approximation scheme are in excellent agreement with the numerical simulations

finite dimensional representations of the quadratic algebra applications to the exclusion process we study the one dimensional partially asymmetric simple exclusion process asep with open boundaries that describes a system of hard core particles hopping stochastically on a chain coupled to reservoirs at both ends derrida and coworkers showed in 1993 that the stationary probability distribution of this model can be represented as a trace on a quadratic algebra closely related to the deformed oscillator algebra we construct all finite dimensional irreducible representations of this algebra this enables us to compute the stationary bulk density as well as all correlation lengths for the asep on a set of special curves of the phase diagram

an exact solution of a one dimensional asymmetric exclusion model with open boundaries a simple asymmetric exclusion model with open boundaries is solved exactly in one dimension the exact solution is obtained by deriving a recursion relation for the steady state if the steady state is known for all system sizes less thann then our equation 8 gives the steady state for sizen using this recursion we obtain closed expressions 48 for the average occupations of all sites the results are compared to the predictions of a mean field theory in particular for infinitely large systems the effect of the boundary decays as the distance to the power 1 2 instead of the inverse of the distance as predicted by the mean field theory

synchronous asymmetric exclusion processes for a fully synchronous asymmetric exclusion process with open or closed boundaries only partial analytic results are known owing to the appearance of strong short range correlations which invalidate simple mean field approximations here we present a new method for calculating basic properties of nonequilibrium steady states and calculate densities fluxes travel times spatial and temporal correlation functions phase diagrams profiles and widths of boundary layers and interfaces between phases in coexistence as well as their microstructures this paper is based on two new elements i a microscopic characterization of order parameters and local configurations in the relevant phases based on the microdynamics of the model and ii an improved mean field approximation which neglects certain four point and higher order correlation functions it is conjectured that the density profiles obtained here are exact up to terms that are exponentially small in the system size

steady state properties of a totally asymmetric exclusion process with periodic structure we study the steady state behavior of totally asymmetric simple exclusion processes taseps that contain periodically varying movement rates in this model particles move to the right at one of two rates p 2 if the particle occupies one of a periodically arranged set of lattice sites p 1 otherwise approximate mean field approaches are used to study the steady state currents and bulk densities of this model these mean field methods are found to provide results in good agreement with data derived from monte carlo simulations finally the condition for particle hole symmetry in the tasep with periodically varying movement rates is specified and the changes in the locations of the boundary limited to maximal current transition lines due to symmetry violation are investigated

jamming transition in a cellular automaton model for traffic flow the cellular automaton model for traffic flow exhibits a jamming transition from a free flow phase to a congested phase in the deterministic case this transition corresponds to a critical point with diverging correlation length in the presence of noise however no consistent picture has emerged up to now we present data from numerical simulations that suggest the absence of critical behavior the transition of the deterministic case is smeared out and one only observes the remnants of the critical point

totally asymmetric exclusion process with extended objects a model for protein synthesis the process of protein synthesis in biological systems resembles a one dimensional driven lattice gas in which the particles have spatial extent covering more than one lattice site we expand the well studied totally asymmetric exclusion process in which particles typically cover a single lattice site to include cases with extended objects exact solutions can be determined for a uniform closed system we analyze the uniform open system through two approaches first a continuum limit produces a modified diffusion equation for particle density profiles second an extremal principle based on domain wall theory accurately predicts the phase diagram and currents in each phase finally we briefly consider approximate approaches to a nonuniform open system with quenched disorder in the particle hopping rates and compare these approaches with monte carlo simulations

extended active constraints in linear optimization with applications in this paper we introduce different relaxations of the concept of active constraint at a given point with respect to a certain linear inequality system with an arbitrary number of constraints we show that these concepts provide useful local information in linear optimization for instance conditions for a given feasible solution to be a unique extreme point optimal solution or a strongly unique optimal solution

cellular automation models and traffic flow a cellular automaton model for the description of traffic flow is investigated it generalizes asymmetric exclusion models which have attracted a lot of interest in the past the authors calculate the so called fundamental diagram flow versus density for parallel dynamics using an improved mean field approximation which takes into account short range correlations for maximum velocity they find that the simplest of these non trivial approximations gives the exact result for higher velocities their results are in excellent agreement with numerical data

on matrix product ground states for reaction diffusion models we discuss a new mechanism leading to a matrix product form for the stationary state of one dimensional stochastic models the corresponding algebra is quadratic and involves four different matrices for the example of a coagulation decoagulation model explicit four dimensional representations are given and exact expressions for various physical quantities are recovered we also find the general structure of n point correlation functions at the phase transition

stability theory for linear inequality systems ii upper semicontinuity of the solution set mapping this paper deals with the upper semicontinuity of the solution set mapping for linear inequality systems complementing a previous work on lower semicontinuity and related stability concepts the main novelty of our approach is that we are not assuming any standard hypothesis about the set indexing the inequalities in the system this set possibly infinite has no topological structure and therefore the functional dependence between the linear inequalities and their associated indices has no qualification at all the space of consistent systems over a fixed index set is endowed with the uniform topology derived from the pseudometric of chebyshev which turns out to be a natural way to measure the size of the perturbations in this context we provide some necessary and some sufficient conditions for the upper semicontinuity of the feasible set map at a given system whose solution set is not necessarily bounded

two channel totally asymmetric simple exclusion processes totally asymmetric simple exclusion processes consisting of two coupled parallel lattice chains with particles interacting with hard core exclusion and moving along the channels and between them are considered in the limit of strong coupling between the channels the particle currents density profiles and a phase diagram are calculated exactly by mapping the system into an effective one channel totally asymmetric exclusion model for intermediate couplings a simple approximate theory that describes the particle dynamics in vertical clusters of two corresponding parallel sites exactly and neglects the correlations between different vertical clusters is developed it is found that similarly to the case of one channel totally asymmetric simple exclusion processes there are three stationary state phases although the phase boundaries and stationary properties strongly depend on inter channel coupling extensive computer monte carlo simulations fully support the theoretical predictions