Matrix product solution to multi-species ASEP with open boundaries

Exact matrix product states for parallel dynamics: Open boundaries and excess mass on the ring

Abstract. In this paper it is shown that the steady-state weights of the asymmetric simple exclusion process (ASEP) with open boundaries and parallel update can be written as a product of a scalar pair-factorized and a matrix-product state. This type of state is also obtained for an ASEP on a ring in which particles can move one or two sites. The dynamics leads to the formation of an excess hol...

Two-Species Asymmetric Simple Exclusion Process with Open Boundaries

We study the steady state of the two-species Asymmetric Simple Exclusion Process (ASEP) with open boundary conditions. The matrix product method works for the determination of the stationary probability distribution. Several physical quantities are calculated through an explicit representation for the matrix products. By making full use of the relation with the continuous big q-Hermite polynomi...

Ansatz for the two species ASEP with different hopping rates

An ASEP with two species of particles and different hopping rates is considered on a ring. Its integrability is proved and the Nested Algebraic Bethe Ansatz is used to derive the Bethe Equations for states with arbitrary numbers of particles of each type, generalizing the results of Derrida and Evans [10]. We present also formulas for the total velocity of particles of a given type and their li...

A product form solution to a system with multi-type jobs and multi-type servers

We consider a memoryless single station service system with servers S = {m1, . . . , mK}, and with job types C = {a, b, . . .}. Service is skill based, so that server mi can serve a subset of job types C(mi). Waiting jobs are served on a first come first served basis, while arriving jobs that find several idle servers are assigned to a feasible server randomly. We show that there exist assignme...

Matrix solution to longitudinal impedance of multi-layer circular structures