Continuous time random walks (CTRWs) are versatile models for anomalous diffusion processes that have found widespread application in the quantitative sciences. Their scaling limits are typically non-Markovian, and the computation of their finitedimensional distributions is an important open problem. This paper develops a general semi-Markov theory for CTRW limit processes in d-dimensional Eucl...

Moving particles that rest along their trajectory lead to time-fractional diffusion equations for the scaling limit distributions. For power law waiting times with infinite mean, the equation contains a fractional time derivative of order between 0 and 1. For finite mean waiting times, the most revealing approach is to employ two time scales, one for the mean and another for deviations from the...

Abstract: In this paper, we study a discrete time queueing system with multiple types of customers and a last-come-first-served general preemptive resume (LCFS-GPR) service discipline (MMAP[K]/PH[K]/1/LCFS-GPR). When the waiting space is infinite, matrix analytic methods are used to find a system stability condition, to derive the distributions of the busy periods and sojourn times, and to obta...

Continuous time random walks (CTRWs) on finite arbitrarily inhomogeneous chains are studied. By introducing a technique of counting all possible trajectories, we derive closed-form solutions in Laplace space for the Green's function (propagator) and for the first passage time probability density function (PDF) for nearest neighbor CTRWs in terms of the input waiting time PDFs. These solutions a...

The MX/G/1 queue with finite waiting room is studied for both the partially rejected model and the totally rejected model. We start by studying the joint distribution of the number of customers at time t and the remaining service time of customer in service. This gives the asymptotic distribution of the number of customers at an arbitrary moment and immediately after a departure. Also the waiti...