Right gut-majorization on M_{n,m}

Let M_{n,m} be the set of all n-by-m matrices with entries from R, and suppose that R^n is the set of all 1-by-n real row vectors. A matrix R is called generalized row stochastic (g-row stochastic) if the sum of entries on every row of R is 1. For X, Y ∈ M_{n,m}, it is said that X is rgut-majorized by Y (denoted by X ≺_{rgut} Y ) if there exists an m-by-m upper triangular g-row stochastic matrix R such that X = Y R. In this paper, the concept right upper triangular generalized row stochastic majorization, or rgut- majorization, is investigated and then the linear preservers and strong linear preservers of this concept are characterized on R^n and M_{n,m}.

Markovian bounds on functions of finite Markov chains

In this paper, we obtain Markovian bounds on a function of a homogeneous discrete time Markov chain. For deriving such bounds, we use well-known results on stochastic majorization of Markov chains and the Rogers–Pitman lumpability criterion. The proposed method of comparison between functions of Markov chains is not equivalent to generalized coupling method of Markov chains, although we obtain same kind of majorization. We derive necessary and sufficient conditions for existence of our Markovian bounds. We also discuss the choice of the geometric invariant related to the lumpability condition that we use.

Stochastic comparisons for fork-join queues with exponential processing times

Consider a fork-join queue, where each job upon arrival splits into k tasks and each joins a separate queue that is attended by a single server. Service times are independent, exponentially distributed random variables. Server i works at rate , where μ is constant. We prove that the departure process becomes stochastically faster as the service rates become more homogeneous in the sense of stochastic majorization. Consequently, when all k servers work with equal rates the departure process is stochastically maximized.

Stochastic comparisons for fork-join queues with exponential processing times

Consider a fork-join queue, where each job upon arrival splits into k tasks and each joins a separate queue that is attended by a single server. Service times are independent, exponentially distributed random variables. Server i works at rate , where μ is constant. We prove that the departure process becomes stochastically faster as the service rates become more homogeneous in the sense of stochastic majorization. Consequently, when all k servers work with equal rates the departure process is stochastically maximized.