We define an analog of Plancherel measure for the set of rooted unlabeled trees on n vertices, and a Markov chain which has this measure as its stationary distribution. Using the combinatorics of commutation relations, we show that order n2 steps are necessary and suffice for convergence to the stationary distribution.

this paper presents a new formulation for warehouse inventory management in a stochastic situation. the primary source of this formulation is derived from fp model, which has been proposed by fletcher and ponnambalam for reservoir management. the new proposed mathematical model is based on the first and the second moments of storage as a stochastic variable. using this model, the expected value...

We consider a certain class of de Rham’s functional equations. We consider Hausdorff dimension of the measure whose distribution function is the solution. We give a necessary and sufficient condition for singularity. We also show that they have a relationship with stationary measures.

We investigate the fairness, smoothness, responsiveness, and aggressiveness of TCP and three representative TCP-friendly congestion control protocols: GAIMD, TFRC, and TEAR. The properties are evaluated both analytically and via simulation by studying protocol responses to three network environment changes. The first environment change is the inherent fluctuations in a stationary network enviro...

We consider a random surface in R d tesselating the space into cells and a random vector eld u which is smooth on each cell but may jump on. Assuming the pair ((; u) stationary we prove an inversion formula expressing the probability of an event under the stationary probability in terms of the Palm probability P deened by the random surface measure associated with. This result involves the ow o...

The stochastic delay di erential equation dX (t) = ∫ [−r;0] X (t + u) a(du) dt + dZ(t); t¿0 is considered, where Z(t) is a process with independent stationary increments and a is a nite signed measure. We obtain necessary and su cient conditions for the existence of a stationary solution to this equation in terms of a and the L evy measure of Z . c © 2000 Elsevier Science B.V. All rights reserved.