Parking functions, labeled trees and DCJ sorting scenarios

In genome rearrangement theory, one of the elusive questions raised in recent years is the enumeration of rearrangement scenarios between two genomes. This problem is related to the uniform generation of rearrangement scenarios, and the derivation of tests of statistical significance of the properties of these scenarios. Here we give an exact formula for the number of double-cut-and-join (DCJ) rearrangement scenarios of co-tailed genomes. We also construct effective bijections between the set of scenarios that sort a cycle and well studied combinatorial objects such as parking functions and labeled trees.Comment: 12 pages, 3 figure

Approximate analysis of exponential queueing systems with blocking

A network of service stations Q 0 Q 1,...,QM is studied. Requests arrive at the centers according to independent Poisson processes; they travel through (part of) the network demanding amounts of service, with independent and negative exponentially distributed lengths, from those centers which they enter, and finally depart from the network. The waiting rooms or buffers at each service station in this exponential service system are finite. When the capacity at Q i is reached, service at all nodes which are currently processing a request destined next for Q i is instantaneously interrupted. The interruption lasts until the service of the request in the saturated node Q i is. completed. This blocking phenomenon makes an exact analysis intractable and a numerical solution computationally infeasible for most exponential systems. We introduce an approximation procedure for a class of exponential systems with blocking and show that it leads to accurate approximations for the marginal equilibrium queue length distributions. The applicability of the approximation method may not be limited to blocking systems

The product form for sojourn time distributions in cyclic exponential queues

Consider a closed cyclic queuing system consisting of M exponential queues. The Laplace-Stieltjes transform of the joint distribution of the consecutive sojourn times of a customer at the M queues is determined and shown to have a product form. The proof is based on a reversibility argument

The product form for sojourn time distributions in cyclic exponential queues

Consider a closed cyclic queuing system consisting of M exponential queues. The Laplace-Stieltjes transform of the joint distribution of the consecutive sojourn times of a customer at the M queues is determined and shown to have a product form. The proof is based on a reversibility argument