Let G be a graph on n vertices with Laplacian matrix L and let b be a binary vector of length n. The pair (L,b) is controllable if the smallest L-invariant subspace containing b is of dimension n. The graph G is called essentially controllable if (L,b) is controllable for every b / ∈ ker(L), completely uncontrollable if (L,b) is uncontrollable for every b, and conditionally controllable if it i...

This study aims to determine the transient behavior of blended queue. Priority customers arrive over time and benefit from a threshold reservation policy, while non-priority ones can be contacted at any time. We show how compute Laplace transforms probabilities. Using uniformization technique, we prove some monotonicty properties expected number in queue, explaining why optimal should lower tha...

A virtual queue can be used to predict when a real queue is about to grow. This memo explains why using a leaky bucket to implement a virtual queue is not useful, despite a superficial similarity. However, it is possible to implement a useful virtual queue using two leaky buckets. It requires a simple trick that can typically be implemented with existing hardware.

This paper addresses the problem of configuring active queue management systems (e.g. WRED and RIO) for service level specifications in Internetworks. In particular, we focus on Assured Forwarding (AF) for non-responsive flows in Differentiated Services networks. The difficulty is to determine the correct queue level thresholds that will result in correct drop rates for various AF precedence le...

This paper considers importance sampling as a tool for rare-event simulation. The system at hand is a so-called tandem queue with slow-down, which essentially means that the server of the first queue (or: upstreanm queue) switches to a lower speed when the second queue (downstream queue) exceeds some threshold. The goal is to assess to what extent such a policy succeeds in protecting the first ...

In this paper, we consider a PH/M/2 queue in which each server has its own queue and arriving customers join the shortest queue. For this model, it has been conjectured that the decay rate of the tail probabilities for the shortest queue length in the steady state is equal to the square of the decay rate for the queue length in the corresponding PH/M/2 model with a single queue. We prove this f...

This paper presents the analysis of a renewal input  finite buffer queue wherein the customers can decide either to  join the queue with a probability or balk. The service process is Markovian service process ($MSP$) governed  by an underlying $m$-state Markov chain. Employing the supplementary  variable and imbedded Markov chain techniques,   the steady-state system length distributions at pre...