We treat a single–server vacation queue with queue–length dependent vacation schedules. This subsumes the single–server vacation queue with exhaustive service discipline and the vacation queue with Bernoulli schedule as special cases. The lengths of vacation times depend on the number of customers in the system at the beginning of a vacation. The arrival process is a batch–Markovian arrival pro...

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 ...