An extremal property of FIFO discipline in G/IFR/1 queues

AN EXTREMAL PROPERTY OF FIFO DISCIPLINE IN G/IFR/l QUEUES

In a recent paper by Shanthikumar and Sumita (1987), it is conjectured that the ergodic sojourn time of a customer in G /IFR/1 queues is minimized by FIFO (first in, first out) discipline in the sense of increasing and convex ordering. This paper shows that their conjecture is true. In fact, FIFO discipline minimizes E[~Z'=l f( iO(k) aO(k)] for any non-decreasing and convex function f, where N ...

An Explicit Control Algorithm for Optical FIFO Queues

With the recent advances in optical technologies, it has become a challenge to build optical queues with minimal complexity. In [2], it was shown that an optical FIFO queue can be constructed recursively by a concatenation of scaled optical memory cells, which in turn are made by 2 × 2 switches and fiber delay lines. However, as the construction is recursive, there is no explicit control algori...

Fast and Scalable k-FIFO Queues

We introduce fast and scalable algorithms that implement boundedand unbounded-size, lock-free, linearizable k-FIFO queues with empty (and full) check. Logically, a k-FIFO queue can be understood as queue where each element may be dequeued out-of-order up to k− 1 or as pool where each element is dequeued within a k-bounded number of dequeue operations. We show experimentally that there exist opt...

An Extremal Property of Fekete Polynomials

An Extremal Property of Turán Graphs

Let Fn,tr(n) denote the family of all graphs on n vertices and tr(n) edges, where tr(n) is the number of edges in the Turán’s graph Tr(n) – the complete r-partite graph on n vertices with partition sizes as equal as possible. For a graph G and a positive integer λ, let PG(λ) denote the number of proper vertex colorings of G with at most λ colors, and let f(n, tr(n), λ) = max{PG(λ) : G ∈ Fn,tr(n...