12,272 research outputs found
Zero-automatic queues and product form
We introduce and study a new model: 0-automatic queues. Roughly, 0-automatic
queues are characterized by a special buffering mechanism evolving like a
random walk on some infinite group or monoid. The salient result is that all
stable 0-automatic queues have a product form stationary distribution and a
Poisson output process. When considering the two simplest and extremal cases of
0-automatic queues, we recover the simple M/M/1 queue, and Gelenbe's G-queue
with positive and negative customers
Accelerated Backpressure Algorithm
We develop an Accelerated Back Pressure (ABP) algorithm using Accelerated
Dual Descent (ADD), a distributed approximate Newton-like algorithm that only
uses local information. Our construction is based on writing the backpressure
algorithm as the solution to a network feasibility problem solved via
stochastic dual subgradient descent. We apply stochastic ADD in place of the
stochastic gradient descent algorithm. We prove that the ABP algorithm
guarantees stable queues. Our numerical experiments demonstrate a significant
improvement in convergence rate, especially when the packet arrival statistics
vary over time.Comment: 9 pages, 4 figures. A version of this work with significantly
extended proofs is being submitted for journal publicatio
A new, analysis-based, change of measure for tandem queues
In this paper, we introduce a simple analytical approximation for the overflow probability of a two-node tandem queue. From this, we derive a change of measure, which turns out to have good performance in almost the entire parameter space. The form of our new change of measure sheds an interesting new light on earlier changes of measure for the same problem, because here the transition zone from one measure to another - that they all have - arises naturally.\u
Steady-state analysis of shortest expected delay routing
We consider a queueing system consisting of two non-identical exponential
servers, where each server has its own dedicated queue and serves the customers
in that queue FCFS. Customers arrive according to a Poisson process and join
the queue promising the shortest expected delay, which is a natural and
near-optimal policy for systems with non-identical servers. This system can be
modeled as an inhomogeneous random walk in the quadrant. By stretching the
boundaries of the compensation approach we prove that the equilibrium
distribution of this random walk can be expressed as a series of product-forms
that can be determined recursively. The resulting series expression is directly
amenable for numerical calculations and it also provides insight in the
asymptotic behavior of the equilibrium probabilities as one of the state
coordinates tends to infinity.Comment: 41 pages, 13 figure
Traffic Control and Route Choice; Capacity Maximization and Stability
Peer reviewedPublisher PD
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