12,203 research outputs found
Perfect Simulation of Queues
In this paper we describe a perfect simulation algorithm for the stable
queue. Sigman (2011: Exact Simulation of the Stationary Distribution of
the FIFO M/G/c Queue. Journal of Applied Probability, 48A, 209--213) showed how
to build a dominated CFTP algorithm for perfect simulation of the super-stable
queue operating under First Come First Served discipline, with
dominating process provided by the corresponding queue (using Wolff's
sample path monotonicity, which applies when service durations are coupled in
order of initiation of service), and exploiting the fact that the workload
process for the queue remains the same under different queueing
disciplines, in particular under the Processor Sharing discipline, for which a
dynamic reversibility property holds. We generalize Sigman's construction to
the stable case by comparing the queue to a copy run under Random
Assignment. This allows us to produce a naive perfect simulation algorithm
based on running the dominating process back to the time it first empties. We
also construct a more efficient algorithm that uses sandwiching by lower and
upper processes constructed as coupled queues started respectively from
the empty state and the state of the queue under Random Assignment. A
careful analysis shows that appropriate ordering relationships can still be
maintained, so long as service durations continue to be coupled in order of
initiation of service. We summarize statistical checks of simulation output,
and demonstrate that the mean run-time is finite so long as the second moment
of the service duration distribution is finite.Comment: 28 pages, 5 figure
Optimal scheduling and fair servicepolicy for STDMA in underwater networks with acoustic communications
In this work, a multi-hop string network with a single sink node is analyzed. A periodic optimal scheduling for TDMA operation that considers the characteristic long propagation delay of the underwater acoustic channel is presented. This planning of transmissions is obtained with the help of a new geometrical method based on a 2D lattice in the space-time domain. In order to
evaluate the performance of this optimal scheduling, two service policies have been compared: FIFO and Round-Robin. Simulation results, including achievable throughput, packet delay, and queue length, are shown. The network fairness has also been quantified with the Gini index
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