6,742 research outputs found
Queueing Analysis of Buffered Switching Networks
This paper provides a method of analyzing the queueing behavior of switching networks constructed from switches that employ shared buffering or parallel bypass input buffering. It extends that queuing models first introduced by Jenq and later generalized by Szymanski and Shaikh to handle these classes of networks. Our analysis explicitly models the state of an entire switch and infers information about the distribution of packets associated with particular inputs or outputs when needed. Earlier analyses of networks constructed from switches using input buffering attempt to infer the state of a switch from the states of individual buffers and cannot be directly applied to the networks of interest here. Moreover the assumption of independence among the buffers in a given switch can lead to substantial inaccuracies of independence among the buffers in a given switch can lead to substantial inaccuracies in some cases, as has been observed by Szymanski and Shaikh. Our approach can also be applied to previously studied systems and yields more accurate results
Sample path large deviations for multiclass feedforward queueing networks in critical loading
We consider multiclass feedforward queueing networks with first in first out
and priority service disciplines at the nodes, and class dependent
deterministic routing between nodes. The random behavior of the network is
constructed from cumulative arrival and service time processes which are
assumed to satisfy an appropriate sample path large deviation principle. We
establish logarithmic asymptotics of large deviations for waiting time, idle
time, queue length, departure and sojourn-time processes in critical loading.
This transfers similar results from Puhalskii about single class queueing
networks with feedback to multiclass feedforward queueing networks, and
complements diffusion approximation results from Peterson. An example with
renewal inter arrival and service time processes yields the rate function of a
reflected Brownian motion. The model directly captures stationary situations.Comment: Published at http://dx.doi.org/10.1214/105051606000000439 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
A Fixed-Point Algorithm for Closed Queueing Networks
In this paper we propose a new efficient iterative scheme for solving closed queueing networks with phase-type service time distributions. The method is especially efficient and accurate in case of large numbers of nodes and large customer populations. We present the method, put it in perspective, and validate it through a large number of test scenarios. In most cases, the method provides accuracies within 5% relative error (in comparison to discrete-event simulation)
Detecting Markov Chain Instability: A Monte Carlo Approach
We devise a Monte Carlo based method for detecting whether a non-negative
Markov chain is stable for a given set of parameter values. More precisely, for
a given subset of the parameter space, we develop an algorithm that is capable
of deciding whether the set has a subset of positive Lebesgue measure for which
the Markov chain is unstable. The approach is based on a variant of simulated
annealing, and consequently only mild assumptions are needed to obtain
performance guarantees.
The theoretical underpinnings of our algorithm are based on a result stating
that the stability of a set of parameters can be phrased in terms of the
stability of a single Markov chain that searches the set for unstable
parameters. Our framework leads to a procedure that is capable of performing
statistically rigorous tests for instability, which has been extensively tested
using several examples of standard and non-standard queueing networks
Structural characterization of decomposition in rate-insensitive stochastic Petri nets
This paper focuses on stochastic Petri nets that have an equilibrium distribution that is a product form over the number of tokens at the places. We formulate a decomposition result for the class of nets that have a product form solution irrespective of the values of the transition rates. These nets where algebraically characterized by Haddad et al.~as nets. By providing an intuitive interpretation of this algebraical characterization, and associating state machines to sets of -invariants, we obtain a one-to-one correspondence between the marking of the original places and the places of the added state machines. This enables us to show that the subclass of stochastic Petri nets under study can be decomposed into subnets that are identified by sets of its -invariants
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