30,265 research outputs found
Equivalent random analysis of a buffered optical switch with general interarrival times
We propose an approximate analytic model of an optical switch with fibre delay lines and wavelength converters by employing Equivalent Random Theory. General arrival traffic is modelled by means of Gamma-distributed interarrival times. The analysis is formulated in terms of virtual traffic flows within the optical switch from which we derive expressions for burst blocking probability, fibre delay line occupancy and mean delay. Emphasis is on approximations that give good numerical efficiency so that the method can be useful for formulating dimensioning problems for large-scale networks. Numerical solution values from the proposed analysis method compare well with results from a discrete-event simulation of an optical burst switch
Imprecise Markov Models for Scalable and Robust Performance Evaluation of Flexi-Grid Spectrum Allocation Policies
The possibility of flexibly assigning spectrum resources with channels of
different sizes greatly improves the spectral efficiency of optical networks,
but can also lead to unwanted spectrum fragmentation.We study this problem in a
scenario where traffic demands are categorised in two types (low or high
bit-rate) by assessing the performance of three allocation policies. Our first
contribution consists of exact Markov chain models for these allocation
policies, which allow us to numerically compute the relevant performance
measures. However, these exact models do not scale to large systems, in the
sense that the computations required to determine the blocking
probabilities---which measure the performance of the allocation
policies---become intractable. In order to address this, we first extend an
approximate reduced-state Markov chain model that is available in the
literature to the three considered allocation policies. These reduced-state
Markov chain models allow us to tractably compute approximations of the
blocking probabilities, but the accuracy of these approximations cannot be
easily verified. Our main contribution then is the introduction of
reduced-state imprecise Markov chain models that allow us to derive guaranteed
lower and upper bounds on blocking probabilities, for the three allocation
policies separately or for all possible allocation policies simultaneously.Comment: 16 pages, 7 figures, 3 table
A tight bound on the throughput of queueing networks with blocking
In this paper, we present a bounding methodology that allows to compute a tight lower bound on the cycle time of fork--join queueing networks with blocking and with general service time distributions. The methodology relies on two ideas. First, probability masses fitting (PMF) discretizes the service time distributions so that the evolution of the modified network can be modelled by a Markov chain. The PMF discretization is simple: the probability masses on regular intervals are computed and aggregated on a single value in the orresponding interval. Second, we take advantage of the concept of critical path, i.e. the sequence of jobs that covers a sample run. We show that the critical path can be computed with the discretized distributions and that the same sequence of jobs offers a lower bound on the original cycle time. The tightness of the bound is shown on computational experiments. Finally, we discuss the extension to split--and--merge networks and approximate estimations of the cycle time.queueing networks, blocking, throughput, bound, probability masses fitting, critical path.
Minimizing Flow Time in the Wireless Gathering Problem
We address the problem of efficient data gathering in a wireless network
through multi-hop communication. We focus on the objective of minimizing the
maximum flow time of a data packet. We prove that no polynomial time algorithm
for this problem can have approximation ratio less than \Omega(m^{1/3) when
packets have to be transmitted, unless . We then use resource
augmentation to assess the performance of a FIFO-like strategy. We prove that
this strategy is 5-speed optimal, i.e., its cost remains within the optimal
cost if we allow the algorithm to transmit data at a speed 5 times higher than
that of the optimal solution we compare to
Efficient estimation of blocking probabilities in non-stationary loss networks
This paper considers estimation of blocking probabilities in a nonstationary loss network. Invoking the so called MOL (Modified Offered Load) approximation, the problem is transformed into one requiring the solution of blocking probabilities in a sequence of stationary loss networks with time varying loads. To estimate the blocking probabilities Monte Carlo simulation is used and to increase the efficiency of the simulation, we develop a likelihood ratio method that enables samples drawn at a one time point to be used at later time points. This reduces the need to draw new samples every time independently as a new time point is considered, thus giving substantial savings in the computational effort of evaluating time dependent blocking probabilities. The accuracy of the method is analyzed by using Taylor series approximations of the variance indicating the direct dependence of the accuracy on the rate of change of the actual load. Finally, three practical applications of the method are provided along with numerical examples to demonstrate the efficiency of the method
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)
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