14,914 research outputs found
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
The snowball effect of customer slowdown in critical many-server systems
Customer slowdown describes the phenomenon that a customer's service
requirement increases with experienced delay. In healthcare settings, there is
substantial empirical evidence for slowdown, particularly when a patient's
delay exceeds a certain threshold. For such threshold slowdown situations, we
design and analyze a many-server system that leads to a two-dimensional Markov
process. Analysis of this system leads to insights into the potentially
detrimental effects of slowdown, especially in heavy-traffic conditions. We
quantify the consequences of underprovisioning due to neglecting slowdown,
demonstrate the presence of a subtle bistable system behavior, and discuss in
detail the snowball effect: A delayed customer has an increased service
requirement, causing longer delays for other customers, who in turn due to
slowdown might require longer service times.Comment: 23 pages, 8 figures -- version 3 fixes a typo in an equation. in
Stochastic Models, 201
Analysis of State-Independent Importance-Sampling Measures for the Two-Node Tandem Queue
We investigate the simulation of overflow of the total population of a Markovian two-node tandem queue model during a busy cycle, using importance sampling with a state-independent change of measure. We show that the only such change of measure that may possibly result in asymptotically efficient simulation for large overflow levels is exchanging the arrival rate with the smallest service rate. For this change of measure, we classify the model's parameter space into regions of asymptotic efficiency, exponential growth of the relative error, and infinite variance, using both analytical and numerical techniques
Efficient T-CONT-agnostic Bandwidth and Wavelength Allocation for NG-PON2
Dynamic bandwidth and wavelength allocation are used to demonstrate high quality of service (QoS) in time wavelength-division multiplexedâpassive optical networks (TWDM-PONs). Both bandwidth and wavelength assignment are performed on the basis of transmission containers (T-CONTs) and therefore by means of upstream service priority traffic flows. Our medium access control (MAC) protocol therefore ensures consistency in processing alike classes of service across all optical network units (ONUs) in agreement with their QoS figures. For evaluation of the MAC protocol performance, a simulator has been implemented in OPNET featuring a 40 km, 40 Gbps TWDM-PON with four stacked wavelengths at 10 Gbps each and 256 ONUs. Simulation results have confirmed the efficiency of allocating bandwidth to each wavelength and the significant increase of network traffic flow due to adaptive polling from 9.04 to 9.74 Gbps. The benefit of T-CONT-centric allocation has also been measured with respect to packet delay and queue occupancy, achieving low packet delay across all T-CONTs. Therefore, improved NG-PON2 performance and greater efficiency are obtained in this first demonstration of T-CONTs allocated to both wavelength and time.Peer reviewe
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Survey of traffic control schemes and error control schemes for ATM networks
Among the techniques proposed for B-ISDN transfer mode, ATM concept is considered to be the most promising transfer technique because of its flexibility and efficiency. This paper surveys and reviews a number of topics related to ATM networks. Those topics cover congestion control, provision of multiple classes of traffic, and error control. Due to the nature of ATM networks, those issues are far more challenging than in conventional networks. Sorne of the more promising solutions to those issues are surveyed, and the corresponding results on performance are summarized. Future research problems in ATM protocol aspect are also presented
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