2,086 research outputs found
A polling model with an autonomous server
Polling models are used as an analytical performance tool in several application areas. In these models, the focus often is on controlling the operation of the server as to optimize some performance measure. For several applications, controlling the server is not an issue as the server moves independently in the system. We present the analysis for such a polling model with a so-called autonomous server. In this model, the server remains for an exogenous random time at a queue, which also implies that service is preemptive. Moreover, in contrast to most of the previous research on polling models, the server does not immediately switch to a next queue when the current queue becomes empty, but rather remains for an exponentially distributed time at a queue. The analysis is based on considering imbedded Markov chains at specific instants. A system of equations for the queue-length distributions at these instant is given and solved for. Besides, we study to which extent the queues in the polling model are independent and identify parameter settings for which this is indeed the case. These results may be used to approximate performance measures for complex multi-queue models by analyzing a simple single-queue model
Optimization of polling systems with Bernoulli schedules
Optimization;Polling Systems;Queueing Theory;operations research
Probabilistic model for fracture mechanics service life analysis
The service longevity of complex propulsion systems, such as the Space Shuttle Main Engine (SSME), can be at risk from several competing failure modes. Conventional life assessment practice focuses upon the most severely life-limited feature of a given component, even though there may be other, less severe, potential failure locations. Primary, secondary, tertiary failure modes, as well as their associated probabilities, must also be considered. Futhermore, these probabilities are functions of accumulated service time. Thus a component may not always succumb to the most severe, or even the most probable failure mode. Propulsion system longevity must be assessed by considering simultaneously the actions of, and interactions among, life-limiting influences. These include, but are not limited to, high frequency fatigue (HFF), low cycle fatigue (LCF), and subsequent crack propagation, thermal and acoustic loadings, and the influence of less-than-ideal nondestructive evaluation (NDE). An outline is provided for a probabilistic model for service life analysis, and the progress towards its implementation is reported
Exploring a new Markov chain model for multiqueue systems.
Traditionally, Markov models have been used to study multiserver systems using exhaustive or gated service.
In addition, exhaustive-limited and gate-limited models have also been used in communication systems to reduce overall latency. Recently the authors have proposed a new Markov Chain approach to study gate-limited service. Multiqueue systems such as polling systems, in which the server serves various queues have also been extensively studied but as a separate branch of queueing theory. This paper proposes to describe multiqueue systems in terms of a new Markov Chain called the Zero-Server Markov Chain (ZSMC). The model is used to derive a formula for the waiting times in an exhaustive polling system. An intuitive result is obtained and this is used to develop an appoximate method which works well over normal operational ranges
Time-Limited and k-Limited Polling Systems: A Matrix Analytic Solution
In this paper, we will develop a tool to analyze polling systems with the
autonomous-server, the time-limited, and the k-limited service discipline. It
is known that these disciplines do not satisfy the well-known branching
property in polling system, therefore, hardly any exact result exists in the
literature for them. Our strategy is to apply an iterative scheme that is based
on relating in closed-form the joint queue-length at the beginning and the end
of a server visit to a queue. These kernel relations are derived using the
theory of absorbing Markov chains. Finally, we will show that our tool works
also in the case of a tandem queueing network with a single server that can
serve one queue at a time
Approximation of discrete-time polling systems via structured Markov chains
We devise an approximation of the marginal queue length distribution in discrete-time polling systems with batch arrivals and fixed packet sizes. The polling server uses the Bernoulli service discipline and Markovian routing. The 1-limited and exhaustive service disciplines are special cases of the Bernoulli service discipline, and traditional cyclic routing is a special case of Markovian routing. The key step of our approximation is the translation of the polling system to a structured Markov chain, while truncating all but one queue. Numerical experiments show that the approximation is very accurate in general. Our study is motivated by networks on chips with multiple masters (e.g., processors) sharing a single slave (e.g., memory)
An Individual-based Probabilistic Model for Fish Stock Simulation
We define an individual-based probabilistic model of a sole (Solea solea)
behaviour. The individual model is given in terms of an Extended Probabilistic
Discrete Timed Automaton (EPDTA), a new formalism that is introduced in the
paper and that is shown to be interpretable as a Markov decision process. A
given EPDTA model can be probabilistically model-checked by giving a suitable
translation into syntax accepted by existing model-checkers. In order to
simulate the dynamics of a given population of soles in different environmental
scenarios, an agent-based simulation environment is defined in which each agent
implements the behaviour of the given EPDTA model. By varying the probabilities
and the characteristic functions embedded in the EPDTA model it is possible to
represent different scenarios and to tune the model itself by comparing the
results of the simulations with real data about the sole stock in the North
Adriatic sea, available from the recent project SoleMon. The simulator is
presented and made available for its adaptation to other species.Comment: In Proceedings AMCA-POP 2010, arXiv:1008.314
- …