6,508 research outputs found
A tool for model-checking Markov chains
Markov chains are widely used in the context of the performance and reliability modeling of various systems. Model checking of such chains with respect to a given (branching) temporal logic formula has been proposed for both discrete [34, 10] and continuous time settings [7, 12]. In this paper, we describe a prototype model checker for discrete and continuous-time Markov chains, the Erlangen-Twente Markov Chain Checker EĂMC2, where properties are expressed in appropriate extensions of CTL. We illustrate the general benefits of this approach and discuss the structure of the tool. Furthermore, we report on successful applications of the tool to some examples, highlighting lessons learned during the development and application of EĂMC2
Analysis of the transient delay in a discrete-time buffer with batch arrivals
We perform a discrete-time analysis of the delay of customers in a FIFO buffer with batch arrivals. The numbers of arrivals per slot are independent and identically distributed variables. Since the arrivals come in batches, the delays of the subsequent customers do not constitute a Markov chain, which complicates the analysis. By using generating functions and the supplementary variable technique, moments of the delay of the k-th customer are calculated
Spectral gap of the Erlang A model in the Halfin-Whitt regime
We consider a hybrid diffusion process that is a combination of two
Ornstein-Uhlenbeck processes with different restraining forces. This process
serves as the heavy-traffic approximation to the Markovian many-server queue
with abandonments in the critical Halfin-Whitt regime. We obtain an expression
for the Laplace transform of the time-dependent probability distribution, from
which the spectral gap is explicitly characterized. The spectral gap gives the
exponential rate of convergence to equilibrium. We further give various
asymptotic results for the spectral gap, in the limits of small and large
abandonment effects. It turns out that convergence to equilibrium becomes
extremely slow for overloaded systems with small abandonment effects.Comment: 48 page
- âŠ