10 research outputs found
Bounding the Equilibrium Distribution of Markov Population Models
Arguing about the equilibrium distribution of continuous-time Markov chains
can be vital for showing properties about the underlying systems. For example
in biological systems, bistability of a chemical reaction network can hint at
its function as a biological switch. Unfortunately, the state space of these
systems is infinite in most cases, preventing the use of traditional steady
state solution techniques. In this paper we develop a new approach to tackle
this problem by first retrieving geometric bounds enclosing a major part of the
steady state probability mass, followed by a more detailed analysis revealing
state-wise bounds.Comment: 4 page
Simon-Ando decomposability and fitness landscapes
In this paper, we investigate fitness landscapes (under point mutation and recombination) from the standpoint of whether the induced evolutionary dynamics have a “fast-slow” time scale associated with the differences in relaxation time between local quasi-equilibria and the global equilibrium. This dynamical hevavior has been formally described in the econometrics literature in terms of the spectral properties of the appropriate operator matrices by Simon and Ando (Econometrica 29 (1961) 111), and we use the relations they derive to ask which fitness functions and mutation/recombination operators satisfy these properties. It turns out that quite a wide range of landscapes satisfy the condition (at least trivially) under point mutation given a sufficiently low mutation rate, while the property appears to be difficult to satisfy under genetic recombination. In spite of the fact that Simon-Ando decomposability can be realized over fairly wide range of parameters, it imposes a number of restriction on which landscape partitionings are possible. For these reasons, the Simon-Ando formalism does not appear to be applicable to other forms of decomposition and aggregation of variables that are important in evolutionary systems
Model Checking CSL for Markov Population Models
Markov population models (MPMs) are a widely used modelling formalism in the
area of computational biology and related areas. The semantics of a MPM is an
infinite-state continuous-time Markov chain. In this paper, we use the
established continuous stochastic logic (CSL) to express properties of Markov
population models. This allows us to express important measures of biological
systems, such as probabilistic reachability, survivability, oscillations,
switching times between attractor regions, and various others. Because of the
infinite state space, available analysis techniques only apply to a very
restricted subset of CSL properties. We present a full algorithm for model
checking CSL for MPMs, and provide experimental evidence showing that our
method is effective.Comment: In Proceedings QAPL 2014, arXiv:1406.156
Asymptotic Expansions for Stationary Distributions of Perturbed Semi-Markov Processes
New algorithms for computing of asymptotic expansions for stationary
distributions of nonlinearly perturbed semi-Markov processes are presented. The
algorithms are based on special techniques of sequential phase space reduction,
which can be applied to processes with asymptotically coupled and uncoupled
finite phase spaces.Comment: 83 page
Comparing Markov Chains: Aggregation and Precedence Relations Applied to Sets of States, with Applications to Assemble-to-Order Systems
International audienceSolving Markov chains is, in general, difficult if the state space of the chain is very large (or infinite) and lacking a simple repeating structure. One alternative to solving such chains is to construct models that are simple to analyze and provide bounds for a reward function of interest. We present a new bounding method for Markov chains inspired by Markov reward theory: Our method constructs bounds by redirecting selected sets of transitions, facilitating an intuitive interpretation of the modifications of the original system. We show that our method is compatible with strong aggregation of Markov chains; thus we can obtain bounds for an initial chain by analyzing a much smaller chain. We illustrate our method by using it to prove monotonicity results and bounds for assemble-to-order systems
On stock rationing policies for continuous review inventory systems
Cataloged from PDF version of article.Rationing is an inventory policy that allows prioritization of different demand
classes. In this thesis, we analyze the stock rationing policies for continuous
review systems. We clarify some of the ambiguities present in the current
literature. Then, we propose a new method for the exact analysis of lot-for-lot
inventory systems with backorders under rationing policy. We show that if
such an inventory system is sampled at multiples of supply leadtime, the state
of the system evolves according to a Markov chain. We provide a recursive
procedure to generate the transition probabilities of the embedded Markov
chain. It is possible to obtain the steady-state probabilities of interest with
desired accuracy by considering a truncated version of the chain. Finally, we
propose a dynamic rationing policy, which makes use of the information on
the status of the outstanding replenishment orders. We conduct a simulation
study to evaluate the performance of the proposed policy.Bulut, ÖnderM.S