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One-dimensional finite range random walk in random medium and invariant measure equation

Julien Brémont (2009)

Annales de l'I.H.P. Probabilités et statistiques

We consider a model of random walks on ℤ with finite range in a stationary and ergodic random environment. We first provide a fine analysis of the geometrical properties of the central left and right Lyapunov eigenvectors of the random matrix naturally associated with the random walk, highlighting the mechanism of the model. This allows us to formulate a criterion for the existence of the absolutely continuous invariant measure for the environments seen from the particle. We then deduce a characterization...

Optimal and Near-Optimal (s,S) Inventory Policies for Levy Demand Processes

Robin O. Roundy, Gennady Samorodnitsky (2010)

RAIRO - Operations Research

A Levy jump process is a continuous-time, real-valued stochastic process which has independent and stationary increments, with no Brownian component. We study some of the fundamental properties of Levy jump processes and develop (s,S) inventory models for them. Of particular interest to us is the gamma-distributed Levy process, in which the demand that occurs in a fixed period of time has a gamma distribution. We study the relevant properties of these processes, and we develop a quadratically convergent...

Optimal control and performance analysis of an M X / M / 1 queue with batches of negative customers

Jesus R. Artalejo, Antonis Economou (2004)

RAIRO - Operations Research - Recherche Opérationnelle

We consider a Markov decision process for an M X / M / 1 queue that is controlled by batches of negative customers. More specifically, we derive conditions that imply threshold-type optimal policies, under either the total discounted cost criterion or the average cost criterion. The performance analysis of the model when it operates under a given threshold-type policy is also studied. We prove a stability condition and a complete stochastic comparison characterization for models operating under different...

Optimal control and performance analysis of an MX/M/1 queue with batches of negative customers

Jesus R. Artalejo, Antonis Economou (2010)

RAIRO - Operations Research

We consider a Markov decision process for an MX/M/1 queue that is controlled by batches of negative customers. More specifically, we derive conditions that imply threshold-type optimal policies, under either the total discounted cost criterion or the average cost criterion. The performance analysis of the model when it operates under a given threshold-type policy is also studied. We prove a stability condition and a complete stochastic comparison characterization for models operating under different...

Optimal control for a BMAP/SM/1 queue with MAP-input of disasters and two operation modes

Olga V. Semenova (2004)

RAIRO - Operations Research - Recherche Opérationnelle

A single-server queueing system with a batch markovian arrival process (BMAP) and MAP-input of disasters causing all customers to leave the system instantaneously is considered. The system has two operation modes, which depend on the current queue length. The embedded and arbitrary time stationary queue length distribution has been derived and the optimal control threshold strategy has been determined.

Optimal control for a BMAP/SM/1 queue with MAP-input of disasters and two operation modes

Olga V. Semenova (2010)

RAIRO - Operations Research

A single-server queueing system with a batch Markovian arrival process (BMAP) and MAP-input of disasters causing all customers to leave the system instantaneously is considered. The system has two operation modes, which depend on the current queue length. The embedded and arbitrary time stationary queue length distribution has been derived and the optimal control threshold strategy has been determined.

Optimal stopping of a 2-vector risk process

Krzysztof Szajowski (2010)

Banach Center Publications

The following problem in risk theory is considered. An insurance company, endowed with an initial capital a > 0, receives insurance premiums and pays out successive claims from two kind of risks. The losses occur according to a marked point process. At any time the company may broaden or narrow down the offer, which entails the change of the parameters of the underlying risk process. These changes concern the rate of income, the intensity of the renewal process and the distribution of claims....

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