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Project Euclid (Hosted at Cornell University Library) (204.217 recursos)
Stochastic Systems
Stochastic Systems
Lakner, Peter; Reed, Josh; Simatos, Florian
We consider the following Markovian dynamic on point processes: at constant rate and with equal probability, either the rightmost atom of the current configuration is removed, or a new atom is added at a random distance from the rightmost atom. Interpreting atoms as limit buy orders, this process was introduced by Lakner et al. [Lakner et al. (2016) High frequency asymptotics for the limit order book. Mark. Microstructure Liq. 2:1650004 [83 pages]] to model a one-sided limit order book.
¶ We consider this model in the regime where the total number of orders converges to a reflected Brownian motion, and complement...
(application/pdf) - 17-mar-2018
Sanders, Jaron; Borst, S. C.; Janssen, A. J. E. M.; Leeuwaarden, J. S. H. van
We consider Markovian many-server systems with admission control operating in a Quality-and-Efficiency-Driven (QED) regime, where the relative utilization approaches unity while the number of servers grows large, providing natural Economies-of-Scale. In order to determine the optimal admission control policy, we adopt a revenue maximization framework, and suppose that the revenue rate attains a maximum when no customers are waiting and no servers are idling. When the revenue function scales properly with the system size, we show that a nondegenerate optimization problem arises in the limit. Detailed analysis demonstrates that the revenue is maximized by nontrivial policies that bar customers from...
(application/pdf) - 17-mar-2018
Mandjes, M.; Patch, B.; Walton, N. S.
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...
(application/pdf) - 17-mar-2018
Biswas, Anup
A Markovian queueing network is considered with d independent customer classes and d server pools in Halfin–Whitt regime. Class i customers has priority for service in pool i for i = 1, …, d, and may access some other pool if the pool has an idle server and all the servers in pool i are busy. We formulate an ergodic control problem where the running cost is given by a non-negative convex function with polynomial growth. We show that the limiting controlled diffusion is modelled by an action space which depends on the state variable. We provide a complete analysis...
(application/pdf) - 17-mar-2018
Bar-Lev, Shaul K.; Boxma, Onno; Mathijsen, Britt; Perry, David
We consider a stochastic model for a blood bank, in which amounts of blood are offered and demanded according to independent compound Poisson processes. Blood is perishable, i.e., blood can only be kept in storage for a limited amount of time. Furthermore, demand for blood is impatient, i.e., a demand for blood may be canceled if it cannot be satisfied soon enough. For a range of perishability functions and demand impatience functions, we derive the steady-state distributions of the amount of blood kept in storage, and of the amount of demand for blood (at any point in time, at most...
(application/pdf) - 17-mar-2018