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pro vyhledávání: '"van Leeuwaarden, J. S. H."'
Heavy-traffic limit theory deals with queues that operate close to criticality and face severe queueing times. Let $W$ denote the steady-state waiting time in the ${\rm GI}/{\rm G}/1$ queue. Kingman (1961) showed that $W$, when appropriately scaled,
Externí odkaz:
http://arxiv.org/abs/2206.09844
The Quality-and-Efficiency-Driven (QED) regime provides a basis for solving asymptotic dimensioning problems that trade off revenue, costs and service quality. We derive bounds for the optimality gaps that capture the differences between the true opt
Externí odkaz:
http://arxiv.org/abs/1511.01798
Publikováno v:
J.Appl.Probab. 53 4 (2016) 1111-1124
We consider a system of $N$ parallel queues with identical exponential service rates and a single dispatcher where tasks arrive as a Poisson process. When a task arrives, the dispatcher always assigns it to an idle server, if there is any, and to a s
Externí odkaz:
http://arxiv.org/abs/1510.02657
We consider Markovian many-server systems with admission control operating in a 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 optim
Externí odkaz:
http://arxiv.org/abs/1411.2808
We develop many-server asymptotics in the QED regime for models with admission control. The admission control, designed to reduce the incoming traffic in periods of congestion, scales with the size of the system. For a class of Markovian models with
Externí odkaz:
http://arxiv.org/abs/1307.1361
Consider the all-time maximum of a Brownian motion with negative drift. Assume that this process is sampled at certain points in time, where the time between two consecutive points is rendered by an Erlang distribution with mean $1/\omega$. The famil
Externí odkaz:
http://arxiv.org/abs/1303.3773
Wireless networks equipped with the CSMA protocol are subject to collisions due to interference. For a given interference range we investigate the tradeoff between collisions (hidden nodes) and unused capacity (exposed nodes). We show that the sensin
Externí odkaz:
http://arxiv.org/abs/1004.1058
Multi-access networks may exhibit severe unfairness in throughput. Recent studies show that this unfairness is due to local differences in the neighborhood structure: Nodes with less neighbors receive better access. We study the unfairness in saturat
Externí odkaz:
http://arxiv.org/abs/1004.1042
Akademický článek
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Publikováno v:
Annals of Applied Probability 2007, Vol. 17, No. 2, 421-439
Let $X_1,X_2,...$ be independent variables, each having a normal distribution with negative mean $-\beta<0$ and variance 1. We consider the partial sums $S_n=X_1+...+X_n$, with $S_0=0$, and refer to the process $\{S_n:n\geq0\}$ as the Gaussian random
Externí odkaz:
http://arxiv.org/abs/math/0703908