We propose a randomized gradient method for the handling of a convex function whose gradient computation is demanding. The method bears a resemblance to the stochastic approximation family. But in contrast to stochastic approximation, the present method builds a model problem.The approach requires that estimates of function values and gradients be provided at the iterates. We present a variance reduction Monte Carlo simulation procedure to provide such estimates in the case of certain probabilistic functions.

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Original scientific paper In the present paper the constant parameters of the (car following) Intelligent Driver Model are calibrated so as to obtain correct flow capacities of a signalized intersection. The calibration is based on measured time-headway parameters of the consecutive vehicles. The measurement data were taken from the work published by Dey et al. The parameters were calibrated partly by numeric calculations and partly by computer simulation, which was developed by the authors of this paper. The simulated environment was a single lane road terminated by a signalized intersection with a queue of stopped cars. As the result of the calibration, the model produced the measured saturated time-headway constant in the stationary flow phase and gave a good approximation of the consecutive time-headways in the initial transient phase. It was found that the calibrated constants of the Intelligent Driver Model considerably differ from the values proposed for modelling traffic on motorways: in a signalized intersection situation higher maximal acceleration and lower safe time gap parameters should be applied. More precisely, the differences are about 30 % in each case. Keywords: Intelligent Driver Model; signalized intersection; traffic simulation Parametri modela inteligentnog vozača u signaliziranim križanjimaIzvorni znanstveni članka U ovom su radu kalibrirani nepromjenjivi parametri Modela inteligentnog vozača (auta koji slijedi) kako bi se dobila točna propusna moć signaliziranog križanja. Kalibriranje se zasniva na izmjerenim parametrima intervala između dvaju vozila u nizu. Podaci mjerenja su uzeti iz rada u izdanju Dey et al. Parametri su kalibrirani djelomično numeričkim kalkulacijama i djelomično računalnom simulacijom, koju su razvili autori ovoga rada. Simulirano okruženje bila je traka koja je završavala signaliziranim križanjem s redom zaustavljenih vozila. Kao rezultat kalibriranja, model je davao izmjerenu konstantu zasićenja između dvaju vozila u nizu u fazi saobraćaja u mirovanju te je dao dobru aproksimaciju vremena između dvaju vozila u nizu u početnoj prolaznoj fazi. Ustanovljeno je da se kalibrirane konstante Modela inteligentnog vozača znatno razlikuju od vrijednosti predloženih za modeliranje prometa na autocestama: kad se radi o signaliziranim križanjima trebalo bi primijeniti parametre većeg maksimalnog ubrzanja i manjeg intervala sigurnog slijeda između dvaju vozila. Točnije, postoje razlike od oko 30 % u svakom slučaju. Ključne riječi:Model inteligentnog vozača; signalizirano križanje; simulacija prometa

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The data tree is a very widely used data structure in many application areas. The tree structure provides an efficient storage and data manipulation for different data lists or data sets. The prefix tree is a special tree structure to store ordered lists of data elements. In the prefix tree, the lists with common prefix part share the same path. As the prefix tree can be involved in many data manipulation algorithms, the cost estimation of the tree is an important component in the cost function of the whole data manipulation algorithm. This paper provides a cost analysis related to the tree size for a random input set of object lists. The analysis includes both analytical and simulation methods and the main result presented in this paper is an approximation function based on the gamma-distribution.