A Lindley-type equation arising from a carousel problem

In this paper we consider a system with two carousels operated by one picker. The items to be picked are randomly located on the carousels and the pick times follow a phase-type distribution. The picker alternates between the two carousels, picking one item at a time. Important performance characteristics are the waiting time of the picker and the throughput of the two carousels. The waiting time of the picker satisfies an equation very similar to Lindley's equation for the waiting time in the PH/U/1 queue. Although the latter equation has no simple solution, we show that the one for the waiting time of the picker can be solved explicitly. Furthermore, it is well known that the mean waiting time in the PH/U/1 queue depends on to the complete interarrival time distribution, but numerical results show that, for the carousel system, the mean waiting time and throughput are rather insensitive to the pick-time distribution.Comment: 10 pages, 1 figure, 19 reference

Decision systems : the relation between problem specification and mathematical analysis

In this paper it is demonstrated that automated support for decision making of a tactical or strategic nature requires a solver-independent medium for describing decision situations. Such a medium may be specific for one environment, but it is also possible to develop media for certain types of environments. By using such a medium one obtains a decoupling of problem formulation and method of analysis. This makes it possible to use (parts of) the problem formulation as input for different types of models. Such problem formulations may provide mathematical models themselves, although they might also contain some less formal features. The decoupling makes it possible to choose problem formulations which are much closer to the original decision situation than would otherwise be possible with formulations in terms of a preselected solver. The argumentation is illustrated by treating a language for specifying goods flow problems in some detail. This language is based on timed coloured Petri-nets

Decision support for natural resource management; models and evaluation methods

When managing natural resources or agrobusinesses, one always has to deal with autonomous processes. These autonomous processes play a core role in designing model-based decision support systems. This chapter tries to give insight into the question of which types of models might be used in which cases. It does so by formulating a rough categorization of decision problems and providing many examples. Particular attention is given to the role of statistical learning theory, which may be used to replace mathematical modeling by training with example

Swaziland die Geologie en Geografie van Swaziland

In 1943 het die eerste werklike grootskaalse kartering van die gebied 'n aanvang geneem. En van 1949 af, met die koms van die eerste stel lugfoto’s, is hierdie tempo versnel. Die basiese opname van die gebied is dan ook in 1957 voltooi. In die eerste stadiums van kartering is die klassifikasie van die verskillende rotstopes gevolg soos wat dit deur Hall en later Van Eeden gedoen is. Soos die werk gevorder het, is veranderings ingevoer om die klassifikasie aan te pas by plaaslike omstandighede, maar nie almal hiervan het die toets van die tyd deurstaan nie

How robust is a thermal photon interpretation of the ALICE low-p_T data?

We present a rigorous theoretical analysis of the ALICE measurement of low-p_T direct-photon production in central lead-lead collisions at the LHC with a centre-of-mass energy of \sqrt{s_{NN}}=2.76 TeV. Using NLO QCD, we compute the relative contributions to prompt-photon production from different initial and final states and the theoretical uncertainties coming from independent variations of the renormalisation and factorisation scales, the nuclear parton densities and the fragmentation functions. Based on different fits to the unsubtracted and prompt-photon subtracted ALICE data, we consistently find T = 304 \pm 58 MeV and 309 \pm 64 MeV for the effective temperature of the quark-gluon plasma (or hot medium) at p_T \in [0.8;2.2] GeV and p_T \in [1.5;3.5] GeV as well as a power-law (p_T^{-4}) behavior for p_T > 4 GeV as predicted by QCD hard scattering.Comment: 18 pages, 7 figures, 1 tabl

Markov programming by successive approximations with respect to weighted supremum norms

Markovian decision processes are considered in the situation of discrete time. countable state space. and general decision space. By introducing a Banach space with a weighted supremum norm, conditions are derived, which guarantee convergence of successive approximations to the value function. These conditions are weaker then those required by the usual supnorm approach. Several properties of the successive approximations are derived