Browsing by Author "Burger, A. P."

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    The effects of incorporating vehicle acceleration explicitly into a microscopic traffic simulation model
    (Southern African Institute for Industrial Engineering, 2013-08) Burger, A. P.; Einhorn, M. D.; Van Vuuren, J. H.
    Explicitly incorporating individual vehicle acceleration into a traffic simulation model is not a trivial task, and typically results in a considerable increase in model complexity. For this reason, alternative implicit techniques have been introduced in the literature to compensate for the delay times associated with acceleration. In this paper, the claim is investigated that these implicit modelling techniques adequately account for the time delays due to vehicle acceleration; the modelling techniques are implemented in a simulated environment, and compared with models in which vehicle acceleration has been incorporated explicitly for a number of traffic network topologies and traffic densities. It is found that considerable discrepancies may result between the two approaches.
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    The evolutionary spatial prisoner's dilemma on a cycle
    (Operations Research Society of South Africa (ORSSA), 2013) Burger, A. P.; Van der Merwe, M.; Van Vuuren, J. H.
    In this paper we consider the Evolutionary Spatial Prisoner's Dilemma (ESPD) in which players are modelled by the vertices of a cycle representing a spatial or organisational structure amongst the players. During each round of the ESPD every pair of adjacent players in the cycle play a classical prisoner's dilemma against each other, and they update their strategies from one round to the next based on the perceived success achieved by the strategies of neighbouring players during the previous round. In this way players are able to adapt and learn from each other's strategies as the game progresses without being able to rationalise good strategies. We characterise all steady states of the game as well as the structures of those initial states that lead to the emergence of persistent substates of cooperation over time. We finally determine analytically (i.e. without using simulation) the probability that the game's states will evolve from a randomly generated initial state towards a steady state which accommodates some form of persistent cooperation. More specifically, we show that there exists a range of game parameter values for which the likelihood of the emergence of persistent cooperation increases to almost certainty as the length of the cycle increases.
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    On the(d)–chromatic number of a complete balanced multipartite graph
    (Operations Research Society of South Africa, 2007) Burger, A. P.; Nieuwoudt, I.; Van Vuuren, J. H.
    In this paper we solve (approximately) the problem of finding the minimum number of colours with which the vertices of a complete, balanced, multipartite graph G may be coloured such that the maximum degrees of all colour class induced subgraphs are at most some specified integer d 2 N. The minimum number of colours in such a colouring is referred to as the (d)–chromatic number of G. The problem of finding the (d)–chromatic number of a complete, balanced, multipartite graph has its roots in an open graph theoretic characterisation problem and has applications conforming to the generic scenario where users of a system are in conflict if they require access to some shared resource. These conflicts are represented by edges in a so–called resource access graph, where vertices represent the users. An efficient resource access schedule is an assignment of the users to a minimum number of groups (modelled by means of colour classes) where some threshold d of conflict may be tolerated in each group. If different colours are associated with different time periods in the schedule, then the minimum number of groupings in an optimal resource access schedule for the above set of users is given by the (d)–chromatic number of the resource access graph. A complete balanced multipartite resource access graph represents a situation of maximum conflict between members of different user groups of the system, but where no conflict occurs between members of the same user group (perhaps due to an allocation of diverse duties to the group members).
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    Skedulering van gade-vermydende gemengde dubbels rondomtalie-tennistoernooie
    (AOSIS, 2009-03) Burger, A. P.; Van Vuuren, J. H.
    By die opstel van ’n gade-vermydende gemengde-dubbels rondomtalie-tennistoernooi van orde n word daar gesoek na ’n spelskedule waarvolgens n getroude pare op so ’n manier in gemengde-dubbels tennispotte kragte meet dat geen speler saam met sy/haar eggenoot in ’n span afgepaar word nie, geen speler teen sy/haar eggenoot te staan kom nie, elke speler presies een keer teen elke ander speler van dieselfde geslag te staan kom, elke speler presies een keer saam met elke speler van die teenoorgestelde geslag (behalwe sy/haar gade) in ’n span afgepaar word, en elke speler presies een keer teen elke speler van die teenoorgestelde geslag (behalwe sy/haar gade) te staan kom. Hierdie potte moet boonop in die kleinste moontlike aantal rondtes ingedeel word sodat geen speler in meer as een pot per rondte meeding nie, en sodat die aantal potte per rondte dieselfde en ’n maksimum is. Spelskedules vir sulke toernooie word vir n ≤ 20 opgestel en ter wille van naslaandoeleindes op ’n gebruikersvriendelike manier gedokumenteer.