Suchergebnisse

Consider the M/G/1 queue, the finite dam M/G/1 with capacity T, and the impatient customer M/G/1 model, where customers become lost customers if their waiting time exceeds τ. In this note we prove that for all three models and each xe(0, r) the distribution of the number of downcrossings of the virtual waiting time process with level x during a busy cycle is identical. This implies the weaker statement that on [0, T) the distribution functions of the steady state distributions of the amount of unprocessed work (virtual waiting time) are proportional. A number of applications is given.

Purpose of the paper: Alexandra was proclaimed in 1912 as the first formal township in South Africa where blacks could obtain ownership. Over the past century, a number of watershed changes in layout and ownership have taken place, most notably the promulgation of the 1913 Land Act that prohibited the proclamation of land for black ownership and a series of expropriations, resulting from apartheid policies that took place from 1950 onwards, culminating in a consolidation in 1985 that led to further expropriations. In 2011, former land owners established land claims. These claims were complicated by the fact that a number of residents had received legal right of ownership.Investigation of the validity of the claims required a comprehensive study of the change of ownership from the original proclamation (1912) to the situation in 2011. Methodology. An analysis of current and historical development and management of Alexandra is provided, supplemented by a visual overview of the changing patterns of ownership and densification. The present status of land claims and their legal implications is summarized and a reliable estimate of the present population of Alexandra is provided.Findings: The total population as determined by this study is more than 60 per cent more than the formal 2011 census estimate, resulting in a density of more than 44 400 persons per hectare. It was also found that Occupiers on one stand can have different kind of rights. However, adequate documentation has been assembled to drive the process of land tenure upgrading.Practical implications: The higher than previously estimated population density has severe implications - physical as well as political - for future planning of this vibrant area. The importance of a reliable estimate of the ownership of property in Alexandra becomes even more apparent when the implications of the Restitution Act are considered.

Consider a sequence of random points placed on the nonnegative integers with i.i.d. geometric (1/2) interpoint spacings yi. Let xi denote the numbers of points placed at integer i. We prove a central limit theorem for the partial sums of the sequence x0y0,x1y1, . . . The problem is connected with a question concerning different bootstrap procedures.