The influenza pandemic of 1918-19 was the most devastating pandemic of the 20th century. It killed an estimated 50-100 million people worldwide. In late 1918, when the severity of the disease was apparent, the Australian Quarantine Service was established. Vessels returning from overseas and inter-state were intercepted, and people were examined for signs of illness and quarantined. Some of these vessels carried the infection throughout their voyage and cases were prevalent by the time the ship arrived at a Quarantine Station. We study four outbreaks that took place on board the Medic, Boonah, Devon, and Manuka in late 1918. These ships had returned from overseas and some of them were carrying troops that served in the First World War. By analysing these outbreaks under a stochastic Bayesian hierarchical modeling framework, we estimate the transmission rates among crew and passengers aboard these ships. Furthermore, we ask whether the removal of infectious, convalescent, and healthy individuals after arriving at a Quarantine Station in Australia was an effective public health response.

A stochastic model is formulated and analyzed to study the advancements of messages under greedy routing in a sensor network with a power-saving scheme. The aim of this model is give a better understanding of stochastic dependencies arising in the system and to offer a method of computing the advancement of message under greedy routing. We observe that the majority of the stochastic dependence from a routing path is captured by including only the previous forwarding node location. We examine a simple uncoordinated power-saving scheme with a new understanding of its effects on local node density. We propose a method for sensibly limiting the number of transmission reattempts before concluding there is no node in the forwarding region. All expressions involving multidimensional integrals are derived and evaluated readily with quasi-Monte Carlo integration methods. An importance sampling function is derived to speed up the quasi-Monte Carlo methods. The integral expressions are compared to simulations and give very agreeable results.

We observe that an effect of ldquodisk resource sharingrdquo of multi-copy movie traffic has great impact on the blocking performance of a video-on-demand system. This observation leads us to establish a conjecture on how to balance the movie traffic load among ldquocombinationrdquo groups of disks to maximize the level of disk resource sharing. For a given file replication instance, the conjecture predicts in general an effective lower bound on the blocking performance of the system. It motivates the design of a numerical index that measures quantitatively the goodness of disk resource sharing on allocation of multi-copy movie files. It also motivates the design of a greedy file allocation method that decides a good quality heuristic solution for each feasible file replication instance. We further develop analytical formulas to obtain approximate results for the bound fast and accurately. These techniques can be utilized by an optimization program to find near-optimal file assignment solutions for the system computationally efficiently.

We present a genetic algorithm for tackling a file assignment problem for a large-scale video-on-demand system. The file assignment problem is to find the optimal replication and allocation of movie files to disks so that the request blocking probability is minimized subject to capacity constraints. We adopt a divide-and-conquer strategy, where the entire solution space of file assignments is divided into subspaces. Each subspace is an exclusive set of solutions sharing a common file replication instance. This allows us to utilize a greedy file allocation method for finding a good-quality heuristic solution within each subspace. We further design two performance indices to measure the quality of the heuristic solution on 1.) its assignment of multicopy movies and 2.) its assignment of single-copy movies. We demonstrate that these techniques, together with ad hoc population handling methods, enable genetic algorithms to operate in a significantly reduced search space and achieve good-quality file assignments in a computationally efficient way.

The designers of a large scale video-on-demand system face an optimization problem of deciding how to assign movies to multiple disks (servers) such that the request blocking probability is minimized subject to capacity constraints. To solve this problem, it is essential to develop scalable and accurate analytical means to evaluate the blocking performance of the system for a given file assignment. The performance analysis is made more complicated by the fact that the request blocking probability depends also on how disks are selected to serve user requests for multicopy movies. In this paper, we analyze several efficient resource selection schemes. Numerical results demonstrate that our analysis is scalable and sufficiently accurate to support the task of file assignment optimization in such a system.

Little and Venkatesh conjectured that, for an interactive VoD system with a single random trial resource selection scheme, the blocking probability of a user's request is minimized when the overall movie traffic load is spread uniformly on each disk in the system. In this paper, we generalize this conjecture to the situation where there can be repeated random trials or where a least busy fit resource selection scheme is used. We support our conjecture with a simulation of a realistic system, and propose a metric following the idea of our conjecture to assess the goodness of movie assignment in the system.

We consider a video-on-demand system in which multiple copies of each movie file are kept in separate disks. Various schemes for file allocation and retrieval are considered and compared. We have introduced a certain easy-to-implement scheme that requires 15% more storage than another certain harder-to-implement scheme.

Presents an efficient algorithm to compute an optimal service-separated virtual path connection network (VPCN) consisting of several logical subnetworks, one for each service class. The algorithm implements a bandwidth market where each VPC computes the prices at which it is willing to buy and sell bandwidth. These prices determine the allocation of bandwidth to virtual path connections (VPCs) in a series of transactions. After each transaction, the VPCN is adjusted, bandwidth supplies and prices are adjusted, and the algorithm computes the next bandwidth transaction. We apply our algorithm and another method to design an optimal service-separated VPCN for a small network consisting of 10 nodes and two service classes. Both methods yield near-identical revenues, though our algorithm requires a fraction of the computational resources required by the other method. We next apply our algorithm to compute optimal service-separated VPCNs for two larger networks of 20 and 55 nodes, each with six service classes.

A convolution algorithm, suitable for nonconvex regions, is derived and used to efficiently evaluate exact normalising constants for systems with product form equilibrium distributions and large state spaces. It is observed that this algorithm is much more efficient for certain systems than the standard convolution algorithms.>

Embedded discrete time processes are used to study a class of SPNs (stochastic Petri nets) which have a closed-form equilibrium distribution. These SPNs have probabilistic output bags, colored tokens, and alternating periods of arbitrarily distributing enabling and firing times (periods of time between transitions becoming enabled and absorption of tokens and between transitions absorbing tokens and depositing them in output places, respectively). In addition, an aggregation procedure is proposed which, in certain nets, not only reduces a complex SPN to a much simpler skeleton SPN but also obtains results for the skeleton SPN with are exact marginal distributions for the original SPN.>