Comment on "Performability analysis: a new algorithm"

The paper “Performability Analysis: A New Algorithm” describes an algorithm for computing the complementary distribution of the accumulated reward over an interval of time in a homogeneous Markov process. In this comment, we show that in two particular cases, one of which is quite frequent, small modifications of the algorithm may reduce significantly its storage complexity.Postprint (published version

A Markov chain model for changes in users’ assessment of search results

Previous research shows that users tend to change their assessment of search results over time. This is a first study that investigates the factors and reasons for these changes, and describes a stochastic model of user behaviour that may explain these changes. In particular, we hypothesise that most of the changes are local, i.e. between results with similar or close relevance to the query, and thus belong to the same ”coarse” relevance category. According to the theory of coarse beliefs and categorical thinking, humans tend to divide the range of values under consideration into coarse categories, and are thus able to distinguish only between cross-category values but not within them. To test this hypothesis we conducted five experiments with about 120 subjects divided into 3 groups. Each student in every group was asked to rank and assign relevance scores to the same set of search results over two or three rounds, with a period of three to nine weeks between each round. The subjects of the last three-round experiment were then exposed to the differences in their judgements and were asked to explain them. We make use of a Markov chain model to measure change in users’ judgments between the different rounds. The Markov chain demonstrates that the changes converge, and that a majority of the changes are local to a neighbouring relevance category. We found that most of the subjects were satisfied with their changes, and did not perceive them as mistakes but rather as a legitimate phenomenon, since they believe that time has influenced their relevance assessment. Both our quantitative analysis and user comments support the hypothesis of the existence of coarse relevance categories resulting from categorical thinking in the context of user evaluation of search results

STATIONARY ANALYSIS OF TANDEM FLUID QUEUES FED BY HOMOGENEOUS ON-OFF SOURCES

Abstract: We consider a fluid system composed of multiple buffers in series. The first buffer receives fluid from a finite superposition of independent identical on-off sources. The active and silent periods of sources are exponentially distributed. The ith buffer releases fluid in the (i + 1)th buffer. Assuming that the input rate of one source is greater than the service rate of the first buffer, the output process of each buffer can be modeled by an on-off source with the active period distributed as the busy period of an M/M/1 queue. For i ≥ 2, the stationary content distribution of the ith buffer is obtained by the use of generating functions which are explicitly inverted

Second Order Fluid Models with General Boundary Behaviour

For applications of stochastic fluid models, such as those related to wildfire spread and containment, one wants a fast method to compute time dependent probabilities. Erlangization is an approximation method that replaces various distributions at a time t by the corresponding ones at a random time with Erlang distribution having mean t. Here, we develop an efficient version of that algorithm for various first passage time distributions of a fluid flow, exploiting recent results on fluid flows, probabilistic underpinnings, and some special structures. Some connections with a familiar Laplace transform inversion algorithm due to Jagerman are also noted up front

Transient analysis of a fluid queue driven by a birth and death process suggested by a chain sequence

We analyse the transient behaviour of a fluid queue driven by a birth and death process (BDP) whose birth and death rates are suggested by a chain sequence. For the BDP suggested by a chain sequence, the stationary probabilities do not exist and hence the stationary buffer content distribution for fluid queues driven by such BDP does not exist. However, their transient distribution is obtained in a simple closed form by two different approaches: the first is the continued fraction approach and the second is an approach in terms of recurrence relation by an analysis similar to that of Sericola (1998). The probability for the buffer content to be empty at an arbitrary time is also studied. The variations in this performance measure are revealed in the form of graphs. Numerical illustrations are included