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

A spectral theory approach for extreme value analysis in a tandem of fluid queues

We consider a model to evaluate performance of streaming media over an unreliable network. Our model consists of a tandem of two fluid queues. The first fluid queue is a Markov modulated fluid queue that models the network congestion, and the second queue represents the play-out buffer

Stationary solution to the fluid queue fed by an M/M/1 queue

We consider an infinite-capacity buffer receiving fluid at a rate depending on the state of an M/M/1 queue. We obtain a new analytic expression for the joint stationary distribution of the buffer level and the state of the M/M/1 queue. This expression is obtained by the use of generating functions which are explicitly inverted. The case of a finite capacity fluid queue is also considered.</jats:p

Performability analysis for degradable computer systems

AbstractDegradable performance of fault-tolerant computer systems has given rise to considerable interest in mathematical models for combined evaluation of performance and reliability. Most of these models are based upon Markov processes. Several methods have been proposed for the computation of the probability distribution of performability upon an interval of time [0, t]. In this paper, we present a new algorithm based on the uniformization technique to compute this distribution for block degradable models. The main advantage of this method is its low polynomial computational complexity and its numerical stability, since it only deals with a nonincreasing sequence of positive numbers bounded by 1. This important property allows us to determine new truncation steps which improve the execution time of the algorithm. We apply this method to a degradable computer system

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