Generalized Markov branching processes

A generalized Markov Brnching Process (GMBP) is a Markov branching model where the infinitesimal branching rates are modified with an interaction index. It is proved that there always exists only one GMBP. An associated differential-integral equation is derived. The extinction probalility and the mean and conditional mean extinction times are obtained. Ergodicity and stability of GMBP with resurrection are also considered. Easy checking criteria are established for ordinary and strong ergodicty. The equilibrium distribution is given in an elegant closed form. The probability meaning of our results is clear and thus explained.

Uniqueness criteria for continuous-time Markov chains with general transition structures

We derive necessary and sufficient conditions for the existence of bounded or summable solutions to systems of linear equations associated with Markov chains. This substantially extends a famous result of G. E. H. Reuter, which provides a convenient means of checking various uniqueness criteria for birth-death processes. Our result allows chains with much more general transition structures to be accommodated. One application is to give a new proof of an important result of M. F. Chen concerning upwardly skip-free processes. We then use our generalization of Reuter's lemma to prove new results for downwardly skip-free chains, such as the Markov branching process and several of its many generalizations. This permits us to establish uniqueness criteria for several models, including the general birth, death, and catastrophe process, extended branching processes, and asymptotic birth-death processes, the latter being neither upwardly skip-free nor downwardly skip-free.

General Harris regularity criterion for non-linear Markov branching processes

We extend the Harris regularity condition for ordinary Markov branching process to a more general case of non-linear Markov branching process. A regularity criterion which is very easy to check is obtained. In particular, we prove that a super-linear Markov branching process is regular if and only if the per capita offspring mean is less than or equal to I while a sub-linear Markov branching process is regular if the per capita offspring mean is finite. The Harris regularity condition then becomes a special case of our criterion.

Probabilistic approach in weighted Markov branching processes

This note provides a new probabilistic approach in discussing the weighted Markov branching process (WMBP) which is a natural generalisation of the ordinary Markov branching process. Using this approach, some important characteristics regarding the hitting times of such processes can be easily obtained. In particular, the closed forms for the mean extinction time and conditional mean extinction time are presented. The explosion behaviour of the process is investigated and the mean explosion time is derived. The mean global holding time and the mean total survival time are also obtained. The close link between these newly developed processes and the well-known compound Poisson processes is investigated. It is revealed that any weighted Markov branching process (WMBP) is a random time change of a compound Poisson process.

A Markov modulated Poisson process model for rainfall increments

The problems encountered when using traditional rectangular pulse hierarchical point processmodels for fine temporal resolution and the growing number of available tip-time records suggest that rainfall increments from tipping-bucket gauges be modelled directly. Poisson processes are used with an arrival rate modulated by a Markov chain in Continuous time. The paper shows how, by using two or three states for this chain, much of the structure of the rainfall intensity distribution and the wet/dry sequences can be represented for time-scales as small as 5 minutes.

Adaptive decision-making in buildingEXODUS

Given the importance of occupant behaviour on evacuation efficiency, a new behavioural feature has been implemented into buildingEXODUS. This feature concerns the response of occupants to exit selection and re-direction. This behaviour is not simply pre-determined by the user as part of the initialisation process, but involves the occupant taking decisions based on their previous experiences and the information available to them. This information concerns the occupants prior knowledge of the enclosure and line-of-sight information concerning queues at neighbouring exits. This new feature is demonstrated and reviewed through several examples.

Adaptive decision-making in response to crowd formations in building EXODUS

Given the importance of occupant behavior on evacuation efficiency, a new behavioral feature has been developed and implemented into buildingEXODUS. This feature concerns the response of occupants to exit selection and re-direction. This behavior is not simply pre-determined by the user as part of the initialization process, but involves the occupant taking decisions based on their previous experiences and the information available to them. This information concerns the occupants prior knowledge of the enclosure and line-of-sight information concerning queues at neighboring exits. This new feature is demonstrated and reviewed through several examples.

Adaptive decision-making in buildingEXODUS in response to exit congestion

Given the importance of occupant behavior on evacuation efficiency, a new behavioral feature has been implemented into building EXODUS. This feature concerns the response of occupants to exit selection and re-direction, given that the occupant is queuing at an external exit. This behavior is not simply pre-determined by the user as part of the initialization process, but involves the occupant taking decisions based on their previous experiences with the enclosure and the information available to them. This information concerns the occupant's prior knowledge of the enclosure and line-of-sight information concerning queues at neighboring exits. This new feature is demonstrated and reviewed through several examples.

Decision models - an analytical framework for the Watertime Project

This paper suggests a possible framework for the encapsulation of the decision making process for the Waterime project. The final outcome maybe a computerised model, but the process advocated is not prescriptive, and involves the production of a "paper model" as mediating representation between the knowledge acquired and any computerised system. This paper model may suffice in terms of the project's goals.

The use of a mathematical multicriteria decision-making model for selecting the fire origin room

Over the last three decades, the fire safety codes have been changing from a prescriptive approach to a performance-based one. Some countries, such as the USA, Sweden, New Zealand, Australia and the UK, are in an advanced stage of development and implementation of the performance-based codes. However, there are some difficulties in this process. Most of them are due to the uncertainties associated with fire design. For instance, one of the questions that need to be answered is how to select the most probable fire origin room (FOR)? On the other hand, to know where the FOR is located is also an important aspect in terms of forensic issues. Given that, to address this question is an important step for the establishment of fire designs (i.e., pre-fire phases) and also for fire investigations (i.e., post-fire phases). This paper proposes a methodology for selecting the FOR through the use of a mathematical multicriteria decision-making model: the analytical hierarchy process (AHP). The proposed method is then applied to a hypothetical study case. The results are presented and discussed in this paper.