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.

Stochastic monotonicity and duality for continuous time Markov chains with general q-Matrix

The key problems in discussing stochastic monotonicity and duality for continuous time Markov chains are to give the criteria for existence and uniqueness and to construct the associated monotone processes in terms of their infinitesimal q -matrices. In their recent paper, Chen and Zhang [6] discussed these problems under the condition that the given q-matrix Q is conservative. The aim of this paper is to generalize their results to a more general case, i.e., the given q-matrix Q is not necessarily conservative. New problems arise 'in removing the conservative assumption. The existence and uniqueness criteria for this general case are given in this paper. Another important problem, the construction of all stochastically monotone Q-processes, is also considered.

Extended model of pedestrian escalator behaviour based on data collected within a Chinese underground station

This paper presents data relating to pedestrian escalator behaviour collected in an underground station in Shanghai, China. While data was not collected under emergency or simulated emergency conditions, it is argued that the data collected under rush-hour conditions - where commuters are under time pressures to get to work on time - may be used to approximate emergency evacuation conditions - where commuters are also under time pressures to exit the building as quickly as possible. Data pertaining to escalator/stair choice, proportion of walkers to riders, walker speeds and side usage are presented. The collected data is used to refine the buildingEXODUS escalator model allowing the agents to select whether to use an escalator or neighbouring parallel stair based on congestion conditiions at the base of the stair/escalator and expected travel times. The new model, together with the collected data, is used to simulate a series of hypothetical evacuation scenarios to demonstrate the impact of escalators on evacuation performance.