The M/M/1 queue with mass exodus and mass arrivals when empty

An M/M/1 queue is subject to mass exodus at rate β and mass immigration at rate {αr; r≥ 1} when idle. A general resolvent approach is used to derive occupation probabilities and high-order moments. This powerful technique is not only considerably easier to apply than a standard direct attack on the forward p.g.f. equation, but it also implicitly yields necessary and sufficient conditions for recurrence, positive recurrence and transience.

Investigating the use of elevators for high-rise building evacuation through computer simulation

This paper presents a description of a new agent based elevator sub-model developed as part of the buildingEXODUS software intended for both evacuation and circulation applications. A description of each component of the newly developed model is presented, including the elevator kinematics and associated pedestrian behaviour. The elevator model is then used to investigate a series of full building evacuation scenarios based on a hypothetical 50 floor building with four staircases and a population of 7,840 agents. The analysis explores the relative merits of using up to 32 elevators (arranged in four banks) and various egress strategies to evacuate the entire building population. Findings from the investigation suggest that the most efficient evacuation strategy utilises a combination of elevators and stairs to empty the building and clear the upper half of the building in minimum time. Combined stair elevator evacuation times have been shown to be as much as 50% faster than stair only evacuation times.

Assessment of existing soakaways for reuse

This paper describes a practical approach for the investigation, assessment and design of existing soakaways. This method can be utilised for measuring the performance and capacity of the systems and examining whether the systems are suitable for reuse when information about the design and installation of the systems is not available. The requirements for field observations and the procedure for a soil infiltration test for the installed system are suggested for successful assessment. The soil infiltration rate of the system is estimated from the field test data without requiring information on the design and construction details of the system. The system's working condition is measured by a performance indicator related to the time taken to empty the soakaway. This is then employed to evaluate the potential reuse of the system. The system's drain capacity is determined by the design principles of current practice and the effect of climate change on its drain capacity is considered. Contamination of soils around the systems after long-term use of discharge service and the water present in soakaway chambers are also investigated. A detailed case study for the reuse of four installed soakaways for a new housing development demonstrates how the proposed approach provides a straightforward process for the infiltration performance and drain capacity assessment of the existing systems. The effectiveness and applicability of the proposed approach are further demonstrated from the assessments for a number of installed systems over various sites