No abstract

In this paper, we consider a PH/M/2 queue in which each server has its own queue and arriving customers join the shortest queue. For this model, it has been conjectured that the decay rate of the tail probabilities for the shortest queue length in the steady state is equal to the square of the decay rate for the queue length in the corresponding PH/M/2 model with a single queue. We prove this fact in the sense that the tail probabilities are asymptotically geometric when the difference of the queue sizes and the arrival phase are fixed. Our proof is based on the matrix analytic approach pioneered by Neuts and recent results on the decay rates.Keywords Shortest queue discipline · Decay rate · Stationary distribution · Phase type arrival · Two parallel queues · Exponential server · Matrix analytic approach · Markov additive process · Quasi-birth and death process AMS subject classifications: 60K25 . 60K20 . 60F10 . 90B22

A high-speed train entering a tunnel generates a compression wave. When the compression wave reaches the exit portal of the tunnel, a micro-pressure wave radiates outward. The magnitude of the micro-pressure wave is approximately proportional to the pressure gradient of the compression wave arriving at the exit portal. As the micro-pressure wave can cause environmental problems, tunnel entrance hoods have been installed at many portals of long slab track tunnels on the Japanese high-speed railway, the Shinkansen to reduce the magnitude of the micro-pressure wave. In this study, field measurements were taken in a Shinkansen long slab track tunnel with a hood at its entrance. The compression wave distorts during its propagation through a long slab track tunnel. The dependence of the propagation characteristics on the initial compression waveform was clarified on the basis of field measurements on different trains and hood window configurations. It was shown that compression waves with a waveform of the pressure gradient that has shallow valleys tend to steepen more easily and that the optimum window pattern of the hood depends on the length of the tunnel. Furthermore, a mathematical model corresponding to the results of the field measurements was proposed to describe the distortion of the compression waves.

Vibration of high-speed trains increases in tunnels caused by aerodynamic force whose mechanism is unknown. To investigate this aerodynamic force, the authors conduct an analysis of the running test data and a numerical simulation. The running test data indicates that the aerodynamic force acts to vibrate the train in the tunnel and it originates from large-scale coherent structures in the space between the tunnel wall and the train. These flow structures develop from the head toward the 6th to 8th cars, and become steady thereafter to the tail of the train set. The computation reveals that the flow becomes unstable under the train. The resulted vortices are spread on the train side by the tunnel wall, and then the unsteady aerodynamic force arises when the vortices pass.