Optimizing the Throughput of Particulate Streams Subject to Blocking

Filtration, flow in narrow channels and traffic flow are examples of processes subject to blocking when the channel conveying the particles becomes too crowded. If the blockage is temporary, which means that after a finite time the channel is flushed and reopened, one expects to observe a maximum throughput for a finite intensity of entering particles. We investigate this phenomenon by introducing a queueing theory inspired, circular Markov model. Particles enter a channel with intensity $\lambda$ and exit at a rate $\mu$. If $N$ particles are present at the same time in the channel, the system becomes blocked and no more particles can enter until the blockage is cleared after an exponentially distributed time with rate $\mu^*$. We obtain an exact expression for the steady state throughput (including the exiting blocked particles) for all values of $N$. For $N=2$ we show that the throughput assumes a maximum value for finite $\lambda$ if $\mu^*/\mu < 1/4$. The time-dependent throughput either monotonically approaches the steady state value, or reaches a maximum value at finite time. We demonstrate that, in the steady state, this model can be mapped to a previously introduced non-Markovian model with fixed transit and blockage times. We also examine an irreversible, non-Markovian blockage process with constant transit time exposed to an entering flux of fixed intensity for a finite time and we show that the first and second moments of the number of exiting particles are maximized for a finite intensity.Comment: 20 pages, 13 figure

Autonomous Discovery and Maintenance of Mobile Frees-Space-Optical Links

Free-Space-Optical (FSO) communication has the potential to play a significant role in future generation wireless networks. It is advantageous in terms of improved spectrum utilization, higher data transfer rate, and lower probability of interception from unwanted sources. FSO communication can provide optical-level wireless communication speeds and can also help solve the wireless capacity problem experienced by the traditional RF-based technologies. Despite these advantages, communications using FSO transceivers require establishment and maintenance of line-of-sight (LOS). We consider autonomous mobile nodes (Unmanned Ground Vehicles or Unmanned Aerial Vehicles), each with one FSO transceiver mounted on a movable head capable of scanning in the horizontal and vertical planes. We propose novel schemes that deal with the problems of automatic discovery, establishment, and maintenance of LOS alignment between these nodes with mechanical steering of the directional FSO transceivers in 2-D and 3-D scenarios. We perform extensive simulations to show the effectiveness of the proposed methods for both neighbor discovery and LOS maintenance. We also present a prototype implementation of such mobile nodes with FSO transceivers. The potency of the neighbor discovery and LOS alignment protocols is evaluated by analyzing the results obtained from both simulations and experiments conducted using the prototype. The results show that, by using such mechanically steerable directional transceivers and the proposed methods, it is possible to establish optical wireless links within practical discovery times and maintain the links in a mobile setting with minimal disruption