TY - JOUR
T1 - Optimizing the throughput of particulate streams subject to blocking
AU - Page, G.
AU - Resing, J.
AU - Viot, P.
AU - Talbot, J.
PY - 2018/7
Y1 - 2018/7
N2 - 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 λ and exit at a rate μ. If N particles are present at the same time in the channel, the system becomes blocked and no more particles can enter. After an exponentially distributed time with rate the blockage is cleared and the system resets to an empty channel. 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 λ if . 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.
AB - 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 λ and exit at a rate μ. If N particles are present at the same time in the channel, the system becomes blocked and no more particles can enter. After an exponentially distributed time with rate the blockage is cleared and the system resets to an empty channel. 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 λ if . 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.
KW - exact results
KW - stochastic processes
KW - traffic models
UR - http://www.scopus.com/inward/record.url?scp=85049679827&partnerID=8YFLogxK
U2 - 10.1088/1742-5468/aac90e
DO - 10.1088/1742-5468/aac90e
M3 - Article
AN - SCOPUS:85049679827
VL - 2018
JO - Journal of Statistical Mechanics : Theory and Experiment
JF - Journal of Statistical Mechanics : Theory and Experiment
SN - 1742-5468
IS - 6
M1 - 063213
ER -