A stochastic process on a network with connections to Laplacian systems of equations
We study an open discrete-time queueing network. We assume data is generated at nodes of the network as a discrete-time Bernoulli process. All nodes in the network maintain a queue and relay data, which is to be finally collected by a designated sink. We prove that the resulting multidimensional Mar...
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| Veröffentlicht in: | Advances in applied probability 2022-03, Vol.54 (1), p.254-278 |
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| creator | Bagchi, Amitabha Gillani, Iqra Altaf Vyavahare, Pooja |
| description | We study an open discrete-time queueing network. We assume data is generated at nodes of the network as a discrete-time Bernoulli process. All nodes in the network maintain a queue and relay data, which is to be finally collected by a designated sink. We prove that the resulting multidimensional Markov chain representing the queue size of nodes has two behavior regimes depending on the value of the rate of data generation. In particular, we show that there is a nontrivial critical value of the data rate below which the chain is ergodic and converges to a stationary distribution and above which it is non-ergodic, i.e., the queues at the nodes grow in an unbounded manner. We show that the rate of convergence to stationarity is geometric in the subcritical regime. |
| doi_str_mv | 10.1017/apr.2021.27 |
| format | Article |
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| subjects | Convergence Data collection Distributed processing Ergodic processes Markov analysis Markov chains Nodes Original Article Probability Queuing theory Stochastic models Stochastic processes |
| title | A stochastic process on a network with connections to Laplacian systems of equations |
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