Stability and Control of Piecewise-Deterministic Queueing Systems
Jin Li, Saurabh Amin

Citation
Jin Li, Saurabh Amin. "Stability and Control of Piecewise-Deterministic Queueing Systems". submitted to IEEE TAC, 2016.

Abstract
Unreliable link capacities cause a significant amount of delay in transportation networks. In this paper, we propose a novel approach to studying the traffic queues due to capacity-reducing events under a class of control policies. First, we propose a Piecewise-Deterministic Queueing (PDQ) model in which the link saturation rates switch between a finite set of values (modes) according to a Markov chain, which captures the occurrence and clearance of capacity-reducing events. Second, we derive results on the stability of PDQ networks, i.e. when the joint distribution of the link queue sizes converges to a unique invariant probability measure. On one hand, a necessary condition for stability is that the average inflow to each link is less than the link's effective capacity. On the other hand, a sufficient condition is that a set of bilinear matrix inequalities involving model parameters and the control policy has a feasible solution. Third, we provide an analytical characterization of the steady-state distribution of bimodal PDQ systems, which enables us to obtain the optimal static/mode-dependent routing policy for bimodal PDQ networks by solving a convex min-cost problem.

Electronic downloads

Internal. This publication has been marked by the author for FORCES-only distribution, so electronic downloads are not available without logging in.

Citation formats

• HTML

  Jin Li, Saurabh Amin. <a
  href="http://www.cps-forces.org/pubs/145.html"
  >Stability and Control of Piecewise-Deterministic
  Queueing Systems</a>, <i>submitted to IEEE
  TAC</i>,  2016.

• Plain text

  Jin Li, Saurabh Amin. "Stability and Control of
  Piecewise-Deterministic Queueing Systems".
  <i>submitted to IEEE TAC</i>,  2016.

• BibTeX

  @article{LiAmin16_StabilityControlOfPiecewiseDeterministicQueueingSystems,
      author = {Jin Li and Saurabh Amin},
      title = {Stability and Control of Piecewise-Deterministic
                Queueing Systems},
      journal = {submitted to IEEE TAC},
      year = {2016},
      abstract = {Unreliable link capacities cause a significant
                amount of delay in transportation networks. In
                this paper, we propose a novel approach to
                studying the traffic queues due to
                capacity-reducing events under a class of control
                policies. First, we propose a
                Piecewise-Deterministic Queueing (PDQ) model in
                which the link saturation rates switch between a
                finite set of values (modes) according to a Markov
                chain, which captures the occurrence and clearance
                of capacity-reducing events. Second, we derive
                results on the stability of PDQ networks, i.e.
                when the joint distribution of the link queue
                sizes converges to a unique invariant probability
                measure. On one hand, a necessary condition for
                stability is that the average inflow to each link
                is less than the link's effective capacity. On the
                other hand, a sufficient condition is that a set
                of bilinear matrix inequalities involving model
                parameters and the control policy has a feasible
                solution. Third, we provide an analytical
                characterization of the steady-state distribution
                of bimodal PDQ systems, which enables us to obtain
                the optimal static/mode-dependent routing policy
                for bimodal PDQ networks by solving a convex
                min-cost problem.},
      URL = {http://cps-forces.org/pubs/145.html}
  }
  

Posted by Saurabh Amin on 16 Apr 2016.
Groups: forces
For additional information, see the Publications FAQ or contact webmaster at cps-forces org.