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Scheduling in Communication Networks: Inherent Limitations and Analytical Tools

Sharifnassab, Arsalan | 2019

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  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 52045 (05)
  4. University: Sharif University of Technology
  5. Department: Electrical Engineering
  6. Advisor(s): Golestani, Jamaloddin
  7. Abstract:
  8. Scheduling algorithms are responsible for allocation of various types of resources, interference management, and choosing the times and paths through which messages are to be delivered in a communication network. We consider certain fundamental problems in network scheduling. Any scheduling algorithm, to be practical, must have tractable computational complexity and tolerable delay. In the first part of the thesis, we address the following question: “for a given class of networks, does there exist a scheduling algorithm that performs polynomially many computations (in terms of the network dimensions), while keeping the expected delay of the network polynomially bounded (again in terms of the network dimensions)?”. We develop a categorical criterion as a necessary and sufficient condition for existence of such polynomial schedulers. The criterion ties the possibility of polynomial scheduling to some benchmark problems in the theory of computational complexity. Moreover, we establish that the popular Max-Weight scheduling algorithm is implementable with polynomial complexity and delay, whenever polynomial complexity and delay can be realized by any scheduling policy.
    In the second part of the thesis, we develop an analytical tool using which we establish several results for Max-Weight policy, and which is also applicable in broader classes of dynamical systems. We study the effect of an external disturbance on the state trajectory of a dynamical system, and say that a system has bounded sensitivity if the magnitude of this effect can be bounded by a constant multiple of the integral of the disturbance. We establish a bounded sensitivity property for some practical classes of systems, including the gradient fields of piecewise constant and convex potential functions (with finitely many pieces). Furthermore, we show that the latter class contains the seemingly larger class of non-expansive and finitely piecewise constant hybrid systems, as well as network dynamics under the Max-Weight scheduling policy. We also study systems of unbounded sensitivity and operations that preserve bounded sensitivity. Using the above machinery, we derive fluctuation bounds for the network dynamics under the Max-Weight scheduling policy, on which we then capitalize to establish several results concerning fluid model and state space collapse in networks
  9. Keywords:
  10. Communication Networks ; Scheduling ; Delay ; Computational Complexity ; Algorithm ; Dynamical Systems ; Senstivity to Perturbarions ; Fluid Model ; State Space Collapse

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