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delay-optimal opportunistic scheduling and approximations: the log rule
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delay-optimal opportunistic scheduling and approximations:
the log rule


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abstract

this project report considers the design of multiuser opportunistic packet schedulers for users sharing a time-varying wireless channel from performance and robustness points of view. for a simplified model falling in the classical markov decision process framework, we numerically compute and characterize mean-delay-optimal scheduling policies. the computed policies exhibit radial sum-rate monotonicity: as users queues grow linearly, the scheduler allocates service in a manner that deemphasizes the balancing of unequal queues in favor of maximizing current system throughput (being opportunistic).
in order to meet performance and robustness objectives, we propose a new class of policies, called the log rule, that are radial sum-rate monotone (rsm) and provably throughput-optimal. in fact, it can also be shown that an rsm policy minimizes the asymptotic probability of sum-queue overflow. when users see heterogeneous channels, we find that emphasizing queue balancing, may excessively compromise the overall delay. finally, we discuss approaches to implement the proposed policies for scheduling and resource allocation in ofdma-based multichannel systems.

existing system

two classes of policies known to be throughput-optimal are maxweight (also known as modied largest weighted work/delay first) exp rule. it is a weak form of performance optimality. thus, it is of interest to study opportunistic policies that are delay-optimal e.g., polices that minimize the overall average delay (per data unit) seen by the users or policies that minimize the probability that either the sum-queue or the largest queue overflows a large buffer. these policies are harder to characterize for servers with time-varying capacity.
the asymptotic probability of max-queue overflow under maxweight scheduler becomes large; the asymptotic probability of max-queue overflow under maxweight approaches the minimum achievable under any other scheduler.

proposed system
we consider a simple model falling in the classical markov decision process framework, where we can numerically compute the optimal scheduling policy. our first contribution is showing through numerical computation that mean-delay optimal policies exhibit radial sum-rate monotonicity (rsm), i.e., when user queues grow linearly (i.e., scaled up by a constant), the scheduler allocates service in a manner that deemphasizes the balancing of unequal queues in favor of maximizing current system throughput (being opportunistic).
our second contribution is to propose a new class of policies, called the log rule, that are radial sum-rate monotone and provably throughput-optimal. these policies are favorable both in terms of reducing mean delay and robustness. the log rule is proposed as a practical solution, but is not provably mean-delay optimal. we also extend the proposed scheduling policies to multichannel systems supporting a large number of users.
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