We present a design of a complete and practical scheduler for the 3GPP Long Term Evolution (LTE) downlink by integrating recent results on resource allocation, fast computational algorithms, and scheduling. Our scheduler has low computational complexity. We define the computational architecture and describe the exact computations that need to be done at each time step (1 milliseconds). Our computational framework is very general, and can be used to implement a wide variety of scheduling rules. For LTE, we provide quantitative performance results for our scheduler for full buffer, streaming video (with loose delay constraints), and live video (with tight delay constraints). Simulations are performed by selectively abstracting the PHY layer, accurately modeling the MAC layer, and following established network evaluation methods. The numerical results demonstrate that queue-and channel-aware QoS schedulers can and should be used in an LTE downlink to offer QoS to a diverse mix of traffic, including delay-sensitive flows. Through these results and via theoretical analysis, we illustrate the various design tradeoffs that need to be made in the selection of a specific queue-and-channel-aware scheduling policy. Moreover, the numerical results show that in many scenarios strict prioritization across traffic classes is suboptimal.

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Abstract-We consider a wireless downlink shared by a dynamic population of flows. The flows of random size (bits) arrive at the base station at random times, and leave when they have been completely transmitted. The transmission rate supported by the wireless channel of each flow while the flow awaits transmission varies randomly over time and is independent of that of the other flows. The scheduling problem in this context is to select a flow for transmission based on the current system state (e.g., backlogs, wait times, and channel states of the contending flows). It has recently been shown that for such a system, the wellknown (backlog-driven) MaxWeight scheduler is not throughput optimal. That is to say, the MaxWeight scheduler will not stabilize a given system even though it is possible to construct a stabilizing scheduler using the various flow-and channel-related statistics. However, in this paper, we show that the delay-driven MaxWeight scheduler is, nevertheless, throughput optimal for such a system. The delay-driven MaxWeight, like its backlog-driven version, does not require any knowledge of the flow-or channel-related statistics.

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Abstract-We consider a wireless node shared by multiple user flows where the channel capacity available to each user varies randomly with time. A scheduling rule in this context selects which flow to serve based on the current channel state and user queues. This involves a tradeoff between maximizing current service rate (being opportunistic) versus balancing unequal queues (enhancing user-diversity to enable future high capacity opportunities). We propose a throughput-optimal scheduling rule, called the pseudo-Log (p-Log) rule, and show that in the case of two users, it maximizes the asymptotic exponential decay rate of the sum-queue distribution. The proof relies on the radial sum-rate monotonicity (RSM) property satisfied by the p-Log rule, whereby as the queues scale up linearly, the scheduling rule de-emphasizes queue-balancing in favor of greedily maximizing the service rate. It also relies on refined sample path large deviation principle recently introduced by Stolyar to study such non-homogenous schedulers.In a companion paper we demonstrate via further analysis and simulations other virtues of RSM opportunistic schedulers (in particular the Log rule) in terms of minimizing overall mean delay, robustness to uncertainty in the traffic and channel statistics etc. The p-Log rule is a slight modification of the Log rule, for the sake of analytical convenience.

A centralized wireless system is considered that is serving a fixed set of users with time varying channel capacities. An opportunistic scheduling rule in this context selects a user (or users) to serve based on the current channel state and user queues. Unless the user traffic is symmetric and/or the underlying capacity region a polymatroid, little is known concerning how performance optimal schedulers should tradeoff maximizing current service rate (being opportunistic) versus balancing unequal queues (enhancing user-diversity to enable future high service rate opportunities). By contrast with currently proposed opportunistic schedulers, e.g., MaxWeight and Exp Rule, a radial sumrate monotonic (RSM) scheduler de-emphasizes queue-balancing in favor of greedily maximizing the system service rate as the queue-lengths are scaled up linearly. In this paper it is shown that an RSM opportunistic scheduler, p-Log Rule, is not only throughput-optimal, but also maximizes the asymptotic exponential decay rate of the sum-queue distribution for a twoqueue system. The result complements existing optimality results for opportunistic scheduling and point to RSM schedulers as a good design choice given the need for robustness in wireless systems with both heterogeneity and high degree of uncertainty.Index Terms-Large deviations, multiuser opportunistic scheduling, queues sharing time-varying server, scheduling unrelated parallel machines. arXiv:0906.4597v2 [cs.IT]Recall the notion of a GFSP and its refined cost function from Section VI. Let J * * denote the lowest refined cost of a GFSP that, under p-Log rule, raises i∈I b i q i (t) to 1 from the initial state q(0) = 0, i.e.,(15) the following must be true over the interval [0, S 1 ] (similarly [S 2 , S]):(a) b, q(0) < b, q(S 1 ) and the cost per unit increase in weighted-sum-queue over the interval [0, S 1 ] is less than J * * * , i.e.J S1 ( f, g) − J 0 ( f, g) b, q(S 1 ) − q(0) ≤ J * * * . 13(b) b, q(0) < b, q(S 1 ) and the cost per unit increase in sum-queue over the interval [0, S 1 ] is strictly greater than J * * * , i.e.J S1 ( f, g) − J 0 ( f, g) b, q(S 1 ) − q(0) > J * * * .

This paper considers the design of opportunistic packet schedulers for users sharing a time-varying wireless channel from the performance and the robustness points of view. Firstly, for a simplified model falling in the classical Markov decision process framework where arrival and channel statistics are known, we numerically compute and evaluate the characteristics of mean-delay-optimal scheduling policies. The computed policies exhibit radial sum-rate monotonicity (RSM), i.e., when users' queues grow linearly (i.e. scaled up by a constant), the scheduler allocates service in a manner that de-emphasizes the balancing of unequal queues in favor of maximizing current system throughput (being opportunistic). This is in sharp contrast to previously proposed policies, e.g., MaxWeight and Exp rule. The latter, however, are throughput-optimal, in that without knowledge of arrival/channel statistics they achieve stability if at all feasible. To meet performance and robustness objectives, secondly, we propose a new class of policies, called the Log rule, that are radial sum-rate monotone and provably throughput optimal. Our simulations for realistic wireless channels confirm the superiority of the Log rule which achieves up to 80% reduction in mean packet delays. However, recent asymptotic analysis showed that Exp rule is optimal in terms of minimizing the asymptotic probability of max-queue overflow. In turn, in a companion paper we have shown that an RSM policy minimizes the asymptotic probability of sum-queue overflow. Finally, we use extensive simulations to explore the various possible design objectives for opportunistic schedulers. When users see heterogenous channels, we find that minimizing the worst asymptotic exponent across users may excessively compromise the overall delay. Our simulations show that only if perfectly tuned to the load will the Exp rule achieve low homogenous tails across users. Otherwise the Log rule achieves a 20-75% reduction in the 99 th percentile for most, if not all, the users. We conclude that for wireless environments, where precise resource allocation is virtually impossible, the Log rule may be more desirable for its robust and graceful degradation to unpredicted changes.

Uplink scheduling/resource allocation under the single-carrier FDMA constraint is investigated, taking into account the queuing dynamics at the transmitters. Under the singlecarrier constraint, the problem of MaxWeight scheduling, as well as that of determining if a given number of packets can be served from all the users, are shown to be NP-complete. Finally, a matching-based scheduling algorithm is presented that requires only a polynomial number of computations per timeslot, and in the case of a system with large bandwidth and user population, provably provides a good delay (small-queue) performance, even under the single-carrier constraint.In summary, the results in first part of the paper support the recent push to remove SCFDMA from the Standards, whereas those in the second part present a way of working around the single-carrier constraint if it remains in the Standards.Index Terms-Uplink scheduling, single-carrier FDMA, Batchand-allocate