We develop a novel auction-based algorithm to allow users to fairly compete for a wireless fading channel. We use the second-price auction mechanism whereby user bids for the channel, during each time slot, based on the fade state of the channel, and the user that makes the highest bid wins use of the channel by paying the second highest bid. Under the assumption that each user has a limited budget for bidding, we show the existence of a Nash equilibrium strategy, and the Nash equilibrium leads to a unique allocation for certain channel state distribution, such as the exponential distribution and the uniform distribution over [0, 1]. For uniformly distributed channel state, we establish that the aggregate throughput received by the users using the Nash equilibrium strategy is at least 3/4 of what can be obtained using an optimal centralized allocation that does not take fairness into account. We also show that the Nash equilibrium strategy leads to an allocation that is Pareto optimal (i.e., it is impossible to make some users better off without making some other users worse off). Based on the Nash equilibrium strategies of the second-price auction with money constraint, we further propose a centralized opportunistic scheduler that does not suffer the shortcomings associated with the proportional fair scheduler.

We study reducing the feedback overheads for users ’ channel state information required for opportunistic scheduling at a base station. We first consider only best effort traffic, here we propose a contention based scheme known as ‘static splitting ’ to reduce the amount of feedback needed. The idea is to divide users into static groups, with users that belong to a group and have their current channel quality above a threshold contending to send their current feedback. We combine static splitting with maximum quantile scheduling – scheduling a user whose current rate is high relative to its distribution, to obtain thresholds that are independent of users ’ channel capacity distributions. Our simulation results show that the proposed scheme can do better than other schemes. Next we consider supporting a mixture of best effort and real-time traffic. Here we combine combine contention based approach with polling subsets of users to propose a joint polling and opportunistic scheduling (JPOS) scheme that reduces the amount of feedback, while meeting real-time users ’ quality of service guarantees. Under fast fading, we prove a lower bound on the service seen by a real-time user under JPOS and propose a heuristic that exploits opportunism across all users. Index Terms – Feedback, opportunistic scheduling, protocols, quality of service. Part of this work was presented at Allerton 2005 as an invited paper. I.

Dedicated to my parents, who have always encouraged me.

Abstract—Channel-aware scheduling in modern wireless networks enables the system to exploit the random rate variations across different users to increase the performance of the system. We analyze channel-aware priority-based downlink scheduling policies at the so-called flow level with a stochastically varying number of users. The priority can be any monotonously increasing function of the instantaneous rate of the user, which generalizes the well-known linear weight-based policies. Also, ties are allowed within a user class, as well as between user classes. As the main result, we characterize when these priority-based policies are stable under an intuitive necessary condition, which holds for arbitrary tie breaking rules and is independent of the flow size distribution. Additionally, for the policies for which the necessary condition is not sufficient, a more stringent condition is derived in the case of two traffic classes. Finally, extensive simulations have been performed to compare the performance of different priority-based and utility-based policies. I.

Abstract. With more and more users subscribing to wireless broadband services, it is desirable for them to have access to both WLAN and UMTS networks. We study globally optimal user-network association in an integrated WLAN and UMTS hybrid cell. The association problem is formulated as a generic MDP (Markov Decision Process) connection routing decision problem. In the formulation, mobile arrivals are assumed to follow Poisson process and a uniformization technique is applied in order to transform the otherwise state-dependent mobile departures into an i.i.d. process. We solve the MDP problem using a particular network model for WLAN and UMTS networks and with rewards comprising financial gain and throughput components. The corresponding Dynamic Programming equation is solved using Value Iteration and a stationary optimal policy with neither convex nor concave type switching curve structure is obtained. Threshold type and symmetric switching curves are observed for the analogous homogenous network cases. 1

Abstract. Proportional Fair (PF), a frequently used scheduling algorithm in 3G wireless networks, can unnecessarily starve "well-behaved " users in practice. One of the main causes behind PF-induced starvation is its inability to distinguish between users who are backlogged and users who are not. In this paper, we describe how a simple parallel PF instance can mitigate such starvation. 1 Introduction Scheduling algorithms play a key role in deciding user performance in wireless networks. In the past, a number of channel-aware scheduling algorithms have been proposed [1-4] to exploit the time-varying nature of user channel conditions without sacrificing fairness. The Proportional Fair (PF) algorithm [5] is one such channel-aware algorithm that has been widely deployed in cellular data networks, especially in 3G networks such as CDMA-based EV-DO [5] and GSM-based HSDPA networks.

Channel conditions in wireless networks exhibit huge variations across space and time, giving rise to vast random fluctuations in the feasible transmission rates. Channel-aware scheduling strategies provide an effective mechanism for improving throughput performance by exploiting such rate variations, and have been extensively investigated at packet level for a static user configuration. In the present paper, we discuss the performance implications at flow level for a dynamic user population, taking into consideration rate variations on a slower time scale and wide-range user mobility as well. First of all, we present simple necessary conditions for flow-level stability, and prove that these are in fact (near-)sufficient for a wide family of utility-based scheduling strategies. It is further shown how the flow-level performance of the Proportional Fair scheduling strategy may be evaluated by means of a multi-class Processor-Sharing model with a statedependent service rate. In addition, we examine the impact of rate variations on a slower time scale, and establish that two limit regimes, termed fluid and quasi-stationary regime, yield explicit, insensitive performance bounds. Finally, we turn attention to a network of several base stations with hand-offs of active sessions governed by wide-range user mobility. It is demonstrated that mobility increases the capacity region, not only in case of globally optimal scheduling, but also when each of the base stations adheres to a local fair sharing discipline. 1

Abstract — We consider the following problem of spatial downlink prioritization. Mobiles arrive at a cell at locations that are determined according to some probability distribution. The further a mobile is from the base station, the weaker is its received power and thus the lower is the transmission rate to it. Beside this uncontrollable phenomenon that differentiates between mobiles according to their location, one can design other controlled mechanisms that differentiate between them. We analyse various priority policies where the assigned priority is given in terms of the distance of the mobiles from the base station. This gives rise to a whole continuum of priority levels. We study the influence that the combined location density and priority policy have on the quality of service of the mobiles and on the network overall performance. Applying our model to a HSDPA system, we calculate a quality of service indicator, the sojourn time, using a priority scheduling strategy, a processor sharing one and a first come first served one. Considering three types of arrival flow, a uniform one, a non uniform one and a flow which generates a constant load in the cell, we show the sojourn time depends on the adopted strategy, but also on the location of the mobile and on the arrival flow type. In particular, a numerical study based on our model shows that a maximum SIR priority does not provide in any case the minimum sojourn time.

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Multi-channel system are becoming more and more available and require new techniques to speed up the channel access, especially when the mobile device is equipped only with a single antenna.