In multiaccess wireless systems, dynamic allocation of resources such as transmit power, bandwidths, and rates is an important means to deal with the time-varying nature of the environment. In this two-part paper, we consider the problem of optimal resource allocation from an information-theoretic point of view. We focus on the multiaccess fading channel with Gaussian noise, and define two notions of capacity depending on whether the traffic is delay-sensitive or not. In Part I, we have analyzed the throughput capacity region which characterizes the long-term achievable rates through the time-varying channel. However, the delay experienced depends on how fast the channel varies. In the present paper, Part II, we introduce a notion of delay-limited capacity which is the maximum rate achievable with delay independent of how slow the fading is. We characterize the delay-limited capacity region of the multiaccess fading channel and the associated optimal resource allocation schemes. We show that successive decoding is optimal, and the optimal decoding order and power allocation can be found explicitly as a function of the fading states; this is a consequence of an underlying polymatroid structure that we exploit.

We consider open and closed multiclass queueing networks with Poisson arrivals (in open networks), exponentially distributed class dependent service times, and with class depen-dent deterministic or probabilistic routing. For open networks, the performance objective is to minimize, over all sequencing and routing policies, a weighted sum of the expected response times of different classes. Using a powerful technique involving quadratic or higher order potential functions, we propose variants of a method to derive polyhedral and non-linear spaces which contain the entire set of achievable response times under stable and preemptive scheduling policies. By optimizing over these spaces, we obtain lower bounds on achievable performance. In particular, we obtain a sequence of progressively more com-plicated nonlinear approximations (relaxations) which are progressively closer to the exact achievable space. In the special case of single station networks (multiclass queues and Klimov's model) and homogenous multiclass networks, our characterization gives exactly the achievable region. Consequently, the proposed method can be viewed as the natural

Transmit power control is a central technique for resource allocation and interference management in spread-spectrum wireless networks. With the increasing popularity of spread-spectrum as a multiple access technique, there has been significant research in the area in recent years. While power control has been considered traditionally as a means to counteract the harmful effect of channel fading, the more general emerging view is that it is a flexible mechanism to provide Quality-of-Service to individual users. In this paper, we will review the main threads of ideas and results in the recent development of this area, with a bias towards issues that have been the focus of our own research. For different receivers of varying complexity, we study both questions about optimal power control as well as the problem of characterizing the resulting network capacity. Although spread-spectrum communications has been traditionally viewed as a physical-layer subject, we argue that by suitable abstr...

We provide a review and synthesis of polyhedral approaches to machine scheduling problems. The choice of decision variables is the prime determinant of various formulations for such problems. Constraints, such as facet inducing inequalities for corresponding polyhedra, are often needed, in addition to those just required for the validity of the initial formulation, in order to obtain useful lower bounds and structural insights. We review formulations based on time–indexed variables; on linear ordering, start time and completion time variables; on assignment and positional date variables; and on traveling salesman variables. We point out relationship between various models, and provide a number of new results, as well as simplified new proofs of known results. In particular, we emphasize the important role that supermodular polyhedra and greedy algorithms play in many formulations and we analyze the strength of the lower and upper bounds obtained from different formulations and relaxations. We discuss separation algorithms for several classes of inequalities, and their potential applicability in generating cutting planes for the practical solution of such scheduling problems. We also review some recent results on approximation algorithms based on some of these formulations.

a primal-dual index heuristic

We consider a general single-server multiclass queueing system that incurs a delay cost Ck ( k) for each class k job that resides k units of time in the system. This paper derives a scheduling policy that minimizes the total cumulative delay cost when the system operates during a nite time horizon. Denote the marginal delay cost and (instantaneous) service rate functions of class k by ck = C 0 k and k, and let ak(t) be the \age " or time that the oldest class k job has been waiting at time t. Wecall the scheduling policy that at time t serves the oldest waiting job of that class k with the highest index k(t)ck(ak(t)), the Generalized c Rule. As a dynamic priority rule that depends on very little data, the Generalized c Rule is attractive to implement. We show that with non-decreasing convex delay costs, the Generalized c Rule is asymptotically optimal if the system operates in heavy tra c, and give explicit expressions for the associated performance characteristics: the delay (throughput time) process and the minimum cumulative delay cost. The optimality result is robust in that it holds for a countable number of classes and several homogeneous servers in a non-stationary, deterministic or stochastic environment where arrival and service processes can be general and interdependent. 1

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This paper develops a polyhedral approach to the design, analysis, and computation of dynamic allocation indices for scheduling binary-action (engage/rest) Markovian stochastic projects which can change state when rested (restless bandits (RBs)), based on partial conservation laws (PCLs). This extends previous work by the author [J. Nino-Mora (2001): Restless bandits, partial conservation laws and indexability. Adv. Appl. Probab. 33, 76--98], where PCLs were shown to imply the optimality of index policies with a postulated structure in stochastic scheduling problems, under admissible linear objectives, and they were deployed to obtain simple sufficient conditions for the existence of Whittle's (1988) RB index (indexability), along with an adaptive-greedy index algorithm. The new contributions include: (i) we develop the polyhedral foundation of the PCL framework, based on the structural and algorithmic properties of a new polytope associated with an accessible set system (J, (F-extended polymatroid); (ii) we present new dynamic allocation indices for RBs, motivated by an admission control model, which extend Whittle's and have a significantly increased scope; (iii) we deploy PCLs to obtain both sufficient conditions for the existence of the new indices (PCL-in- dexability), and a new adaptive-greedy index algorithm; (iv) we interpret PCL-indexability as a form of the classic economics law of diminishing marginal returns, and characterize the index as an optimal marginal cost rate; we further solve a related optimal constrained control problem; (v) we carry out a PCL-indexability analysis of the motivating admission control model, under time-discounted and long-run average criteria; this gives, under mild conditions, a new index characterization of optimal threshold...

Abstract — As a natural multi-class generalization of the well-known (egalitarian) Processor Sharing (PS) service discipline, Discriminatory Processor Sharing (DPS) is of great interest in many application areas, including telecommunications. Under DPS, the mean response time conditional on the service requirement is only known in closed form when all classes have exponential service requirement distributions. For generally distributed service requirements, Fayolle et al. [1] showed that the expected conditional response times satisfy a system of integrodifferential equations. In this paper, we exploit that result to prove that, provided the system is stable, for each class the expected unconditional response time is finite and that the expected conditional response time has an asymptote. The asymptotic bias of each class is found in closed form, involving the mean service requirements of all classes and the second moments of all classes but the one under consideration. In the course of the development we prove two other results that are of independent interest: we establish a conservation law for the time average unfinished work of all classes and, using a stochastic coupling argument, we show that the response times of different classes are stochastically ordered according to the DPS weights. Finally, we study DPS as a tool to achieve size based scheduling and we provide guidelines as to how the weights of DPS must be chosen such that DPS outperforms PS. I.

the second author through the award of grants GR/K03043 and GR/M09308. We would also like to thank colleagues in the Department of Statistics, Newcastle University for their constructive comments on earlier drafts of the paper. The work of the third author was initiated during his stay at the Center for Operations Research and Econometrics (CORE) of the Universite catholique de Louvain, Belgium, where it was supported by EC individual Marie Curie Postdoctoral Fellowship no. ERBFMBICT961480. Further research support is acknowledged from Universitat Pompeu Fabra. The achievable region approach seeks solutions to stochastic optimisation problems by: (i) characterising the space of all possible performances (the achievable region) of the system of interest, and (ii) optimising the overall system-wide performance objective over this space. This is radically di erent from conventional formulations based on dynamic programming. The approach is explained with reference to a simple two-class queueing system. Powerful new methodologies due to the authors and co-workers are deployed to analyse a general multiclass queueing system with parallel servers and then to develop an approach to optimal load distribution across a network of interconnected stations. Finally, the approach is used for the rst time to analyse a class of intensity control problems.