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22
Maxweight scheduling in a generalized switch: State space collapse and workload minimization in heavy traffic. The Annals of Applied Probability,
, 2004
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Pathwise optimality of the exponential scheduling rule for wireless channels
 Advances in Applied Probability
, 2004
"... We consider the problem of scheduling transmissions of multiple data users (flows) sharing the same wireless channel (server). The unique feature of this problem is the fact that the capacity (service rate) of the channel varies randomly with time and asynchronously for different users. We study a s ..."
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Cited by 61 (19 self)
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We consider the problem of scheduling transmissions of multiple data users (flows) sharing the same wireless channel (server). The unique feature of this problem is the fact that the capacity (service rate) of the channel varies randomly with time and asynchronously for different users. We study a scheduling policy called Exponential scheduling rule, which was introduced in an earlier paper. Given a system with N users, and any set of positive numbers {an},n = 1,2,...,N, we show that in a heavytraffic limit, under a nonrestrictive complete resource pooling condition, this algorithm has the property that, for each time t, it (asymptotically) minimizes maxn an˜qn(t), where ˜qn(t) is user n queue length in the heavy traffic regime.
Individual and mass behaviour in large population stochastic wireless power control problems: centralized and Nash equilibrium solutions
 in Proc. IEEE Conf. on Decision and Control, Maui, HI
"... Abstract — We consider uplink power control for lognormal fading channels in the large population case. First, we examine the structure of the control law in a centralized stochastic optimal control setup. We analyze the effect of large populations on the individual control inputs. Next, we split th ..."
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Cited by 48 (14 self)
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Abstract — We consider uplink power control for lognormal fading channels in the large population case. First, we examine the structure of the control law in a centralized stochastic optimal control setup. We analyze the effect of large populations on the individual control inputs. Next, we split the centralized cost to approach the problem in a game theoretic framework. In this context, we introduce an auxiliary LQG control system and analyze the resulting εNash equilibrium for the control law; subsequently we generalize the methodology developed for the LQG problem to the wireless power control problem to get an approximation for the collective effect of all other users on a given user. The obtained state aggregation technique leads to highly localized control configurations in contrast to the full state based optimal control strategy. I.
Limited feedback beamforming over temporallycorrelated channels
 IEEE Trans. Signal Process
, 2009
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Uplink power adjustment in wireless communication systems: a stochastic control analysis. Under revision for
 IEEE Trans. Autontat. Contr
, 2003
"... Abstract—This paper considers mobile to base station power control for lognormal fading channels in wireless communication systems within a centralized information stochastic optimal control framework. Under a bounded power rate of change constraint, the stochastic control problem and its associated ..."
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Cited by 20 (7 self)
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Abstract—This paper considers mobile to base station power control for lognormal fading channels in wireless communication systems within a centralized information stochastic optimal control framework. Under a bounded power rate of change constraint, the stochastic control problem and its associated Hamilton–Jacobi–Bellman (HJB) equation are analyzed by the viscosity solution method; then the degenerate HJB equation is perturbed to admit a classical solution and a suboptimal control law is designed based on the perturbed HJB equation. When a quadratic type cost is used without a bound constraint on the control, the value function is a classical solution to the degenerate HJB equation and the feedback control is affine in the system power. In addition, in this case we develop approximate, but highly scalable, solutions to the HJB equation in terms of a local polynomial expansion of the exact solution. When the channel parameters are not known a priori, one can obtain online estimates of the parameters and get adaptive versions of the control laws. In numerical experiments with both of the above cost functions, the following phenomenon is observed: whenever the users have different initial conditions, there is an initial convergence of the power levels to a common level and then subsequent approximately equal behavior which converges toward a stochastically varying optimum. Index Terms—Dynamic programming, Hamilton–Jacobi– Bellman (HJB) equations, lognormal fading channels, power control, quality of service. I.
Stability and Control of Mobile Communications Systems With Time Varying Channels
 IEEE Transactions on Automatic Control
, 2001
"... Consider the forward link of a mobile communications system with a single transmitter and rather arbitrary randomly time varying channels connecting the base to the mobiles. Data arrives at the base in some random way (and might have a bursty character) and is queued according to the destination unt ..."
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Cited by 14 (2 self)
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Consider the forward link of a mobile communications system with a single transmitter and rather arbitrary randomly time varying channels connecting the base to the mobiles. Data arrives at the base in some random way (and might have a bursty character) and is queued according to the destination until transmitted. The main issues are the allocation of transmitter power and time to the various queues in a queue and channelstate dependent way to assure stability and good operation. The control decisions are made at the beginning of the (small) scheduling intervals. Stability methods are used to allocate time and power. Many schemes of current interest can be handled: For example, CDMA with control over the bit interval and power per bit, TDMA with control over the time allocated, power per bit, and bit interval, as well as arbitrary combinations. There might be random errors in transmission which require retransmission. The channelstate process might be known or only partially known. The details of the scheme are not directly involved; all essential factors are incorporated into a "rate" and "error" function. The system and channel process are scaled by speed. Under a stability assumption on a model obtained from the "mean drift," and some other natural conditions, it is shown that the scaled physical system can be controlled to be stable, uniformly in the speed, for fast enough speeds. Owing to the nonMarkov nature of the problem, we use the perturbed Liapunov function method, which is very useful for the analysis of nonMarkovian systems. Finally, the stability method is used to actually choose the power and time allocations. The allocation will depend on the Liapunov function. But each such function corresponds loosely to an optimization problem for some performance...
Stochastic power control for timevarying longterm fading wireless channels
 in Proceedings of the American Control Conference
"... The power control (PC) of wireless networks is formulated using a stochastic optimal control framework. The performance of stochastic optimal power control for timevarying long term fading channels, in which the evolution of the dynamical channel is described by a stochastic differential equations ..."
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Cited by 12 (6 self)
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The power control (PC) of wireless networks is formulated using a stochastic optimal control framework. The performance of stochastic optimal power control for timevarying long term fading channels, in which the evolution of the dynamical channel is described by a stochastic differential equations (SDE) is determined. Unlike the common random or free space static models usually encountered in the literature, the SDE essentially capture the spatialtemporal variations of lognormal fading wireless channels as well as the randomness. The solution of the stochastic optimal control is obtained through pathwise optimization, which is solved by linear programming using predictable power control strategies (PPCS). The algorithm can be implemented using an iterative numerical scheme. The performance measure of the algorithm is interference or outage probability. Simulation results show that the performance of PPCS using stochastic models outperforms the performance of PC based on static models. The PPCS algorithm can be used as long as the channel model does not change significantly. If predictable control strategies do not hold, it is shown that the proposed power control problem reduces to particular convex optimizations.
Optimal Power Allocation for a TimeVarying Wireless Channel under HeavyTraffic Approximation Paper TAC05258 — Revised 11/26/05
"... Abstract — This paper studies the problem of minimizing the queueing delay for a timevarying channel with a single queue, subject to constraints on the average and peak power. First, by separating the timescales of the arrival process, the channel process and the queueing dynamics it derives a hea ..."
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Cited by 8 (0 self)
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Abstract — This paper studies the problem of minimizing the queueing delay for a timevarying channel with a single queue, subject to constraints on the average and peak power. First, by separating the timescales of the arrival process, the channel process and the queueing dynamics it derives a heavytraffic limit for the queue length in the form of a reflected diffusion process. Given a monotone function of the queuelength process that serves as a penalty, and constraints on the average and peak available power, it shows that the optimal power allocation policy is a channelstate based threshold policy. For each channel state j there corresponds a threshold value of the queue length, and it is optimal to transmit at peak power if the queue length exceeds this threshold, and not transmit otherwise. Numerical results compare the optimal policy for the original Markovian dynamics to the threshold policy which is optimal for the heavytraffic approximation, to conclude that that latter performs very well even outside the heavytraffic operating regime. Index Terms — power allocation, heavytraffic, controlled diffusion, fading channel I.
CONTROL FOR WIRELESS COMMUNICATION SYSTEMS
, 2007
"... have examined the final electronic copy of this dissertation for form and content and ..."
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Cited by 5 (0 self)
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have examined the final electronic copy of this dissertation for form and content and
Heavy Traffic Limits in a Wireless Queueing Model with Long Range Dependence
"... Abstract — Highspeed wireless networks carrying multimedia applications are becoming a reality and the transmitted data exhibit long range dependence and heavytailed properties. We consider the heavy traffic approach in working towards queue models under these properties, extending the model in [2 ..."
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Cited by 2 (1 self)
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Abstract — Highspeed wireless networks carrying multimedia applications are becoming a reality and the transmitted data exhibit long range dependence and heavytailed properties. We consider the heavy traffic approach in working towards queue models under these properties, extending the model in [2]. Our focus is on the scalings used in the heavy traffic approach which are determined by combinations of the source rate of an infinite source Poisson model of the arrival process, the tail distribution of data transmitted by these sources, and the rate of variation of the random process (channel process) modeling the wireless medium. A fundamental inequality between the exponent in the power tail distribution of the data from the source and the parameter specifying the rate of channel variations is obtain. This inequality is important in both the “fast growth ” and “slow growth ” regimes for the arrival process and along with the source rate is used to define the possible cases for obtaining limit models for the queueing process. Across the cases, the possible limit models include reflected Brownian motion, reflected stable Lévy motion, or reflected fractional Brownian motion. I.