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... VOL. 16, NO. 2, APRIL 2008, PP. 396-409 3 simultaneously, extending the stability results developed in [20]-[28]. This work presents a fundamental approach to stochastic network optimization [1] [2] =-=[3]-=- [4]. We note that alternative optimization approaches have recently been considered in [29] [35] using fluid limit models, and in [36] using stochastic gradient theory (see, for example, [37]). Our L...

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...(t)Cdc ¯ = φ̂ (15) where the expectations above are with respect to the stationary distribution of (W (t), S(t)) and the randomized control decisions. Proof. This result follows from the framework in =-=[19]-=- and is omitted for brevity. It should be noted that while it is possible to characterize and potentially compute such a policy, it may not be feasible for the original problem P1 as it could violate ...

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...he network throughput region. To address this, throughput-optimal 1 routing and scheduling, first developed in the seminal work of [1], has been extensively studied [2], [3], [4], [5], [6], [7], [8], =-=[9]-=-, [12], [13], [14], [15]. We refer to [10], [11] for a comprehensive survey. While these algorithms maximize the network throughput region, additional issues need to be considered for practical deploy...

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...elops Lyapunov techniques for treating stability and performance optimization simultaneously (extending the Lyapunov stability results developed, for example, in [14]-[19]). These results are used in =-=[10]-=- to develop simple stabilizing algorithms for general multi-hop wireless networks that yield average power within O(1/V ) of the minimum power required for stability (for any control parameter V > 0)....

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...n end-to-end network delay. The proof of necessity uses the finite state space assumption for the topology state variable S(t), and is related to similar proofs of capacity and minimum energy in [18] =-=[19]-=- [17] (see Appendix A). Sufficiency does not require the finite state space property, and is proven in the next section, where a simple dynamic control algorithm is constructed that can be implemented...

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..., and E {˜µsum,k(t)} ≤ 1 for all t, the process B(t) satisfies E {B(t)} ≤ B for all t (where B is a finite constant). It follows that the queueing network is strongly stable and hence E {Qi(t)/t} → 0 =-=[18]-=-. Thus: It follows that: lim sup t→∞ 1 t t−1 1 lim t→∞ t τ=0 ∑t−1 τ=0 1 2 ∑ E {˜µsum,k(τ)} = λsum,k E {B(τ)} = [ λtot + ∑ k E { A 2 sum,k which completes the proof of Theorem 2. } − 2 ∑ k λ2 ] sum,kI...

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...ogramming algorithm for the scheduling decisions of the renewable energy supplier. In this paper we build a similar model and utilize the technique of Lyapunov optimization initially developed in [10]=-=[11]-=-[12] for dynamic control of queueing systems for wireless networks. We show that the queuing model naturally fits in the renewable supplier scheduling problem and present a simple energy allocation al...

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...sed backpressure, conveniently called differential backlog. The technique was first applied to wireless multi-hop networks by Tassiulas and Ephremides [31] and later used in several follow-up studies =-=[22]-=-, [23], [26]. We call our adapted version of differential backlog as DiffQ. DiffQ implements router-assisted rate control, source rate control and MAC scheduling over an IEEE 802.11 driver. DiffQ is c...