This paper considers a widely studied stochastic control problem arising from opportunistic spectrum access in a multichannel system, with the goal of providing a unifying analytical framework whereby a number of prior results may be viewed as special cases. Specifically, we consider a single wireless transceiver/user with access to N channels, each modeled as an independent identically distributed discrete-time two-state Markov chain. In each time step, the user is allowed to sense k ≤ N channels, and subsequently use up to m ≤ k channels out of those sensed to be available. Channel sensing is assumed to be perfect, and for each channel used in each time step the user gets a unit reward. The user's objective is to maximize its total discounted or average reward over a finite or infinite horizon. This problem has previously been studied in various special cases including k = 1 and m = k ≤ N, often cast as a restless bandit problem, with optimality results derived for a myopic policy that seeks to maximize the immediate one-step reward when the two-state Markov chain model is positively correlated. In this paper, we study the general problem with 1 m ≤ k ≤ N, and derive sufficient conditions under which the myopic policy is optimal for the finite and infinite horizon reward criteria, respectively. It is shown that these results reduce to those derived in prior studies under the corresponding special cases, and thus may be viewed as a set of unifying optimality conditions. Numerical examples are also presented to highlight how and why an optimal policy may deviate from the otherwise-optimal myopic sensing given additional exploration opportunities, i.e., when m ≤ k.

In this paper, we introduce and analyze the properties of a class of games, the atomic congestion games on graphs (ACGGs), which is a generalization of the classical congestion games. In particular, an ACGG captures the spatial information that is often ignored in a classical congestion game. This is useful in many networking problems, e.g., wireless networks where interference among the users heavily depends on the spatial information. In an ACGG, a player's payoff for using a resource is a function of the number of players who interact with it and use the same resource. Such spatial information can be captured by a graph. We study fundamental properties of the ACGGs: under what conditions these games possess a pure strategy Nash equilibrium (PNE), or the finite improvement property (FIP), which is sufficient for the existence of a PNE. We show that a PNE may not exist in general, but that it does exist in many important special cases including tree, loop, or regular bipartite networks. The FIP holds for important special cases including systems with two resources or identical payoff functions for each resource. Finally, we present two wireless network applications of ACGGs: power control and channel contention under IEEE 802.11.

This paper considers opportunistic communication over multiple channels where the state (ldquogoodrdquo or ldquobadrdquo) of each channel evolves as independent and identically distributed (i.i.d.) Markov processes. A user, with limited channel sensing capability, chooses one channel to sense and decides whether to use the channel (based on the sensing result) in each time slot. A reward is obtained whenever the user senses and accesses a ldquogoodrdquo channel. The objective is to design a channel selection policy that maximizes the expected total (discounted or average) reward accrued over a finite or infinite horizon. This problem can be cast as a partially observed Markov decision process (POMDP) or a restless multiarmed bandit process, to which optimal solutions are often intractable. This paper shows that a myopic policy that maximizes the immediate one-step reward is optimal when the state transitions are positively correlated over time. When the state transitions are negatively correlated, we show that the same policy is optimal when the number of channels is limited to two or three, while presenting a counterexample for the case of four channels. This result finds applications in opportunistic transmission scheduling in a fading environment, cognitive radio networks for spectrum overlay, and resource-constrained jamming and antijamming.

In this correspondence, we study the capacity region of a general wireless network by deriving fundamental upper bounds on a class of linear functionals of the rate tuples at which joint reliable communication can take place. The widely studied transport capacity is a specific linear functional: the coefficient of the rate between a pair of nodes is equal to the Euclidean distance between them. The upper bound on the linear functionals of the capacity region is used to derive upper bounds to scaling laws for generalized transport capacity: the coefficient of the rate between a pair of nodes is equal to some arbitrary function of the Euclidean distance between them, for a class of minimum distance networks. This upper bound to the scaling law meets that achievable by multihop communication over these networks for a wide class of channel conditions; this shows the optimality, in the scaling-law sense, of multihop communication when studying generalized transport capacity of wireless networks.