Connectivity and capacity analysis of ad hoc networks has usually focused on asymptotic results in the number of nodes in the network. In this letter we analyze finite ad hoc networks. With the standard assumption of uniform distribution of nodes in [0 ],0, for a one-dimensional network, we obtain the exact formula for the probability that the network is connected. We then extend this result to find bounds for the connectivity in a two-dimensional network in [0 ] 2 . Index Terms-Connectivity, finite ad hoc networks, one-dimensional ad hoc networks.

Routing and wavelength assignment (RWA) problems in wavelength-routed optical networks are typically solved using a combination of integer programming and graph coloring. Such techniques are complex and make extensive use of heuristics. We explore an alternative solution technique in the well-known maximum edge disjoint paths (EDP) problem which can be naturally adapted to the RWA problem. Maximum EDP is NP-hard, but now it is known that simple greedy algorithms for it are as good as any of the more complex heuristic solutions. In this paper we investigate the performance of a simple greedy maximum edge disjoint paths algorithm applied to the RWA problem and compare it with a previously known solution method.

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We consider a restless multi-armed bandit in which each arm can be in one of two states. When an arm is sampled, the state of the arm is not available to the sampler. Instead, a binary signal with a known randomness that depends on the state of the arm is available. No signal is available if the arm is not sampled. An arm-dependent reward is accrued from each sampling. In each time step, each arm changes state according to known transition probabilities which in turn depend on whether the arm is sampled or not sampled. Since the state of the arm is never visible and has to be inferred from the current belief and a possible binary signal, we call this the hidden Markov bandit. Our interest is in a policy to select the arm(s) in each time step that maximizes the infinite horizon discounted reward. Specifically, we seek the use of Whittle's index in selecting the arms.We first analyze the single-armed bandit and show that in general, it admits an approximate threshold-type optimal policy when there is a positive reward for the 'no-sample' action. We also identify several special cases for which the threshold policy is indeed the optimal policy. Next, we show that such a singlearmed bandit also satisfies an approximate-indexability property. For the case when the single-armed bandit admits a thresholdtype optimal policy, we perform the calculation of the Whittle index for each arm. Numerical examples illustrate the analytical results.