In communication systems, three major objectives of resource allocation problems are data rate increase, power reduction, and delay limiting or quality of service (QoS). This thesis investigates these three objectives in various scenarios for the application of crosstalking binders of telephone lines.;The first part introduces a new dynamic spectrum management method, which influences the spectrum usage by modifying the standard bit-loading algorithms for the digital-subscriber-lines (DSL) modems. In this method, a spectrum management center (SMC) first assesses whether some modems should protect other modems on certain frequency bands - such a method is generally called a band-preference spectrum management algorithm. Then, the SMC classifies modems as strong or weak, and sends a bit indicating whether each modem has to protect other modems or not. Once a modem knows that it should be polite, it moves bits from the less preferred tones to the preferred tones. In this way, the SMC only needs to send a one-bit indication to each user; each user then autonomously manages its spectrum based on its own information.;The second part considers energy minimization for a fast-fading random-access network. Each user transmits a single fixed-length packet within a strict delay-limit in a way to minimize energy. As channels vary within the delay limit, a packet can be transmitted with minimum energy when the channel gain is the largest. However, the time-slot with the largest channel gain can not be chosen in advance because future channel states are unknown. Also, the transmission can be deferred to subsequent time slots only up to the delay limit because a packet will be dropped if it does not satisfy the delay limit The proposed algorithms assume that each user causally knows its current channel state information. With the channel distribution known to all users, the proposed dynamic-programming solution provides an optimal scheduler that minimizes the sum of energy used to transmit a packet and outage cost incurred by a packet drop.;The third part characterizes the delay region that is quite useful for multi-user packet scheduling. In a quasi-static channel, the optimal delay region is defined as every set of total delay vectors achieved by some scheduling policies when there are no further packet arrivals. Each user's total delay is equivalent to the amount of time until that user's queue backlog is cleared. The optimal delay region shows the fundamental limit on each user's achievable queueing delay and describes the trade-off among the users in terms of queueing delay when different scheduling policies are applied. In addition, the concept of the delay region is shown to be extendable to each packet's average delay as well as total delay.
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