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In this paper, we consider packet scheduling for the downlink in a wireless network, where each packet's service preferences are captured by a utility function that depends on the total delay incurred. The goal is to schedule packet transmissions to maximize the total utility. In this setting, we examine a simple gradient-based scheduling algorithm called the U/spl dot/R-rule, which is a type of generalized c/spl mu/-rule (Gc/spl mu/) that takes into account both a user's channel condition and derived utility when making scheduling decisions. We study the performance of this scheduling rule for a draining problem, where there is a given set of initial packets and no further arrivals. We formulate a "large system" fluid model for this draining problem where the number of packets becomes large while the packet-size decreases to zero, and give a complete characterization of the behavior of the U/spl dot/R scheduling rule in this limiting regime. Comparison with simulation results show that the fluid limit accurately predicts the corresponding behavior of finite systems of interest. We then give an optimal control formulation for finding the optimal scheduling policy for the fluid draining model. Using Pontryagin's minimum principle, we show that, when the user rates are chosen from a TDM-type of capacity region, the U/spl dot/R rule is in fact optimal in many cases. Sufficient conditions for optimality are also given. Finally, we consider a general capacity region and show that the U/spl dot/R rule is optimal only in special cases.

In next-generation wireless communication systems, packet-oriented data transmission will be implemented in addition to standard mobile telephony. We take an information-theoretic view of some simple protocols for reliable packet communication based on "hybrid-ARQ," over a slotted multiple-access Gaussian channel with fading and study their throughput (total bit per second per hertz) and average delay under idealized but fairly general assumptions. As an application of the renewal-reward theorem, we obtain closed-form throughput formulas. Then, we consider asymptotic behaviors with respect to various system parameters. The throughput of automatic retransmission request (ARQ) protocols is compared to that of code division multiple access (CDMA) with conventional decoding. Interestingly, the ARQ systems are not interference-limited even if no multiuser detection or joint decoding is used, as opposed to conventional CDMA.

Results on the modeling of interference in a radio communication network and performance measures for the link as a function of distance are presented. It is assumed that a transmitter-receiver pair in a radio network is affected by a set of interferers, using the same modulation and power, whose positions are modeled as a Poisson field in the plane. Assuming a 1/r/sup gamma / propagation power loss law, the probability distributions for the noise at the receiver are found to be the stable distributions. Results are given for the probability of symbol error and link capacity as a function of the distance between the transmitter and receiver for direct sequence and frequency hopping spread spectrum schemes. It is found that the frequency hopping schemes are inherently superior and their performance is not dependent on the synchronization of the hopping times for the different users. >

A multihop packet radio network is considered with a single traffic class and given end-to-end transmission requirements. A transmission schedule specifies at each time instant the set of links which are allowed to transmit. The purpose of a schedule is to prevent interference among transmissions from neighboring links. Given amounts of information are residing initially at a subset of the network nodes and must be delivered to a prespecified set of destination nodes. The transmission schedule that evacuates the network in minimum time is specified. The decomposition of the problem into a pure routing and a pure scheduling problem is crucial for the characterization of the optimal transmission schedule. >

The connectivity of a two-dimensional radio network as a function of the range of the transmitters is still an open problem. It has bee conjectured that the critical range of this problem is the same as the one for the covering problem. The analysis of the one-dimensional problem makes it clear that situations can exist where these two ranges are different. It is conjectured that the critical ranges of the two-dimensional problems are also different. The author presents results to substantiate this conjecture. >

A model of a packet radio network in which transmitters with range R are distributed according to a two-dimensional Poisson point process with density D is examined. To ensure network connectivity, it is shown that pi R/sup 2/D, the expected number of nearest neighbors of a transmitter, must grow logarithmically with the area of the network. For an infinite area there exists an infinite connected component with nonzero probability if pi R/sup 2/D>N/sub 0/, for some critical value N/sub 0/. It is shown that 2.195 >

It is shown that the decision problem regarding the membership of a point in the capacity region of a packet radio network is nondeterministic polynomial time hard (NP hard). The capacity region is the set of all feasible origin-to-destination message rates where feasibility is defined as the existence of any set of rules for moving the data through the network so that the desired rates are satisfied.

A system with many nodes accessing a common receiver is considered. The forward channel is a time-slotted collision-type common radio channel. Due to a nonreliable forward channel, the receiver may misinterpret the actual event of a slot. For instance, an idle or a success slot can be interpreted as a conflict and a conflict or a success slot can be interpreted as an idle slot. The former kind of error is called a noise error, while the latter is called an erasure. Splitting multiple-access algorithms are introduced that can handle erasures as well as noise errors. A remarkable feature of the algorithms is that they ensure that, under stable operation, all packets are eventually successfully transmitted, including the erased packets (those packets that were involved in an erasure). The property that is exploited in devising these algorithms is that nodes whose packets were erased can detect that situation as they transmit and acknowledge that the slot was idle. Consequently, they can either retransmit immediately or wait until some agreed point in time (such as the end of a collision resolution interval) and then transmit. The performances of the proposed algorithms are evaluated according to the maximal throughput they can support for Poisson arrival process. The performance degradation due to erasures and noise errors is quantified.

The performance of frequency-hop transmission in a packet communication network is analyzed. Satellite multiple-access broadcast channels for packet switching and terrestrial packet radio networks are the primary examples of the type of network considered. An analysis of the effects of multiple-access interference in frequency-hop radio networks is presented. New measures of "local" performance are defined and evaluated for networks of this type, and new concepts that are important in the design of these networks are introduced. In particular, error probabilities and local throughput are evaluated for a frequency-hop radio network which incorporates the standard slotted and unslotted ALOHA channel-access protocols, asynchronous frequency hopping, and Reed-Solomon error-control coding. The performance of frequency-hop multiple access with error-control coding is compared with the performance of conventional ALOHA random access using narrow-band radios.

The development of the ALOHA system packet broadcasting network at the University of Hawaii illustrates a number of general principles about the relationship between information theory and the design of real information systems. An anecdotal account is given of the development of the ALOHA system, emphasizing the interaction of the theory and the design of the experimental network. In addition, some preliminary results are described on the comparison of ALOHA channels and spread spectrum channels when used for packet communications.