In cellular wireless communication systems, transmitted power is regulated to provide each user an acceptable connection by limiting the interference caused by other users. Several models have been considered including: (1) xed base station assignment where the assignment of users to base stations is xed, (2) minimum power assignment where a user is iteratively assigned to the base station at which its signal to interference ratio is highest, and (3) diversity reception, where a user's signal is combined from several or perhaps all base stations. For the above models, the uplink power control problem can be reduced to nding a vector p of users' transmitter powers satisfying p I(p) where the jth constraint p j I j (p) describes the interference that user j must overcome to achieve an acceptable connection. This work uni es results found for these systems by identifying common properties of the interference constraints. It is also shown that systems in which transmitter powers are subject to maximum power limitations share these common properties. These properties permit a general proof of the synchronous and totally asynchronous convergence of the iteration p(t + 1) = I(p(t)) to a unique xed point at which total transmitted power is minimized.

Abstract-Increasingly ubiquitous communication networks and connectivity via portable devices have engendered a host of applications in which sources, for example people and environmental sensors, send updates of their status to interested recipients. These applications desire status updates at the recipients to be as timely as possible; however, this is typically constrained by limited network resources. In this paper, we employ a timeaverage age metric for the performance evaluation of status update systems. We derive general methods for calculating the age metric that can be applied to a broad class of service systems. We apply these methods to queue-theoretic system abstractions consisting of a source, a service facility and monitors, with the model of the service facility (physical constraints) a given. The queue discipline of first-come-first-served (FCFS) is explored. We show the existence of an optimal rate at which a source must generate its information to keep its status as timely as possible at all its monitors. This rate differs from those that maximize utilization (throughput) or minimize status packet delivery delay. While our abstractions are simpler than their real-world counterparts, the insights obtained, we believe, are a useful starting point in understanding and designing systems that support real time status updates.

Abstract-In this work, we study how to optimally manage the freshness of information updates sent from a source node to a destination via a channel. A proper metric for data freshness at the destination is the age-of-information, or simply age, which is defined as how old the freshest received update is since the moment that this update was generated at the source node (e.g., a sensor). A reasonable update policy is the zero-wait policy, i.e., the source node submits a fresh update once the previous update is delivered and the channel becomes free, which achieves the maximum throughput and the minimum delay. Surprisingly, this zero-wait policy does not always minimize the age. This counter-intuitive phenomenon motivates us to study how to optimally control information updates to keep the data fresh and to understand when the zero-wait policy is optimal. We introduce a general age penalty function to characterize the level of dissatisfaction on data staleness and formulate the average age penalty minimization problem as a constrained semiMarkov decision problem (SMDP) with an uncountable state space. We develop efficient algorithms to find the optimal update policy among all causal policies, and establish sufficient and necessary conditions for the optimality of the zero-wait policy. Our investigation shows that the zero-wait policy is far from the optimum if (i) the age penalty function grows quickly with respect to the age, (ii) the packet transmission times over the channel are positively correlated over time, or (iii) the packet transmission times are highly random (e.g., following a heavy-tail distribution).

We study information-theoretic security for discrete memoryless interference and broadcast channels with independent confidential messages sent to two receivers. Confidential messages are transmitted to their respective receivers with informationtheoretic secrecy. That is, each receiver is kept in total ignorance with respect to the message intended for the other receiver. The secrecy level is measured by the equivocation rate at the eavesdropping receiver. In this paper, we present inner and outer bounds on secrecy capacity regions for these two communication systems. The derived outer bounds have an identical mutual information expression that applies to both channel models. The difference is in the input distributions over which the expression is optimized. The inner bound rate regions are achieved by random binning techniques. For the broadcast channel, a doublebinning coding scheme allows for both joint encoding and preserving of confidentiality. Furthermore, we show that, for a special case of the interference channel, referred to as the switch channel, the two bound bounds meet. Finally, we describe several transmission schemes for Gaussian interference channels and derive their achievable rate regions while ensuring mutual information-theoretic secrecy. An encoding scheme in which transmitters dedicate some of their power to create artificial noise is proposed and shown to outperform both time-sharing and simple multiplexed transmission of the confidential messages.

We examine multiple independent sources providing status updates to a monitor through simple queues. We formulate an Age of Information (AoI) timeliness metric and derive a general result for the AoI that is applicable to a wide variety of multiple source service systems. For first-come first-served and two types of last-come first-served systems with Poisson arrivals and exponential service times, we find the region of feasible average status ages for multiple updating sources. We then use these results to characterize how a service facility can be shared among multiple updating sources. A new simplified technique for evaluating the AoI in finite-state continuous-time queueing systems is also derived. Based on stochastic hybrid systems, this method makes AoI evaluation to be comparable in complexity to finding the stationary distribution of a finite-state Markov chain. Index TermsAge of information, status updates, queueing systems, random processes, communication networks. update age or simply the age, is the random process ∆(t) = t − u(t) and the AoI is the average ∆(t). The monitor's requirement of timely updating corresponds to small AoI. AoI is an application-independent metric that permits evaluation of the network performance, separate from application-specific metrics that may be too complex to employ in the design of the network.However, AoI can also be useful in specific applications by designing the communication network to meet statistical requirements, such as expected value and variance, of the age process. For example, if a status updating system is reporting sample values of a Wiener process X(t) with variance αt [7], then the monitor's MMSE estimate of X(t) given the status age ∆(t) isX(t) = X(t − ∆(t)). The variance of this estimate is α∆(t).Traditionally, network performance has been characterized by tradeoffs in rate, delay, throughput and loss. The data rate can be increased, but this induces additional delay in lossless systems 3 or increased packet dropping in lossy systems. Furthermore, comparisons between lossless and lossy networks are generally problematic. By contrast, we will see that AoI is fundamentally different; the age metric enables direct comparison of lossless and lossy systems. Moreover, the goal of timely updating is neither the same as maximizing the throughput or utilization of the communication system, nor of ensuring that generated status updates are received with minimum delay. Utilization is maximized when sensors send updates as fast as possible. However, this can lead to the monitor receiving delayed updates because the status messages become backlogged in the communication system. Instead, we will see that sources can minimize their AoI by optimizing their updating rates in response to the available system resources.We further observe that it may also be desirable to redesign systems to facilitate timely updating. A basic property of the first-come first-served (FCFS) queue model is that new update messages can be queued behind outdated messages that were generated...