One stochastic process and its application to multiple access insupercritical region

A discrete-argument stochastic process is presented. The process is a generalization of the Cinlar (1975) semiregenerative process and process η(t) given in Tsybakov (1993). For this process, the theorem, which is similar to the Smith regenerative process theorem, is given. We use this theorem to find the transmission rate and mean packet delay for stack and part-and-try random multiple access algorithms in their supercritical regions. For the part-and-try algorithm, the results are new. For the stack algorithm, we give a new method of finding the rate and delay     

File transmission over wireless fast fading downlink

The third-generation code division multiple access (3G CDMA) mobile communication networks are designed to transmit voice and data over wireless channels. Fundamental problems need to be solved for such mobile communication networks to operate efficiently. One of the problems is finding optimal scheduling algorithms for file transmission over the fading downlink channel from a base station to mobile users. Here, the problem is solved in the case of transmission of a given number of files. Optimal algorithms that minimize the delay and the transmission time are found. Also, specific nonoptimal algorithms are considered and compared numerically with the optimal ones. We consider a slotted downlink with channels to the mobile users that are dependent in the same slot but independent for different slots. Additionally, some generalizations are presented.     

On self-similar traffic in ATM queues: definitions, overflowprobability bound, and cell delay distribution

Recent traffic measurements in corporate local-area networks (LANs), variable-bit-rate video sources, ISDN control-channels, and other communication systems, have indicated traffic behaviour of self-similar nature. This paper first discusses some definitions and properties of (second-order) self-similarity and gives simpler criteria for it. It then gives a model of self-similar traffic suitable for queuing system analysis of an asynchronous transfer mode (ATM) queue. A lower bound to the overflow probability of a finite ATM buffer is obtained, as also a lower bound to the cell loss probability. Finally, the stationary distribution of the cell delay in an infinite ATM buffer is obtained     

Busy Periods in a System with Heterogeneous Servers or Channels

We consider a multiple communication channel system having channels with different transmission rates. We give a solution for the problem (of interest for such a system) of finding the probability densities and probability distribution functions of the N-busy period length. A solution in the case of identical channels (servers) was given in [1].     

Recursive Aggregation of Estimators by the Mirror Descent Algorithm with Averaging

We consider a recursive algorithm to construct an aggregated estimator from a finite number of base decision rules in the classification problem. The estimator approximately minimizes a convex risk functional under the ?₁-constraint. It is defined by a stochastic version of the mirror descent algorithm which performs descent of the gradient type in the dual space with an additional averaging. The main result of the paper is an upper bound for the expected accuracy of the proposed estimator. This bound is of the order \(C\sqrt {(\log M)/t}\) with an explicit and small constant factor C, where M is the dimension of the problem and t stands for the sample size. A similar bound is proved for a more general setting, which covers, in particular, the regression model with squared loss.     

Some Constructions of Conflict-Avoiding Codes

Constructions of conflict-avoiding codes are presented. These codes can be used as protocol sequences for successful packet transmission over a collision channel without feedback. We give a relation between codes that avoid conflicts of different numbers of colliding users. Upper bounds on the maximum code size and three particular code constructions are presented.     

Aggregation by exponential weighting, sharp PAC-Bayesian bounds and sparsity

We study the problem of aggregation under the squared loss in the model of regression with deterministic design. We obtain sharp PAC-Bayesian risk bounds for aggregates defined via exponential weights, under general assumptions on the distribution of errors and on the functions to aggregate. We then apply these results to derive sparsity oracle inequalities.