Boris Tsybakov

Packet multiple access for channel with binary feedback, capture, and multiple reception

This paper considers the multiple access of mobile users to a common wireless channel. The channel is slotted and the binary feedback (empty slot/nonempty slot) is sent to all accessing users. If a slot was not empty and only one user transmitted in it, the transmission is considered successful. Only the user, which had the successful transmission, receives information about its success. In the Introduction, the paper gives a review of known multiple-access algorithms for such a channel. Then our algorithm is constructed that has none of the weaknesses of the algorithms discussed in the Introduction. The algorithm is stable, in contrast to the ALOHA algorithm. It can work in a channel with capture and multiple reception. Without them, the algorithm has a throughput of 0.2891. It is shown how capture and multiple reception can increase the algorithm throughput to 0.6548 and decrease the packet delay for some fading models. The average packet delay and variance are found for two fading models. The models are Rayleigh fading with incoherent and coherent combining of joint interference power. The accessing traffic is Poisson.

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.

Overflow and losses in a network queue with a self-similar input

This paper considers a discrete time queuing system that models a communication network multiplexer which is fed by a self-similar packet traffic. The model has a finite buffer of size h, a number of servers with unit service time, and an input traffic which is an aggregation of independent source-active periods having Pareto-distributed lengths and arriving as Poisson batches. The new asymptotic upper and lower bounds to the buffer-overflow and packet-loss probabilities P are obtained. The bounds give an exact asymptotic of log P/log h when h → to ∞. These bounds decay algebraically slow with buffer-size growth and exponentially fast with excess of channel capacity over traffic rate. Such behavior of the probabilities shows that one can better combat traffic losses in communication networks by increasing channel capacity rather than buffer size. A comparison of the obtained bounds and the known upper and lower bounds is done.

Overflow and loss probabilities in a finite ATM buffer fed by self-similar traffic

In [13], real-time measurements from LANs, variable-bit-rate video sources, ISDN control-channels, the World Wide Web and other communication systems have shown that traffic exhibits a behaviour of self-similar nature. In this paper, we give new lower bounds to buffer-overflow and cell-loss probabilities for an ATM queue system with a self-similar cell input traffic and finite buffer. The bounds are better than those obtained in [20], in an important region of parameters. As in [20], they decay hyperbolically with buffer size, when the latter goes to infinity. However, in some region, a factor which accompanies the decay is higher in this paper than in [20].

Probability of heavy traffic period in third generation CDMA mobile communication

The paper considers a problem of deriving the multidimensional distribution of a segment of a long-range dependent traffic in the third generation mobile communication network. An exact expression for the probability is found when a self-similar process from [8] models the traffic. The probability of heavy-traffic period, the outage probability, and the level-crossing probability are found. It is shown that the level crossing probability depends on the average call length only. Further, this probability for traffic with dependent samples is lower than for traffic with independent samples. Also, it is shown that there is a linear dependence between the average heavy traffic interval and the average call length.

One stochastic process and its application to multiple access in supercritical region

A discrete-argument stochastic process is presented. The process is a generalization of the Cinlar (1975) semiregenerative process and process /spl eta/(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.

Busy periods in M/M/∞ systems with heterogeneous servers

This note gives a solution for the problem of finding the probability density and probability distribution functions of the N-busy-period length for the M/M/∞ system where the servers are not necessarily the same. A solution in case of the same servers was done in [3].

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].

Optimum Discarding in a Bufferless System

This paper considers queueing systems without buffer. The problem is finding an optimum discipline that gives the minimal number of request discards in a given interval or the minimum discard probability. In the case of a single server fed by an arbitrary request input flow, it is proved that the discipline that discards the request having the maximum residual life is optimal. This result is extended to the system with more than one server. For G/G/1/0, it is given a condition under which the discipline that discards the request in service minimizes the discard probability. Also for a G/G/1/0, we state the problem of finding optimum discipline in terms of the discrete age Markov chain. The problem of minimization of one-step discard probability is stated. It is solved for a system with C servers and general point process of new arrivals.

Buffer overflow under self-similar packet traffic

Actual measurements of high-speed traffic in communications networks argue convincingly that self-similar stochastic processes should model it. These measurements have also revealed that overall buffer packet loss decreases very slowly with increasing buffer size, in sharp contrast to traditional queuing theory models where losses decrease exponentially fast with increasing buffer size. In the paper, our problem is to analytically study overflow and loss probabilities in a queue with self-similar packet traffic and get the asymptotic lower bounds to them.