Informatica

Queueing systems with a single device are well developed (see, for example, Borovkov, 1972; 1980). But there are only several works in the theory of multiphase queueing systems in heavy traffic (see Iglehart, Whitt, 1970b) and no proof of laws of the iterated logarithm for the probabilistic characteristics of multiphase queuing systems in heavy traffic. The law of the iterated logarithm for the waiting time of a customer is proved in the first part of the paper (see Minkevičius, 1995). In this work, theorems on laws of the iterated logarithm for the other main characteristics of multiphase queuing systems in heavy traffic (a summary queue length of customers, a queue length of customers, a waiting time of a customer) are proved.

The queueing system theory is well developed. Such an important problem as the efficient of customer service in efficiency a multichannel queueing system with different productivity of service channels is well developed, too. Exact formulas are obtained from which the loss probability can be computed (if the input stream of customers distributed as Poisson and service time of the customer is the exponential service time). However, these formulas are very complex. So, in this paper, two theorems are proved, in which upper and lower estimates of the loss probability are presented. These estimates are simple formulas that don't become more complex with the growing number of service channels in the queueing system.

A stochastic discrete neuronetwork is defined. In the investigation of discrete neuronetworks probability methods are applied – a weak convergence of probability measures. Limit theorems (the strong law of large number and normal law) are proved for the stream of signals, going out of neurons.