Analysis of delays in medium access control devices in cognitive radio systems with correlation of time intervals in request flows

This article is about the development of a method for analyzing the average waiting time of a request in a queue with correlated inter-arrival and service times. The ON-OFF process is often used to model the primary user channel occupancy in different questions related to cognitive radio, such as resource allocation, medium access control protocols, spectrum handoff and others. It is assumed that the time intervals of the ON- and OFF- periods are not correlated. More realistic models of primary user activity require the presence of correlation not only between consequent periods, but also the presence of correlation between channel occupancy and other quantities interpreted as service time in models based on queuing systems. As a result, here is proposed a variant of constructing the probability density function of a random variable which is the difference between the service time of the i-th request and the time interval between the moments of arriving of the i-th and (i-1)-th requests with correlated inter-arrival and service times. Solution based on the use of a two-dimensional characteristic function, so in this case it is possible to more purposefully specify the components of the statistical connection of previously described sequences. These components are the cumulants of the described distribution. For a queuing system with hyperexponential distribution of inter-arrival and service intervals, an analytical expression for the average waiting time of a request in a queue is found.