TWO ALGORITHMS FOR FORMING A GROUP QUASI-POISSON STREAM

The aim of the work is to create a model of the flow of burst telecommunication traffic. A modernized model of a group flow of requests in queuing systems is considered. In such a flow, requests arrive in batches, the number of requests in each batch are independent identically distributed discrete random variables. The flow differs from the group Poisson flow in that the time interval between the moments of arrival of successive batches is equal to the sum of a certain constant interval and an independent exponentially distributed random variable. Two different algorithms for forming such flows are considered for the purpose of their generation during simulation modeling. Analytical formulas that determine the average values of queues in queuing systems with such flows are obtained. The results of simulation modeling are in good agreement with the results of analytical calculations using the specified formulas. Having all the advantages of a group Poisson flow, a group quasi-Poisson flow provides the ability to change the characteristics of the average values of queues for large load factors, with an unchanged slope of the specified characteristics in the initial section. This flow model provides a very high-quality approximation of real burst traffic in telecommunication systems, and obtained very simple analytical relationships allow easy calculation of queues in QS with such flows.