GI / G / 1 Lakatos-Type Queueing System with T-Retrials

We consider the Lakatos-type GI / G /1 queueing system with T-retrials, i.e., the system with the FCFS service discipline and a constant orbit cycle time T. We have constructed a Markov chain for the system, proved its ergodicity condition, solved a system of equations for the stationary distributions of the system state probabilities, and derived formulas for the average number of requests and the average number of orbit cycles at specific relations of service and orbit time. We have developed an algorithm for statistical modeling of the considered system as well. Results of analytical and statistical modeling show consistency between them. We have indicated an essential property of the Lakatos-type system, namely, the fact that it can be used to evaluate a system in which the FCFS service discipline is not necessary.