Weak Regeneration for Modeling of Queueing Processes1

We discuss new possibilities which the weakly regenerative approach (when a dependence between two adjacent regeneration cycles is allowed) opens in modeling and simulation of queueing network processes. First we extend the class of regenerative inputs constructing weak regeneration for a superposition of n independent, stationary renewal processes in which case generally, classical regeneration does not exist. We assume that process i is generated by the i.i.d. interrenewal times {ξ n }n with d.f. Fi and expectation ai ∈ (0,∞), i = 1, . . . , n. Let ξi(t), (ξ̃i(t)) be right-continuous unfinished (attained) renewal time at instant t in the renewal process i. By the stationarity,