Conditioned limit theorem for the pair of waiting time and queue line processes

The pair (W(t), L(t)t?0, of the virtual waiting time and the queue line processes is considered in the GI/G/1 queueing system with the traffic intensity one. An asymptotic of $$left( {frac{1}{{sqrt t }}W(t), frac{1}{{sqrt t }}L(t)} right)$$ ) conditioned on the event {T>t} is given ast→∞, whereT is the length of the first busy period. A similar result is also given in the situation whent runs over the arrival moments of customers.