This paper is concerned with quality of service guarantees in an environmen
t with bursty traffic streams, such as those in the emerging ATM-based broa
dband ISDN.(4) For virtually any traffic stream, new performance bounds are
obtained in terms of effective bandwidths and burstiness constraints. The
new bounds are tighter than those previously available and are asymptotical
ly achievable, potentially resulting in better performance when used in tra
ffic management. Various performance measures are considered. It is shown t
hat the effective bandwidth of a departing traffic is bounded by that of th
e incoming traffic. For traffic streams having independent increments and M
arkov-modulated processes, the bounds are further refined to a point close
to the exact values in some cases. Computationally, evaluation of the bound
s requires less effort than finding effective bandwidths and burstiness con
straints. Finally, the bounds are applied to routing control to find the ne
ar-optimal probabilistic routing policy.