References C: Finite Number of Subexponential On-oo Sources: Upper Bound

50 KAR30] J. Karamata, \Sur un mode de croissance r eguili ere des fonctions," Mathematica (Cluj), 1930. \Tail probabilities for M/G/1 input processes (i): Preliminary asymptotics," preprint. RES96] S. Resnick and G. Samorodnitsky, \Performance decay in a single server queueing model with long range dependence," preprint. References 49 COH73] J. W. Cohen, \Some results on regular variation for distributions in queueing and uctuation theory," J. Appl. Probability, 1973. \Fundamental bounds and approximations for atm multiplexers with applications to video teleconferencing," IEEE Samorodnitsky, \Heavy tails and long range dependence in on/oo processes and associated uid models," preprint. JLA95g] P. R. Jelenkovi c and A. A. Lazar, \Subexponential asymptotics of a markov-modulated random walk with queueing applications," \Stochastic theory of a data handling system with multiple sources," Bell Syst. Techn. ANA95] V. Anantharam, \On the sojourn time of sessions at an atm buuer with long-range dependent input traac," in For a nite number of long tailed On-OO sources we can obtain the following general upper bound.