Subexponential Asymptotics of a Markov-Modulated Random Walk with Queueing Applications

and approximations for atm multiplexers with applications to video teleconferencing," \Logarithmic asymptotics for steady-state tail probabilities in a single-server queue," Studies in Appl. KAR30] J. Karamata, \Sur un mode de croissance r eguili ere des fonctions," Mathematica (Cluj), 1930. ARN80] K. Arndt, \Asymptotic properties of the distributions of the supremum of random walk on a markov chain," Theory of Probability and its Applications, 1980. ASM89] S. Asmussen, \Aspects of matrix wiener-hopf factorization in applied probability," Math. 33 When all c i > 0, b) follows from AHK94], Lemma 4.2. The case when some of the c i = 0 we prove using the method of stochastic dominance. Without loss of generality we may assume that the rst n coeecients c i = 0; 1 i n m; and that the rest are strictly positive. Then, for any > 0, there exists an a > 0 such that for all x > a,