In this paper we develop a framework for computing upper and lower bounds of an exponential form for a class of single server queueing systems with non-renewal inputs. These bounds generalize Kingman's bounds for queues with renewal inputs. Keywords: Queues; Exponential bounds; General state space Markov chain D. Towsley was supported in part by NSF under grant NCR-9116183. 0 1 Introduction Let(\Omega ; F) be a measurable space large enough to carry a IR+ -valued random variable (r.v.) X 0 , a sequence of IE-valued r.v.'s fY n ; n = 0; 1; : : :g and a sequence of IR-valued r.v.'s f n ; n = 0; 1; : : :g. The set IR (resp. IR+ ) denotes the set of all real numbers (resp. the set of all nonnegative real numbers) endowed with the oe-algebra R (resp. R+ ). We will assume that IE is a general space endowed with the oe-algebra E. Let fF (x; \Delta ); x 2 IEg and fQ(x; \Delta ); x 2 IEg be two fixed families of probability measures on IR and IE, respectively, and let and be probab..
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