Abstract. We consider a sequence X n = (X n t ) t≥0 , n ≥ 1 of semimartingales. Each X n is a weak solution to an Itô equation with respect to a Wiener process and a Poissonian martingale measure and is in general non-Markovian process. For this sequence, we prove the large deviation principle in the Skorokhod space D = D [0,∞) . We use a new approach based on of exponential tightness. This allows us to establish the large deviation principle under weaker assumptions than before.Main notationsthe set of stopping times (relative to a filtration F not exceeding L;the Skorokhod space of all right continuous, having left hand limits real valued functionsthe space of all right continuous functions fromthe Lindvall-Skorokhod metric on D;" P − → ′′ , convergence in probability; x ∧ y = min(x, y), x ∨ y = max(x, y);1991 Mathematics Subject Classification. 60F10.

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This paper models primary computer storage in the context of a general (GI/GI/l) queueing system. Queued items are described by sizes, or storage requirements, as well as by arrival and service times; the sum of the sizes of the items in the system is the occupied storage. Capacity constraints are represented by two different protocols for determining whether an arriving item is admitted to the system: (1) an item is accepted if and only if at its arrival time the currently occupied storage does not exceed a given constantC> 0, and (2) an item is accepted if and only if at its arrival time the occupied storage is at mostC, and the occupied storage plus the item's size is at mostC(l + ε) for some given ε > 0. We prove for both systems that in heavy traffic the occupied storage, suitably normalized, converges weakly to reflected Brownian motion with boundaries at 0 and atC. A distinctive feature of the proof is the characterization of reflected Brownian motion as a limit of unrestricted penalized processes.These results make more plausible an earlier conjecture of the authors, i.e., that one obtains the same heavy traffic limit when the admission rule is: accept an item if and only if at its arrival time the occupied storage plus the item's size is no greater thanC.

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