Queueing analysis of discrete-time buffer systems with compound arrival process and variable service capacity
The subject of this paper is the analysis of a fairly general discrete-time queueing model by means of an analytical technique involving complex contour integration. The specific model we consider consists of a buffer system with infinite waiting room to which customers (messages) arrive according to a compound arrival process, characterized by general independent interarrivai times (intervals between consecutive arrival instants) and general independent bulk-sizes (numbers of arriving messages at arrival instants). The service times of the messages are assumed to be deterministically equal to one discrete time-unit (or “slot”), but the “service capacity” of the system, i.e., the number of messages that can be served simultaneously during each slot is assumed to have an arbitrary probability distribution. Various well-known discrete-time queueing models can be observed to be merely special cases of this general framework, but the model also includes many queueing sytems which have, so far, never been thoroughly analyzed.
KeywordsInterarrival Time Service Capacity System Content Arrival Instant Multiserver Queue
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