Abstract
We consider a discrete-time multi-server finite-capacity queueing system with correlated batch arrivals and deterministic service times (of single slot), which has a variety of potential applications in slotted digital telecommunication systems and other related areas. For this queueing system, we present, based on Markov chain analysis, not only the steady-state distributions but also the transient distributions of the system length and of the system waiting time in a simple and unified manner. From these distributions, important performance measures of practical interest can be easily obtained. Numerical examples concerning the superposition of certain video traffics are presented at the end.
Highlights
The discrete-time multi-server queue with deterministic service times has gained importance in view of a number of potential practical applications to slotted digital telecommunication systems and other related areas (Bruneel and Wuyts [1])
We consider a discrete-time multi-server finite-capacity queueing system with correlated batch arrivals and deterministic service times, which has a variety of potential applications in slotted digital telecommunication systems and other related areas
It has been observed that arrival streams to these systems, in particular, tend to be correlated. To model this correlated nature, a versatile point process called the discrete-time batch Markovian arrival process (D-BMAP) is introduced by Blondia and Casals [4] and widely used for analytical studies. This rich class of arrival processes contains a number of well-known arrival processes such as the Bernoulli process with independent identically distributed batch arrivals, the Markov modulated Bernoulli process, and a superposition of D-BMAP themselves
Summary
The discrete-time multi-server queue with deterministic service times has gained importance in view of a number of potential practical applications to slotted digital telecommunication systems and other related areas (Bruneel and Wuyts [1]). It has been observed that arrival streams to these systems, in particular, tend to be correlated (see, e.g., Wittevrongel and Bruneel [2,3]) To model this correlated nature, a versatile point process called the discrete-time batch Markovian arrival process (D-BMAP) is introduced by Blondia and Casals [4] and widely used for analytical studies. We assume the finite-capacity model for the following three practical reasons. Queueing models with finite capacity can serve as excellent approximations (by taking the system capacity N sufficiently large) for their corresponding infinite-capacity counterparts (see Remark 2 at the end of this paper). We end the paper with a remark on the finite-capacity model
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