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Queueing systems with batch Markovian arrival process (BMAP) have paramountapplications in the domain of wireless communication. The BMAP has been used tomodel the superposition of video sources and to approximate the super-positionof data, voice and video traffic. This paper analyzes an infinite-buffergenerally distributed batch-service queue with BMAP, general bulk service($a,b$) rule and batch-size-dependent service time. In this proposed analysis,we mainly focus on deriving the bivariate vector generating function of queueand server content distribution together at departure epoch using supplementaryvariable technique. The mathematical procedure for the complete extraction ofdistribution at departure epoch has been discussed and using those extractedprobabilities, we achieve the queue and server content distribution atarbitrary epoch. Finally, numerical illustrations have been carried out inorder to make a deep insight to the readers which contains deterministic aswell as phase-type service time distributions.

Stationary queue and server content distribution of a batch-size-dependent service queue with batch Markovian arrival process: BMAP/G^{(a,b)}_n/1