Sankhya: The Indian Journal of Statistics

2000, Volume 62, Series B, Pt. 3, pp. 448-462

THE STOCHASTIC DECOMPOSITION RESULTS OF BATCH ARRIVAL POISSON QUEUE WITH A GRAND VACATION PROCESS

By

GAUTAM CHOUDHURY, Institute of Advanced Study in Science and Technology, Guwahati, India

and

ARUN BORTHAKUR, Gauhati University, Guwahati, India

SUMMARY. Recently many authors have obtained various steady state results of batch arrival queues with single and multiple vacations through analytical methods. In this paper we discuss and derive analytically some stochastic decompostion results for a class of batch arrival Poisson queues with a grand vacation process (see Lee et al. (1994a) at various points of time (e.g. random point of time, departure point of time, stationary point of time in distribution(s)). Also, we obtain some new results as generalizations of known results for the vacation model, which lead to a remarkable simplification when solving more complex MX/M/1 type of queues.

AMS (1991) subject classification. Primary 60K25, secondary 60J15.

Key words and phrases. MX/M/1 queue, queue size, stochastic decomposition result, grand vacation process.

Full paper (PDF)

This article in Mathematical Reviews