A Unified Queue Length Formula for Bmap/G/1 Queue With Generalized Vacations

Analysis of Queues with Markovian Service Processes

“…However, it seems difficult to give a stochastic interpretation to the matrix part. Reference [3] shows that a similar matrix-type factorization also holds in the BMAP/G/1 queue with generalized vacations.…”

A factorization property for BMAP/G/1 vacation queues under variable service speed

“…Lee et al (2001) and Chang et al (2002) showed that the vector generating functions (GF) of the queue length at an arbitrary time and at an arbitrary departure in the BMAP/G/1 queues with generalized vacations is decomposed into two parts, one of which is the queue length vector GF at an arbitrary point of time during the idle period. To be more specific they proved the following types of decompositions:…”

“…The studies on MAP(BMAP)/G/1 queues with vacations and/or control policies can be found in Chang et al (2002), Lee and Ahn (2002), Lee et al (2001Lee et al ( , 2003, Lee and Baek (2005) and Lee and Song (2004). Lee et al (2001) and Chang et al (2002) showed that the vector generating functions (GF) of the queue length at an arbitrary time and at an arbitrary departure in the BMAP/G/1 queues with generalized vacations is decomposed into two parts, one of which is the queue length vector GF at an arbitrary point of time during the idle period.…”

Analysis of BMAP/G/1 Vacation Model of Non-M/G/1-Type

“…Chang et al [8] provided a factorization formula for the BM AP/G/1 queue with generalized vacations:…”

“…Chang and Takine [7] applied the factorization property (presented by Chang et al [8]) to get analytical results for queueing models of M/G/1-type with or without vacations using exhaustive discipline. The factorization property states that the vector probability-generating function (vector PGF or vector GF) of the stationary queue length is factored into two PGFs of proper random variables.…”