On the Finite Buffer Queue with Renewal Input and Batch Markovian Service Process: GI/BMSP/1/N

We consider a finite-buffer single-server queue with renewal input where the service is provided in batches of random size according to batch Markovian service process (BMSP). Steady-state distribution of number of customers in the system at pre-arrival and arbitrary epochs have been obtained along with some important performance measures. The model has potential applications in the areas of computer networks, telecommunication systems, and manufacturing systems, etc.

[1]  P. P. Bocharov,et al.  The Stationary Characteristics of the G/MSP/1/r Queueing System , 2003 .

[2]  M. Neuts.  A Versatile Markovian Point Process , 1979 .

[3]  Antonis Economou,et al.  On the Stationary Distribution of the GI X /M Y /1 Queueing System , 2003 .

[4]  Evgenia Smirni,et al.  Characterizing the BMAP/MAP/1 Departure Process via the ETAQA Truncation , 2005 .

[5]  Winfried K. Grassmann,et al.  Regenerative Analysis and Steady State Distributions for Markov Chains , 1985, Oper. Res..

[6]  Mohan L. Chaudhry,et al.  COMPUTATIONAL ASPECTS OF BULK-SERVICE QUEUEING SYSTEM WITH VARIABLE CAPACITY AND FINITE WAITING SPACE: M/G_Y/1/N+B , 1991 .

[7]  M. L. Chaudhry,et al.  A first course in bulk queues , 1983 .

[8]  S. Chakravarthy.  Analysis of a finite MAP/G/1 queue with group services , 1993, Queueing Syst. Theory Appl..

[9]  U. C. Gupta,et al.  Complete analysis of finite and infinite buffer GI/MSP/1 queue - A computational approach , 2007, Oper. Res. Lett..

[10]  Srinivas R. Chakravarthy.  A finite capacity GI/PH/1 queue with group services , 1992 .

[11]  Fumiaki Machihara.  A BMAP/SM/1 queue with service times depending on the arrival process , 1999, Queueing Syst. Theory Appl..

[12]  Marcel F. Neuts,et al.  Matrix-geometric solutions in stochastic models - an algorithmic approach , 1982 .

[13]  M. Neuts,et al.  A single-server queue with server vacations and a class of non-renewal arrival processes , 1990, Advances in Applied Probability.

[14]  T. P. Bagchi,et al.  Finite waiting space bulk queueing systems , 1973 .

[15]  U. C. Gupta,et al.  Analysis of the MAP/Ga,b/1/N Queue , 2001, Queueing Syst. Theory Appl..

[16]  G. Brière,et al.  Computational analysis of single-server bulk-service queues, M/GY / 1 , 1989, Advances in Applied Probability.

[17]  David M. Lucantoni,et al.  New results for the single server queue with a batch Markovian arrival process , 1991 .