Research ArticleOpen AccessGoogle Scholar indexed
A Complete and Simple Solution to a Discrete-Time Finite-Capacity BMAP/D/c Queue
Department of Industrial Engineering, Chonnam National University, Gwangju, South Korea
Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, Canada
Defense Management College, Korea National Defense University, Seoul, South Korea
Department of Management Engineering, Sangmyung University, Cheonan, South Korea
- 1 Department of Industrial Engineering, Chonnam National University, Gwangju, South Korea
- 2 Department of Mathematics and Computer Science, Royal Military College of Canada, Kingston, Canada
- 3 Defense Management College, Korea National Defense University, Seoul, South Korea
- 4 Department of Management Engineering, Sangmyung University, Cheonan, South Korea
Applied Mathematics·Volume 03 (2012)·Pages 2169–2173·Published 28 December 2012·DOI10.4236/am.2012.312A297
Copy link · social · email
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.
KeywordsDiscrete-Time QueueBatch Markovian Arrival ProcessDeterministic Service TimeMultiple Server
- A H. Bruneel and I. Wuyts, “Analysis of Discrete-Time Multiserver Queueing Models with Constant Service Times,” Operations Research Letters, Vol. 15, No. 5, 1994, pp. 231-236. doi:10.1016/0167-6377(94)90082-5
- S. Wittevrongel and H. Bruneel, “Exact Calculation of Buffer Contents Variance and Delay Jitter in a Discrete-Time Queue with Correlated Input Traffic,” Electronics Letters, Vol. 32, No. 14, 1996, pp. 1258-1259. doi:10.1049/el:19960848
- S. Wittevrongel and H. Bruneel, “Discrete-Time Queues with Correlated Arrivals and Constant Service Times,” Computers & Operations Research, Vol. 26, No. 2, 1999, pp. 93-108. doi:10.1016/S0305-0548(98)00053-7
- C. Blondia and O. Casals, “Statistical Multiplexing of VBR Sources: A Matrix-Analytic Approach,” Performance Evaluation, Vol. 16, No. 1-3, 1992, pp. 5-20. doi:10.1016/0166-5316(92)90064-N
- H. Takagi, “Queueing Analysis,” Vol. 3, Discrete-Time Systems, North-Holland, Amsterdam, 1993.
- K. Sohraby and J. Zhang, “Spectral Decomposition Approach for Transient Analysis of Multi-Server Discrete-Time Queues,” Performance Evaluation, Vol. 21, No. 1-2, 1994, pp. 131-150. doi:10.1016/0166-5316(94)90031-0
- A. S. Alfa, “Algorithmic Analysis of the BMAP/D/k System in Discrete Time,” Advances in Applied Probability, Vol. 35, No. 4, 2003, pp. 1131-1152. doi:10.1239/aap/1067436338
- P. Gao, S. Wittevrongel and H. Bruneel, “On the Behavior of Multiserver Buffers with Geometric Service Times and Bursty Input Traffic,” IEICE TRANSACTIONS on Communications, Vol. E87-B, No. 12, 2004, pp. 3576-3583.
- P. Gao, S. Wittevrongel, J. Walraevens and H. Bruneel, “Analytic Study of Multiserver Buffers with Two-State Markovian Arrivals and Constant Service Times of Multiple Slots,” Mathematical Methods of Operations Research, Vol. 67, No. 2, 2008, pp. 269-284. doi:10.1007/s00186-007-0163-z