Abstract
Markovian Arrival Processes (MAPs) [9] are a general class of point processes which admits, hyper-exponential, Erlang, and Markov Modulated Poisson Processes (MMPPs) as special cases. MAPs can be easily integrated within queueing models. This makes MAPs useful for evaluating the impact of non-Poisson workloads in networking and for quantifying the performance of multi-tiered e-commerce applications and disk drives [8, 10].
- A. T. Andersen, B. F. Nielsen. A Markovian approach for Modeling Packet traffic with Long-Range Dependence. IEEE JSAC, 16(5), 719--732, 1998. Google ScholarDigital Library
- P. Buchholz, A. Panchenko. A Two-Step EM Algorithm for MAP Fitting. LNCS 3280, 217--227, 2004, Springer.Google ScholarCross Ref
- A. Heindl, K. Mitchell, A. van de Liefvoort. Correlation bounds for second-order MAPs with application to queueing network decomposition. PEVA, 63(6), 2006. Google ScholarDigital Library
- F. E. Hohn. Elementary Linear Algebra. Dover, 1973.Google Scholar
- G. Horvath, P. Buchholz, M. Telek. A MAP fitting approach with independent approximation of the inter-arrival time distribution and the lag correlation, in Proc. of QEST 2005, 124--133, 2005, IEEE Press. Google ScholarDigital Library
- L. A. Kulkarni, S. Li. Transient behaviour of queueing systems with correlated traffic. PEVA 27, 1996. Google ScholarDigital Library
- R. M. M. Leao, E. de Souza e Silva, S. C. de Lucena. A Set of Tools for Traffic Modeling, Analysis and Experimentation LNCS 1786, 40--55, 2000, Springer. Google ScholarDigital Library
- N. Mi, Q. Zhang, A. Riska, E. Smirni, E. Riedel Performance Impacts of Autocorrelation Flows in Systems. To appear in Performance 2007. Google ScholarDigital Library
- M. F. Neuts. Structured Stochastic Matrices of M/G/1 Type and Their Applications. Marcel Dekker, 1989.Google Scholar
- A. Riska, E. Riedel. Disk Drive Level Workload Characterization. Proc. USENIX 2006, 97--102, 2006. Google ScholarDigital Library
- M. Telek, G. Horwath A minimal representation of Markov arrival processes and a moments matching method. To appear in Performance 2007. Google ScholarDigital Library
Index Terms
- Characterization of moments and autocorrelation in MAPs
Recommendations
The Impact of Autocorrelation on Queuing Systems
The performance of single-server queues with independent interarrival intervals and service demands is well understood, and often analytically tractable. In particular, the M/M/1 queue has been thoroughly studied, due to its analytical tractability. ...
A Characterization of M/G/1 Queues with Renewal Departure Processes
Burke [Burke, P. J. 1956. The output of a queueing system. Oper. Res.4 699--704.] showed that the departure process from an M/M/1 queue with infinite capacity was in fact a Poisson process. Using methods from semi-Markov process theory, this paper ...
Higher moments of the waiting time distribution in M/G/1 retrial queues
This work analyzes the waiting time distribution in the M/G/1 retrial queue. The first two moments of the waiting time distribution are known from the literature. In this work we obtain all the moments of the waiting time distribution.
Comments