ABSTRACT
With the increased availability of wireless networks, performance evaluation of these networks has become more important in recent years. Adequate models of wireless networks have to account for the user mobility as the movements of the users can have a large influence on the network performance. In many cases data recorded from real networks serves as basis to model the user mobility. Therefore, appropriate distributions have to be found to model characteristics like dwelltimes from the real world data and different general distributions like Lognormal, Weibull or Pareto have been used in the past. In this paper we present an extensive comparison for the fitting quality of those general distributions with Phase-type distributions (PHDs). Our results suggest that in most cases even small PHDs with four or five states yield a better approximation of the real data than the general distributions.
- S. Asmussen, O. Nerman, and M. Olsson. 1996. Fitting phase type distributions via the EM algorithm. Scand. J. Statist 23 (1996), 419--441.Google Scholar
- A. Balachandran, G.M. Voelker, P. Bahl, and P. Rangan. 2002. Characterizing User Behavior and Network Performance in a Public Wireless LAN. In Proc. of SIGMETRICS '02. Google ScholarDigital Library
- F. Bause, P. Buchholz, and J. Kriege. 2010. ProFiDo - The Processes Fitting Toolkit Dortmund. In Proc. of QEST 2010. Google ScholarDigital Library
- A. Bobbio, A. Horváth, and M. Telek. 2005. Matching Three Moments with Minimal Acyclic Phase Type Distributions. Stochastic Models 21, 2--3 (2005).Google ScholarCross Ref
- P. Buchholz. 2003. An EM-Algorithm for MAP Fitting from Real Traffic Data. In Computer Performance Evaluation / TOOLS.Google Scholar
- P. Buchholz and J. Kriege. 2014. Markov Modeling of Availability and Unavailability Data. In Proc. of EDCC 2014. Google ScholarDigital Library
- P. Buchholz, J. Kriege, and I. Felko. 2014. Input Modeling with Phase-Type Distributions and Markov Models - Theory and Applications. Springer. Google ScholarDigital Library
- M. Delignette-Muller and C. Dutang. 2015. fitdistrplus: An R Package for Fitting Distributions. Journal of Statistical Software 64, 4 (2015).Google ScholarCross Ref
- W. Gao and G. Cao. 2010. Fine-grained Mobility Characterization: Steady and Transient State Behaviors. In Proc. of MobiHoc '10. Google ScholarDigital Library
- T. Henderson, D. Kotz, and I. Abyzov. 2008. The changing usage of a mature campus-wide wireless network. Computer Networks 52, 14 (2008). Google ScholarDigital Library
- A. Horváth and M. Telek. 2007. Matching more than three moments with acyclic phase type distributions. Stochastic Models 23 (2007), 167--194.Google ScholarCross Ref
- G. Horváth. 2013. Moment Matching-Based Distribution Fitting with Generalized Hyper-Erlang Distributions. In Proc. of ASMTA '13.Google ScholarCross Ref
- W. Hsu and A. Helmy. 2005. IMPACT: Investigation of Mobile-user Patterns Across University Campuses using WLAN Trace Analysis. Technical Report.Google Scholar
- P. Hui, A. Chaintreau, J. Scott, R. Gass, J. Crowcroft, and C. Diot. 2005. Pocket Switched Networks and Human Mobility in Conference Environments. In Proc. of WDTN' 05. Google ScholarDigital Library
- B. Javadi, D. Kondo, A. Iosup, and D. H. J. Epema. 2013. The Failure Trace Archive: Enabling the comparison of failure measurements and models of distributed systems. J. Parallel Distrib. Comput. 73, 8 (2013), 1208--1223. Google ScholarDigital Library
- M. Kim, D. Kotz, and S. Kim. 2006. Extracting a Mobility Model from Real User Traces. In Proc. of INFOCOM.Google Scholar
- D. Kondo, B. Javadi, A. Iosup, and D. H. J. Epema. 2010. The Failure Trace Archive: Enabling Comparative Analysis of Failures in Diverse Distributed Systems. In CCGRID. IEEE, 398--407. Google ScholarDigital Library
- D. Kotz and K. Essien. 2005. Analysis of a Campus-Wide Wireless Network. Wireless Networks 11, 1 (2005). Google ScholarDigital Library
- D. Kotz and T. Henderson. 2005. CRAWDAD: A Community Resource for Archiving Wireless Data at Dartmouth. IEEE Pervasive Computing 4, 4 (2005). Google ScholarDigital Library
- P. L. L'Ecuyer, L. Meliani, and J. Vaucher. 2002. SSJ: a framework for stochastic simulation in Java. In Proc. of WSC'02. Google ScholarDigital Library
- D. Lelescu, U. Kozat, R. Jain, and M. Balakrishnan. 2006. Model T++: An Empirical Joint Space-time Registration Model. In Proc. of MobiHoc '06. Google ScholarDigital Library
- W. Navidi and T. Camp. 2004. Stationary distributions for random waypoint models. IEEE Transactions on Mobile Computing (2004). Google ScholarDigital Library
- M. F. Neuts. 1979. A versatile Markovian point process. Journ. of Appl. Prob. (1979).Google Scholar
- P. Reinecke, T. Krauß, and K. Wolter. 2012. HyperStar: Phase-Type Fitting Made Easy. In Proc. of QEST'12. Google ScholarDigital Library
- I. Rhee, M. Shin, S. Hong, K. Lee, S.J. Kim, and S. Chong. 2011. On the Levy-Walk Nature of Human Mobility. IEEE/ACM Transactions on Networking 19, 3 (2011). Google ScholarDigital Library
- D. Tang and M. Baker. 2000. Analysis of a Local-area Wireless Network. In Proc. of MobiCom '00. Google ScholarDigital Library
- A. Thümmler, P. Buchholz, and M. Telek. 2006. A Novel Approach for Phase-Type Fitting with the EM Algorithm. IEEE Trans. Dep. Sec. Comput. 3, 3 (2006). Google ScholarDigital Library
- C. Tuduce and T.R. Gross. 2005. A mobility model based on WLAN traces and its validation. In Proc. of INFOCOM.Google Scholar
- J. Yoon, B.D. Noble, M. Liu, and M. Kim. 2006. Building realistic mobility models from coarse-grained traces. In Proc. of MobiSys. Google ScholarDigital Library
Index Terms
- Markovian Modeling of Wireless Trace Data
Recommendations
Tail probabilities of low-priority waiting times and queue lengths in {MAP}/{GI}/1 queues
We consider the problem of estimating tail probabilities of waiting times in statistical multiplexing systems with two classes of sources - one with high priority and the other with low priority. The priority discipline is assumed to be nonpreemptive. ...
An EM-based technique for approximating long-tailed data sets with PH distributions
Internet performance symposium (IPS 2002)We propose a new technique for fitting long-tailed data sets into phase-type (PH) distributions. This technique fits data sets with non-monotone densities into a mixture of Erlang and hyperexponential distributions, and data sets with completely ...
Predicting departure times in multi-stage queueing systems
We develop an approximation model for the state-dependent sojourn time distribution of customers or orders in a multi-stage, multi-server queueing system, when interarrival and service times can take on general distributions. The model can be used to ...
Comments