Phase-type models for cellular networks supporting voice, video and data traffic

Authors:
S. Dharmaraja;Vaneeta Jindal;Attahiru Sule Alfa
Affiliations:
Department of Mathematics, Indian Institute of Technology, Delhi, New Delhi-110016, India;Department of Mathematics, Indian Institute of Technology, Delhi, New Delhi-110016, India;Department of ECE, University of Manitoba, Winnipeg, Manitoba, R3T 5V6, Canada
Venue:
Mathematical and Computer Modelling: An International Journal
Year:
2008

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Abstract

This paper presents an analytical model for cellular networks supporting voice, video and data traffic. Self-similar and bursty nature of the incoming traffic causes correlation in inter-arrival times of the incoming traffic. Therefore, arrival of calls is modeled with Markovian arrival process as it allows for the correlation. Call holding times, cell residence times and retrial times are modeled as phase-type distributions. We consider that the cells in a cellular network are statistically homogeneous, so it is enough to investigate a single cell for the performance analysis of the entire networks. With appropriate assumptions, the stochastic process that describes the state of a cell is a Quasi-birth-death (QBD) process. We derive explicit expressions for the infinitesimal generator matrix of this QBD process. Also, expressions for performance measures are obtained. Further, complexity involved in computing the steady-state probabilities is discussed. Finally, queueing examples are provided that can be obtained as particular cases of the proposed analytical model.