Abstract
We propose a queueing network model which can be used for the integration of the mobility and teletraffic aspects that are characteristic of wireless networks. In the general case, the model is an open network of infinite server queues where customers arrive according to a non-homogeneous Poisson process. The movement of a customer in the network is described by a Markov renewal process. Moreover, customers have attributes, such as a teletraffic state, that are driven by continuous time Markov chains and, therefore, change as they move through the network. We investigate the transient and limit number of customers in disjoint sets of nodes and attributes. These turn out to be independent Poisson random variables. We also calculate the covariances of the number of customers in two sets of nodes and attributes at different time epochs. Moreover, we conclude that the arrival process per attribute to a node is the sum of independent Poisson cluster processes and derive its univariate probability generating function. In addition, the arrival process to an outside node of the network is a non-homogeneous Poisson process. We illustrate the applications of the queueing network model and the results derived in a particular wireless network.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
N. Antunes, A. Pacheco and R. Rocha, Traffic modelling for broadband wireless networks: The highway scenario, Adv. Perform. Anal. 3 (2000) 109-136.
N. Antunes, A. Pacheco and R. Rocha, An integrated traffic model for multimedia wireless networks, Computer Networks 38 (2002) 25-41.
N. Antunes, R. Rocha, P. Pinto and A. Pacheco, Impact of next-generation wireless networks requirements on teletraffic modeling, Interoperable Commun. Networks 1 (1998) 706-715.
F. Baccelli, M. Klein, M. Lebourges and S. Zuyev, Stochastic geometry and architecture of communications networks, Telecommun. Systems 7 (1997) 209-227.
F. Baccelli and S. Zuyev, Stochastic geometry models of mobile communication networks, in: Frontiers in Queueing, Probab. Stochastics Series (CRC, Boca Raton, FL, 1997) pp. 227-243.
D. Baum and V. Kalashnikov, Stochastic models for communication networks with moving customers, Inform. Process. 1 (2001) 33-49.
R.J. Boucherie and N.M. van Dijk, On a queueing network model for cellular mobile telecommunications networks, Oper. Res. 48 (2000) 38-49.
E. Çinlar, Introduction to Stochastic Processes (Prentice-Hall, Englewood Cliffs, NJ, 1975).
N.G. Duffield and W. Whitt, Control and recovery from rare congestion events in a large multi-server system, Queueing Systems 26 (1997) 69-104.
N.G. Duffield and W. Whitt, A source traffic model and its transient analysis for network control, Stochastic Models 14 (1998) 51-78.
S. El-Dolil, W. Wong and R. Steele, Teletraffic performance of highway microcells with overlay macrocell, IEEE J. Selected Areas Commun. 7 (1989) 71-78.
D. Hong and S.S. Rappaport, Traffic model and performance analysis for cellular mobile radio telephone systems with prioritized and nonprioritized handoff procedures, IEEE Trans. Vehicular Technol. 35 (1986) 77-92.
X. Huang and R. Serfozo, Spatial queueing systems, Math. Oper. Res. 24 (1999) 865-886.
V.G. Kulkarni, Modelling and Analysis of Stochastic Systems (Chapman & Hall, London, 1995).
K. Leung, W.A. Massey and W. Whitt, Traffic models for wireless communication networks, IEEE J. Selected Areas Commun. 12 (1994) 1353-1364.
W.A. Massey and W. Whitt, Networks of infinite-server queues with nonstationary Poisson input, Queueing Systems 13 (1993) 183-250.
K. Mitchell and K. Sohraby, An analysis of the effects of mobility on bandwidth allocation strategies in multi-class cellular wireless networks, in: Proc.of the IEEE INFOCOM' 01 (2001) pp. 1005-1011.
N.U. Prabhu, Markov-renewal and Markov-additive processes-A review and some new results, in: Analysis and Geometry 1991 (Korea Adv. Inst. Sci. Tech., Taejon, 1991) pp. 57-94.
M. Rajaratnam and F. Takawira, Performance analysis of highway cellular networks using generalised arrival and generalised service time distributions, in: Proc.of ITC-16 (1999) pp. 11-22.
T.S. Rappaport, Wireless Communications (Prentice-Hall, Englewood Cliffs, NJ, 1996).
S. Resnick, Adventures in Stochastic Processes (Birkhäuser, Boston, 1992).
R. Serfozo, Introduction to Stochastic Networks (Springer, New York, 1999).
M. Sidi and D. Starobinski, New call blocking versus handoff blocking in cellular networks, in: Proc.of the IEEE INFOCOM' 96 (1996) pp. 35-42.
K. Sohraby, Mobility calculus in cellular wireless networks, in: Proc.of the IEEE ICC '96 (1996) pp. 1258-1262.
W. Whitt, Dynamic staffing in a telephone call center aiming to immediately answer all calls, Oper. Res. Lett. 24 (1999) 205-212.
M. Zonoozi and P. Dassanayake, User mobility modeling and characterization of mobility patterns, IEEE J. Selected Areas Commun. 15 (1997) 1239-1252.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Antunes, N., Pacheco, A. & Rocha, R. A Markov Renewal Based Model for Wireless Networks. Queueing Systems 40, 247–281 (2002). https://doi.org/10.1023/A:1014759412902
Issue Date:
DOI: https://doi.org/10.1023/A:1014759412902