A closed-form expression for queuing delay in Rayleigh fading channels using stochastic network calculus

Stochastic Network Calculus is a modern theory for studying the delay performance of a queuing system. So far, this theory proved very effective in studying QoS in the wireline transmission media. In fact, it provides an upper bound to the probability tail of the queuing delay and requires only the expression of an arrival curve, which models the traffic source, and of a service curve, which models the scheduling discipline. In this paper, we propose a model of the wireless channel based on Stochastic Network Calculus and provide an analytical expression for the first two moments of the service curve of a wireless channel capacity varies over time according to a Rayleigh fading process, such as in the WiMAX and LTE systems. We also provide an approximate closed-form expression for the probability tail of the queuing delay. Finally, we compare our results to simulations in order to assess the validity of our approach.

[1]  Georgios B. Giannakis,et al.  Queuing with adaptive modulation and coding over wireless links: cross-Layer analysis and design , 2005, IEEE Transactions on Wireless Communications.

[2]  Ness B. Shroff,et al.  A central-limit-theorem-based approach for analyzing queue behavior in high-speed networks , 1998, TNET.

[3]  Jeffrey G. Andrews,et al.  Fundamentals of WiMAX: Understanding Broadband Wireless Networking , 2007 .

[4]  Elizabeth L. Wilmer,et al.  Markov Chains and Mixing Times , 2008 .

[5]  Hong Shen Wang,et al.  Finite-state Markov channel-a useful model for radio communication channels , 1995 .

[6]  Saleem A. Kassam,et al.  Finite-state Markov model for Rayleigh fading channels , 1999, IEEE Trans. Commun..

[7]  Edward W. Knightly.  Enforceable quality of service guarantees for bursty traffic streams , 1998, Proceedings. IEEE INFOCOM '98, the Conference on Computer Communications. Seventeenth Annual Joint Conference of the IEEE Computer and Communications Societies. Gateway to the 21st Century (Cat. No.98.

[8]  Loutfi Nuaymi,et al.  Wimax Technology for Broadband Wireless Access , 2007 .

[9]  Paolo Giacomazzi,et al.  Closed-form analysis of end-to-end network delay with Markov-modulated Poisson and fluid traffic , 2009, Comput. Commun..

[10]  Chaiwat Oottamakorn,et al.  Statistical service assurances for traffic scheduling algorithms , 2000, IEEE Journal on Selected Areas in Communications.

[11]  Giacomo Verticale,et al.  An Analytical Expression for Service Curves of Fading Channels , 2009, GLOBECOM 2009 - 2009 IEEE Global Telecommunications Conference.

[12]  Cecilio Pimentel,et al.  Finite-state Markov modeling of correlated Rician-fading channels , 2004, IEEE Transactions on Vehicular Technology.

[13]  M. Yacoub,et al.  On higher order statistics of the Nakagami-m distribution , 1999 .

[14]  Moshe Sidi,et al.  Performance and stability of communication networks via robust exponential bounds , 1993, TNET.

[15]  Dapeng Wu,et al.  Effective capacity: a wireless link model for support of quality of service , 2003, IEEE Trans. Wirel. Commun..

[16]  Antti Toskala,et al.  HSDPA/HSUPA for UMTS: High Speed Radio Access for Mobile Communications , 2006 .

[17]  Jeffrey G. Andrews,et al.  Fundamentals of WiMAX: Understanding Broadband Wireless Networking (Prentice Hall Communications Engineering and Emerging Technologies Series) , 2007 .

[18]  Florin Ciucu,et al.  Scaling properties of statistical end-to-end bounds in the network calculus , 2006, IEEE Transactions on Information Theory.

[19]  Antti Toskala,et al.  LTE for UMTS - OFDMA and SC-FDMA Based Radio Access , 2009 .